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Text File  |  1991-06-14  |  90KB  |  3,497 lines
  1. C
  2. C Two-loop large Higgs mass correction to the ro-parameter.
  3. C J.van der Bij and M. Veltman, Nucl. Phys. B231 (1984) 205.
  4. C
  5. C RO-parameter 1.  Divergencies of one-loop diagrams, two external lines.
  6. C RO-parameter 2.  Divergencies of one-loop diagrams, three external lines.
  7. C RO-parameter 3.  Divergencies of one-loop diagrams, four external lines.
  8. C RO-parameter 4.  Divergencies of one-loop diagrams, ghost external lines.
  9. C RO-parameter 5.  Two-loop self-energy diagrams.
  10. C RO-parameter 6.  One-loop subtractions. RO-parameter result.
  11. C RO-parameter 7.  Two-loop self-energy diagrams. A-A wave-function.
  12. C RO-parameter 8.  Two-loop self-energy diagrams. A-W wave-function.
  13. C RO-parameter 9.  Subtractions for A-A and A-W wave-functions.
  14. C RO-parameter 10. Tadpoles in A-A wave-function.
  15. C RO-parameter 11. Diagrams with tadpole insertions.
  16. C RO-parameter 12. Counter-term Lagrangian for the standard model.
  17. C RO-parameter 13. Counter terms for the Ghost Lagrangian, standard model.
  18. C RO-parameter 14. Rationalization.
  19. C RO-parameter 15. Epsilon expansion and projection operators.
  20. C RO-parameter 16. Differentiating F111.
  21. C RO-parameter 17. Differentiating F211.
  22. C RO-parameter 18. Expansion of F211(SM,M1,M2) for large SM.
  23. C RO-parameter 19. Higher orders of F211(M,M0,SM) expansion for large SM.
  24. C RO-parameter 20. Expansion of F211(SM,SM,M) for large SM.
  25. *end
  26.  
  27. C RO-parameter 1. Divergencies of one-loop diagrams, two external lines.
  28.  
  29. C ONE-LOOP DIAGRAMS WITH TWO EXTERNAL LINES.
  30. C CALCULATION OF ONE-LOOP DIVERGENCIES.
  31. C CHECKING OF COUNTERTERMS ALSO DONE.
  32.  
  33. C Running time (CPU only) on Lansing CDC: 27 sec.
  34. C The new character sum techniques give about a factor 2 improvement.
  35.  
  36. Oldnew i=I
  37. P ninp
  38. Read Roblocks.e
  39. C P input
  40. VERT{,,,,}
  41. X NUM(K1,K2)=1.-2.*DT(K1-9)*DT(K2-9)
  42. *fix
  43. P ninput
  44. BLOCK WORK{TADP}
  45. P ninput
  46. Id,SELF(I1~,I2~)=
  47.    DS(I1;J1;J2;Sym;J1;J2;TAP,1,(DIB(I1,J1,-J1,J2,-J2,I2)
  48.   *DC("F,TFE,-1,J1,J2) ))
  49.  + DS(I1;J3;-J3;I2;Sym;J3,-J3;TAP,2,(DIC(I1,J3,-J3,I2) ))
  50.     +CONTR(I1,I2)*DLP/EP
  51.  
  52. Id,Anti,TAP
  53. Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)=
  54.    VE3(I1,K1,K3,*,MU,Q,*,L1,-K,*,L3,P)*
  55.    VE3(K2,I2,K4,*,L2,K,*,NU,-Q,*,L4,-P)*
  56.    PROP(K1,K2,*,L1,K,*,L2,K)*
  57.    PROP(K3,K4,*,L3,P,*,L4,P)
  58. Id,DIC(I1~,K1~,K2~,I2~)=
  59.    VE4(I1,K1,K2,I2,*,MU,*,L1,*,L2,*,NU)*
  60.    PROP(K1,K2,*,L1,P,*,L2,P)
  61. B EP,I,PI2,DEL,TIPI2
  62. Id,Compo,<X>,VE4,VE3,PROP
  63. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  64. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  65.        AA(MU,P0,L2,Q,L1,P)
  66. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  67. Id,Commu,NOM
  68. Id,NOM(P,M~)*NOM(K,M0~)=F2(M,M0)
  69. Al,NOM(P,M~)=F1(M)
  70. Id,P(MU~)*F1(M~)=0.
  71. *yep
  72. Id,2,K(MU~)=P(MU)+Q(MU)
  73. Al,PDQ*F2(M~,M0~)=QDQ*B1(M,M0)
  74. Al,PDK*F2(M~,M0~)=PDP*F2(M,M0)+QDQ*B1(M,M0)
  75. Al,QDK*F2(M~,M0~)=QDQ*F2(M,M0)+QDQ*B1(M,M0)
  76. Id,PDP*F2(M~,M0~)=F1(M0)-M**2*F2(M,M0)
  77. Al,KDK*F2(M~,M0~)=F1(M)-M0**2*F2(M,M0)
  78. Id,P(MU~)*P(NU~)*F2(M~,M0~)=D(MU,NU)*B22(M,M0)
  79.           +Q(MU)*Q(NU)*B21(M,M0)
  80. Id,P(MU~)*F2(M~,M0~)=Q(MU)*B1(M,M0)
  81. *yep
  82. Id,B22(M~,M0~)=(-0.5*F1(M0)+M**2*F2(M,M0)
  83.       -0.5*(QDQ+M0**2-M**2)*B1(M,M0))/OMN
  84. Id,B21(M~,M0~)=-((0.5*N-1)*F1(M0)
  85.        -0.5*N*(QDQ+M0**2-M**2)*B1(M,M0)
  86.        +M**2*F2(M,M0) )/QDQ/OMN
  87. Id,B1(M~,M0~)=(0.5*F1(M)-0.5*F1(M0)
  88.               -0.5*(QDQ+M0**2-M**2)*F2(M,M0) )/QDQ
  89. Id,F1(PM)=0.
  90. Al,PM=0.
  91. Al,Multi,M0**2=M**2/C**2
  92. Al,C2MS2=2*C**2-1
  93. Id,Multi,S**2=1.-C**2
  94. *yep
  95. Id,F1(M~)=TIPI2*M**2/EP-0.5*TIPI2*M**2*(1.-LG(M))
  96.   +0.5*EP*TIPI2*M**2*(PI2/24+0.5-0.5*LG(M)+0.25*LG(M)*LG(M))
  97. Al,N*OMN**-1=-4/3+EP/9-EP**2/27
  98. Al,N=4.+EP
  99. Al,OMN**-1=-1/3+EP/9-EP**2/27
  100. Al,Symme,F2,1,2
  101. Id,ZTAG*F2(SM,SM)=-0.5*TIPI2*(PI/W3-2)*(QDQ+SM**2)/SM**2
  102.    -TIPI2/EP - 0.5*TIPI2*(LG(SM)-2+PI/W3)
  103. Al,ZTAG*F2(M~,M~)=0.5*TIPI2*(LG(SM)-LG(M)-2)*(QDQ+SM**2)/SM**2
  104.    -TIPI2/EP-0.5*TIPI2*(LG(SM)-2)
  105. Id,F2(M~,M~)=-TIPI2/EP-0.5*TIPI2*LG(M)+QDQ*BB0(M,M)/M**2
  106.    -0.5*TIPI2*EP*(PI2/24+0.25*LG(M)*LG(M))
  107.    +EP*QDQ*BB0E(M,M)/M**2
  108. Al,F2(M~,SM)=-TIPI2/EP+0.5*TIPI2*(1.-LG(SM)
  109.   +M**2*LG(M,SM)/SM**2-0.5*QDQ/SM**2)
  110.   +TIPI2*EP*(-0.25-PI2/48+0.25*LG(SM)-LG(SM)*LG(SM)/8
  111.   +1/SM**2*(3*QDQ/16-QDQ*LG(SM)/8-M**2/4*LG(M,SM)
  112.   +M**2/8*LG(M)*LG(M)-M**2/8*LG(SM)*LG(SM)))
  113. Al,F2(M~,M0~)=-TIPI2/EP+0.5*TIPI2-0.5*TIPI2*LG(M0)
  114.     -0.5*TIPI2*M**2*DIF(M,M0)*LG(M,M0)+QDQ*BB0(M,M0)/M0**2
  115.   +EP*BB0E(M,M0)
  116. Id,Multi,EP**2=0
  117. Al,PM=0
  118. Al,Multi,M0**2=M**2/C**2
  119. Al,ZTAG=1
  120. Id,EP**-1=ATEL9**10*DEL/TIPI2
  121. Al,F1F(SM)=F1F(SM)*ATEL9**2
  122. Id,Count,1,ATEL9,1,SM,1,CONTR,4,ET,2
  123. Id,ATEL9=1.
  124. Id,LG(M,S~)=LG(M)-LG(S)
  125. Al,LG(M0,S~)=LG(M0)-LG(S)
  126. Al,LG(SM,S~)=LG(SM)-LG(S)
  127. Id,DIF(PM,M~)=-1./M**2
  128. Al,DIF(M,M0)=-C**2/M**2/S**2
  129. Id,Multi,C**2=1.-S**2
  130. Id,Multi,S**2=1.-C**2
  131. *yep
  132. SVERT{,~,~}
  133. Id,CONTR(I1~,I2~)=CONT(I1,I2,"N,*,MU,Q,*,NU,-Q,*,AL,P0)
  134. Id,Compo,<X>,CONT
  135. Id,CONT(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P)
  136. E1EZF{,,,,}
  137. Id,EP**-1=DEL/TIPI2
  138. Al,C2MS2=2*C**2-1
  139. Id,Multi,S**2=1-C**2
  140. Id,EP*DEL=TIPI2
  141. Al,EP**2*DEL=TIPI2*EP
  142. P output
  143. *yep
  144. Id,DLP=-1
  145. *next
  146. P input
  147. ENDBLOCK
  148. Z TADP=DS(J1,1,16,(0.5*NUM(J1,J1)*
  149.    DIB("Z,CHG(J1),CHH(J1) ) ))
  150.    -M*SM**2*ET*DLP/EP
  151. Id,DIB(K1~,K2~,K3~)=
  152.    VE3(K1,K2,K3,*,L1,P0,*,L2,-P,*,L3,P)*
  153.    PROP(K2,K3,*,L2,P,*,L3,P)
  154.    *ATEL9**10
  155. WORK{TADP}
  156. Z IAA=SELF("A,"A)
  157. WORK{IAA}
  158. Z IAF=SELF("A,"F)
  159. WORK{IAF}
  160. Z IAW=SELF("A,"W)
  161. WORK{IAW}
  162. Z IAZ=SELF("A,"Z)
  163. WORK{IAZ}
  164. Z IFF=SELF("F,"F)
  165. WORK{IFF}
  166. Z IFW=SELF("F,"W)
  167. WORK{IFW}
  168. Z IFZ=SELF("F,"Z)
  169. WORK{IFZ}
  170. Z IGH=SELF("G,"G_)
  171. WORK{IGH}
  172. Z IGV=SELF("G,"U_)
  173. WORK{IGV}
  174. Z IHU=SELF("G_,"U)
  175. WORK{IHU}
  176. Z IUV=SELF("U,"U_)
  177. WORK{IUV}
  178. Z IWW=SELF("W,"W)
  179. WORK{IWW}
  180. Z IWZ=SELF("W,"Z)
  181. WORK{IWZ}
  182. Z IZZ=SELF("Z,"Z)*ZTAG
  183. C SET QDQ=-SM**2 TO FIND THAT MASS RENORMALIZATION OK.
  184. C NO COUNTER-TERMS PROPORTIONAL TO EP HAVE BEEN INTRODUCED.
  185. C SUCH TERMS HAVE ALSO BEEN NEGLECTED IN THE CALCULATION.
  186. WORK{IZZ}
  187. Z IOP=SELF("P_,"P)
  188. WORK{IOP}
  189. Z IQR=SELF("R_,"R)
  190. WORK{IQR}
  191. Z IQT=SELF("R_,"T)
  192. WORK{IQT}
  193. Z IRS=SELF("R,"T_)
  194. WORK{IRS}
  195. Z IST=SELF("T_,"T)
  196. WORK{IST}
  197. Z IXY=SELF("Y_,"Y)
  198. WORK{IXY}
  199. *end
  200.  
  201. C RO-parameter 2. Divergencies of one-loop diagrams, three external lines.
  202.  
  203. C ONE-LOOP DIAGRAMS WITH THREE EXTERNAL LINES.
  204. C CALCULATION OF ONE-LOOP DIVERGENCIES.
  205. C COUNTER-TERMS ARE CHECKED.
  206. C CDC CPU time: 35.2 sec.
  207.  
  208. Oldnew i=I
  209. P ninput
  210. Read Roblocks.e
  211. C P input
  212. VERT{,,,,}
  213. V R,T,U,V
  214. X HUM(K1,K2)=1.-0.5*DK(K1,K2)
  215. *fix
  216. P ninput
  217. BLOCK WORK{TADP}
  218. P ninput
  219. Id,VERT(K1~,K2~,K3~)=
  220.   DS(K1;J1;-J2;TAP,(DS(K2;-J1;J3;TAP,(
  221.   DIB(K1,K2,K3,J1,-J1,J3,-J3,J2,-J2)*DC("F,TFE,-1,J1,J2) ))))
  222.  +DS(K1;K2;J4;-J5;Sym;J4;-J5;TAP,(VIR1(K1,K2,K3,J4,-J4,-J5,J5) ))
  223.  +DS(K2;K3;J6;-J7;Sym;J6;-J7;TAP,(VIR2(K1,K2,K3,J6,-J6,-J7,J7) ))
  224.  +DS(K1;K3;J8;-J9;Sym;J8;-J9;TAP,(VIR3(K1,K2,K3,J8,-J8,-J9,J9) ))
  225.  
  226.     +CONTR(K1,K2,K3)
  227.  
  228. Id,Anti,TAP
  229.  
  230. Id,DIB(K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~)=
  231.    VE3(K1,K4,K9,*,MU,Q,*,L4,P,*,L9,-R)*
  232.    VE3(K2,K5,K6,*,NU,T,*,L5,-P,*,L6,V)*
  233.    VE3(K3,K7,K8,*,AL,K,*,L7,-V,*,L8,R)*
  234.    PROP(K4,K5,*,L4,P,*,L5,P)*
  235.    PROP(K6,K7,*,L6,V,*,L7,V)*
  236.    PROP(K8,K9,*,L8,R,*,L9,R)
  237. Al,VIR1(K1~,K2~,K3~,K4~,K5~,K6~,K7~)=
  238.    VE4(K1,K2,K4,K6,*,MU,*,NU,*,L4,*,L6)*
  239.    VE3(K3,K5,K7,*,AL,K,*,L5,P,*,L7,-U)*
  240.   PROP(K6,K7,*,L6,U,*,L7,U)*PROP(K4,K5,*,L4,P,*,L5,P)
  241. Al,VIR2(K1~,K2~,K3~,K4~,K5~,K6~,K7~)=
  242.    VE4(K2,K3,K4,K6,*,NU,*,AL,*,L4,*,L6)*
  243.    VE3(K1,K5,K7,*,MU,Q,*,L5,P,*,L7,-R)*
  244.   PROP(K6,K7,*,L6,R,*,L7,R)*PROP(K4,K5,*,L4,P,*,L5,P)
  245. Al,VIR3(K1~,K2~,K3~,K4~,K5~,K6~,K7~)=
  246.    VE4(K1,K3,K4,K6,*,MU,*,AL,*,L5,*,L7)*
  247.    VE3(K2,K5,K7,*,NU,T,*,L4,-P,*,L6,V)*
  248.   PROP(K4,K5,*,L4,P,*,L5,P)*PROP(K6,K7,*,L6,V,*,L7,V)
  249. B EP,I,TIPI2
  250. Id,Compo,<X>,VE4,VE3,PROP
  251. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  252. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  253.        AA(MU,P0,L2,Q,L1,P)
  254. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  255. Id,P0(MU~)=0.
  256. Al,Dotpr,P0(MU~)=0.
  257. Id,Commu,NOM
  258. Id,NOM(P,M~)*NOM(R,M0~)*NOM(V,SM~)=1.
  259. Al,NOM(P,M~)*NOM(Q~,M0~)=F2(Q)
  260. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  261. *yep
  262. Id,R(MU~)=P(MU)+Q(MU)
  263. Id,V(MU~)=P(MU)+Q(MU)+K(MU)
  264. Id,U(MU~)=P(MU)+K(MU)
  265. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  266. Id,RDR=PDP+2.*PDQ
  267. Al,VDV=PDP-2.*PDT
  268. Al,PDR=PDP+PDQ
  269. Al,PDV=PDP-PDT
  270. Al,VDR=PDP+2.*PDQ+PDK-QDT
  271. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  272. Id,VDK=PDK
  273. Al,VDT=PDT
  274. Al,VDQ=PDQ
  275. Al,RDK=PDK
  276. Al,RDT=PDT
  277. Al,RDQ=PDQ
  278. Al,N=4
  279. Al,C2MS2=2.*C**2-1
  280. *yep
  281. Id,P(MU~)*P(NU~)*P(AL~)=D3(MU,NU,AL,Q)*DEL*TIPI2/EP/6.
  282.      +D3(MU,NU,AL,K)*DEL*TIPI2/EP/12.
  283. Id,P(MU~)*PDP=Q(MU)*DEL*TIPI2/EP+K(MU)*DEL*TIPI2/EP/2.
  284. Al,PDP=-DEL*TIPI2/EP
  285. Id,P(MU~)*P(NU~)=-0.25*D(MU,NU)*DEL*TIPI2/EP
  286. Id,P(MU~)*PDK=-0.25*K(MU)*DEL*TIPI2/EP
  287. Id,P(MU~)*PDQ=-0.25*Q(MU)*DEL*TIPI2/EP
  288. Id,P(MU~)*PDT=-0.25*DEL*TIPI2/EP*T(MU)
  289. Id,P(MU~)*F2(R)=0.5*DEL*TIPI2/EP*Q(MU)
  290. Id,P(MU~)*F2(U)=0.5*DEL*TIPI2/EP*K(MU)
  291. Id,P(MU~)*F2(V)=0.5*DEL*TIPI2/EP*(Q(MU)+K(MU))
  292. Id,F2(Q~)=-DEL*TIPI2/EP
  293. *yep
  294. Id,T(MU~)=-K(MU)-Q(MU)
  295. Al,TDT=QDQ+KDK+2.*QDK
  296. Id,Dotpr,T(MU~)=-K(MU)-Q(MU)
  297. Id,D3(MU~,NU~,AL~,Q~)=D(MU,NU)*Q(AL)+D(MU,AL)*Q(NU)+D(NU,AL)*Q(MU)
  298. Id,Multi,S**2=1.-C**2
  299. Keep 'TADP'
  300. Nprint 'TADP'
  301. *next
  302. SVERT{~,,~}
  303. Z 'TADP'='TADP'(AL,P,BE,Q,GA,K)
  304. Id,CONTR(K1~,K2~,K3~)=CONT(K1,K2,K3,/,"K)*
  305.     VE3(K1,K2,K3,*,AL,P,*,BE,Q,*,GA,K)/EP
  306. Id,Compo,<SS>,CONT,<X>,VE3
  307. Id,CONT(S~)=S
  308. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P)
  309. *yep
  310. CVERT{,~,~}
  311. SCVERT{,~,~}
  312. Id,C2MS2=2*C**2-1
  313. *yep
  314. E1EZF{,,~,~,~}
  315. Id,Count,1,EP,-2,E1F,-2,EZF,-2
  316. B EP,I,TIPI2
  317. Id,Multi,S**2=1-C**2
  318. Al,Q(MU~)=-P(MU)-K(MU)
  319. P output
  320. *yep
  321. Id,DEL=-1.
  322. *next
  323. P input
  324. ENDBLOCK
  325. P input
  326. Z IUVW(MU,Q,NU,T,AL,K)=VERT("U,"U_,"W)
  327. WORK{IUVW}
  328. Z IAUV(MU,Q,NU,T,AL,K)=VERT("A,"U,"U_)
  329. WORK{IAUV}
  330. Z IUVZ(MU,Q,NU,T,AL,K)=VERT("U,"U_,"Z)
  331. WORK{IUVZ}
  332. Z IFHU(MU,Q,NU,T,AL,K)=VERT("F,"G_,"U)
  333. WORK{IFHU}
  334. Z IAHU(MU,Q,NU,T,AL,K)=VERT("A,"G_,"U)
  335. WORK{IAHU}
  336. Z IFFZ(MU,Q,NU,T,AL,K)=VERT("F,"F,"Z)
  337. WORK{IFFZ}
  338. Z IZZZ(MU,Q,NU,T,AL,K)=VERT("Z,"Z,"Z)
  339. WORK{IZZZ}
  340. Z IAGH(MU,Q,NU,T,AL,K)=VERT("A,"G,"G_)
  341. WORK{IAGH}
  342. Z IAGV(MU,Q,NU,T,AL,K)=VERT("A,"G,"U_)
  343. WORK{IAGV}
  344. Z IFGV(MU,Q,NU,T,AL,K)=VERT("F,"G,"U_)
  345. WORK{IFGV}
  346. Z IFWZ(MU,Q,NU,T,AL,K)=VERT("F,"W,"Z)
  347. WORK{IFWZ}
  348. Z IGHZ(MU,Q,NU,T,AL,K)=VERT("G,"G_,"Z)
  349. WORK{IGHZ}
  350. Z IGHW(MU,Q,NU,T,AL,K)=VERT("G,"G_,"W)
  351. WORK{IGHW}
  352. Z IGVW(MU,Q,NU,T,AL,K)=VERT("G,"U_,"W)
  353. WORK{IGVW}
  354. Z IGVZ(MU,Q,NU,T,AL,K)=VERT("G,"U_,"Z)
  355. WORK{IGVZ}
  356. Z IHUW(MU,Q,NU,T,AL,K)=VERT("G_,"U,"W)
  357. WORK{IHUW}
  358. Z IHUZ(MU,Q,NU,T,AL,K)=VERT("G_,"U,"Z)
  359. WORK{IHUZ}
  360. Z IWWZ(MU,Q,NU,T,AL,K)=VERT("W,"W,"Z)
  361. WORK{IWWZ}
  362. Z IAFZ(MU,Q,NU,T,AL,K)=VERT("A,"F,"Z)
  363. WORK{IAFZ}
  364. Z IAWZ(MU,Q,NU,T,AL,K)=VERT("A,"W,"Z)
  365. WORK{IAWZ}
  366. *end
  367.  
  368. C RO-parameter 3. Divergencies of one-loop diagrams, four external lines.
  369.  
  370. C ONE-LOOP DIAGRAMS WITH FOUR EXTERNAL LINES.
  371. C CALCULATION OF ONE-LOOP DIVERGENCIES.
  372. C COMPARISON WITH COUTERTERMS INCLUDED.
  373. C CDC CPU time: 178.37 sec.
  374.  
  375. Oldnew i=I
  376. P ninput
  377. Read Roblocks.e
  378. VERT{,~,,,~}
  379. I LA=N,LB=N
  380. X HUM(K1,K2)=1.-0.5*DK(K1,K2)
  381. *fix
  382. P ninput
  383. BLOCK WORK{TADP}
  384. P ninput
  385. Id,VIERP(K1~,K2~,K3~,K4~)=
  386.    VIER(K1,K2,K3,K4,L1,L2,L3,L4) +
  387.    VIER(K1,K3,K2,K4,L1,L3,L2,L4) +
  388.    VIER(K1,K2,K4,K3,L1,L2,L4,L3)
  389.     +CONTR(K1,K2,K3,K4)
  390.  
  391. Id,VIER(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~)=
  392.   DS(K1;J1;-J2;TAP,(
  393.     DS(K2;J2;-J3;TAP,(
  394.       DS(K3;J3;-J4;TAP,(
  395.     VIE(K1,K2,K3,K4,L1,L2,L3,L4,J1,-J2,J2,-J3,J3,-J4,J4,-J1)
  396.      * DC("F,TFE,-1,J1,J2) ))) )))
  397.  
  398.    + DS(K1;K3;J5;-J6;TAP,(
  399.        DS(K4;J6;-J7;TAP,(
  400.     VIE1(K1,K2,K3,K4,L1,L2,L3,L4,J5,-J6,J6,-J7,J7,-J5) )) ))
  401.  
  402.    + DS(K2;K4;J8;-J9;TAP,(
  403.        DS(K1;J9;-J0;TAP,(
  404.      VIE2(K1,K2,K3,K4,L1,L2,L3,L4,J8,-J9,J9,-J0,J0,-J8) )) ))
  405.  
  406.    + DS(K1;K3;JA;-JB;Sym;JA;-JB;TAP,(
  407.      VIE3(K1,K2,K3,K4,L1,L2,L3,L4,JA,-JB,JB,-JA) ) )
  408.  
  409. Id,Anti,TAP
  410.  
  411. Id,VIE(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~,
  412.     KA~,KB~)=
  413.    VE3(K1,K5,K6,*,L1,P0,*,L5,P,*,L6,-P)*
  414.    VE3(K2,K7,K8,*,L2,P0,*,L70,P,*,L8,-P)*
  415.    VE3(K3,K9,K0,*,L3,P0,*,L9,P,*,L0,-P)*
  416.    VE3(K4,KA,KB,*,L4,P0,*,LA,P,*,LB,-P)*
  417.    PR8*D(L6,L70)*D(L8,L9)*D(L0,LA)*D(LB,L5)
  418. Al,VIE1(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  419.    VE4(K1,K3,K5,K6,*,L1,*,L3,*,L5,*,L6)*
  420.    VE3(K4,K7,K8,*,L4,P0,*,L71,P,*,L8,-P)*
  421.    VE3(K2,K9,K0,*,L2,P0,*,L9,P,*,L0,-P)*
  422.    PR6*D(L0,L5)*D(L6,L71)*D(L8,L9)
  423. Al,VIE2(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  424.    VE4(K2,K4,K5,K6,*,L2,*,L4,*,L5,*,L6)*
  425.    VE3(K1,K7,K8,*,L1,P0,*,L72,P,*,L8,-P)*
  426.    VE3(K3,K9,K0,*,L3,P0,*,L9,P,*,L0,-P)*
  427.    PR6*D(L0,L5)*D(L6,L72)*D(L8,L9)
  428. Al,VIE3(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~)=
  429.    VE4(K2,K4,K7,K8,*,L2,*,L4,*,L73,*,L8)*
  430.    VE4(K1,K3,K5,K6,*,L1,*,L3,*,L5,*,L6)*
  431.    PR4*D(L5,L8)*D(L6,L73)
  432. Id,Stats
  433. Id,Compo,<X>,VE4,VE3,PROP
  434. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  435. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  436.        AA(MU,P0,L2,Q,L1,P)
  437. Al,Stats,1
  438. C AL,PROP(AA+,L4+,Q+,L3+,P+)=AA(L4,L3,Q)
  439. Id,Count,-4,P,1,PR8,-8,PR6,-6,PR4,-4
  440. Id,PR8*PDP**2=-DEL*TIPI2/EP
  441. Al,PR6*PDP=-DEL*TIPI2/EP
  442. Al,PR4=-DEL*TIPI2/EP
  443. Id,PR8*PDP*P(MU~)*P(NU~)=-0.25*DEL*TIPI2/EP*D(MU,NU)
  444. Al,PR6*P(MU~)*P(NU~)=-0.25*DEL*TIPI2/EP*D(MU,NU)
  445. Id,PR8*P(MU~)*P(NU~)*P(AL~)*P(BE~)=-DEL*TIPI2/EP/24*D4(MU,NU,AL,BE)
  446. Id,Symme,D4,1,2,3,4
  447. Al,N=4
  448. Al,PR8=0
  449. B EP,TIPI2
  450. *yep
  451. Id,D4(L1~,L2~,L3~,L4~)=D(L1,L2)*D(L3,L4)+D(L1,L3)*D(L2,L4)
  452.                       +D(L1,L4)*D(L2,L3)
  453. Al,C2MS2=2*C**2-1
  454. Al,Multi,S**2=1-C**2
  455. Keep 'TADP'
  456. Nprint 'TADP'
  457. *next
  458. SVERT{~,~,}
  459. Z 'TADP'='TADP'
  460. Id,CONTR(K1~,K2~,K3~,K4~)=CONT(K1,K2,K3,K4,/,"K)*
  461.        VE4(K1,K2,K3,K4,*,L1,*,L2,*,L3,*,L4)/EP
  462. Id,Compo,<SS>,CONT,<X>,VE4
  463. Id,CONT(S~)=S
  464. Al,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  465. B EP,TIPI2
  466. *yep
  467. CVERT{~,,~}
  468. SCVERT{~,,~}
  469. *yep
  470. Id,C2MS2=2*C**2-1
  471. E1EZF{,,~,~,~}
  472. Id,Count,1,EP,-2,EZF,-2,E1F,-2
  473. Id,Multi,S**2=1-C**2
  474. P output
  475. *yep
  476. P input
  477. Id,DEL=-1.
  478. *next
  479. ENDBLOCK
  480. Z IAAUV=VIERP("A,"A,"U,"U_)
  481. WORK{IAAUV}
  482. Z IAFGV=VIERP("A,"F,"G,"U_)
  483. WORK{IAFGV}
  484. Z IAFHU=VIERP("A,"F,"G_,"U)
  485. WORK{IAFHU}
  486. Z IAGHW=VIERP("A,"G,"G_,"W)
  487. WORK{IAGHW}
  488. Z IAGVZ=VIERP("A,"G,"U_,"Z)
  489. WORK{IAGVZ}
  490. Z IAHUZ=VIERP("A,"G_,"U,"Z)
  491. WORK{IAHUZ}
  492. Z IAUVW=VIERP("A,"U,"U_,"W)
  493. WORK{IAUVW}
  494. Z IAAGH=VIERP("A,"A,"G,"G_)
  495. WORK{IAAGH}
  496. Z IAAUV=VIERP("A,"A,"U,"U_)
  497. WORK{IAAUV}
  498. Z IFGVW=VIERP("F,"G,"U_,"W)
  499. WORK{IFGVW}
  500. Z IFHUW=VIERP("F,"G_,"U,"W)
  501. WORK{IFHUW}
  502. Z IFFGH=VIERP("F,"F,"G,"G_)
  503. WORK{IFFGH}
  504. Z IFFUV=VIERP("F,"F,"U,"U_)
  505. WORK{IFFUV}
  506. Z IFFWW=VIERP("F,"F,"W,"W)
  507. WORK{IFFWW}
  508. Z IFFZZ=VIERP("F,"F,"Z,"Z)
  509. WORK{IFFZZ}
  510. Z IFFFF=VIERP("F,"F,"F,"F)
  511. WORK{IFFFF}
  512. Z IGHUV=VIERP("G,"G_,"U,"U_)
  513. WORK{IGHUV}
  514. Z IGHWW=VIERP("G,"G_,"W,"W)
  515. WORK{IGHWW}
  516. Z IGHZZ=VIERP("G,"G_,"Z,"Z)
  517. WORK{IGHZZ}
  518. Z IGVWZ=VIERP("G,"U_,"W,"Z)
  519. WORK{IGVWZ}
  520. Z IGGHH=VIERP("G,"G,"G_,"G_)
  521. WORK{IGGHH}
  522. Z IHUWZ=VIERP("G_,"U,"W,"Z)
  523. WORK{IHUWZ}
  524. Z IUUVV=VIERP("U,"U,"U_,"U_)
  525. WORK{IUUVV}
  526. Z IUVZZ=VIERP("U,"U_,"Z,"Z)
  527. WORK{IUVZZ}
  528. Z IUVWW=VIERP("U,"U_,"W,"W)
  529. WORK{IUVWW}
  530. Z IWWZZ=VIERP("W,"W,"Z,"Z)
  531. WORK{IWWZZ}
  532. Z IZZZZ=VIERP("Z,"Z,"Z,"Z)
  533. WORK{IZZZZ}
  534. Z IAFFW=VIERP("A,"F,"F,"W)
  535. WORK{IAFFW}
  536. Z IAWZZ=VIERP("A,"W,"Z,"Z)
  537. WORK{IAWZZ}
  538. *end
  539.  
  540. C RO-parameter 4. Divergencies of one-loop diagrams, ghost external lines.
  541.  
  542. C ONE-LOOP THREE-POINT DIAGRAMS WITH EXTERNAL GHOST LINES.
  543. C CALCULATION OF ONE-LOOP DIVERGENCIES.
  544. C COUNTERTERMS ARE ALSO CHECKED.
  545. C CDC CPU time: 16.09 sec.
  546.  
  547. Oldnew i=I
  548. P ninput
  549. Read Roblocks.e
  550. VERT{,,~,,}
  551. V R,T,U,V
  552. *fix
  553. P ninput
  554. BLOCK WORK{TADP}
  555. P ninput
  556. Id,VERT(K1~,K2~,K3~)=
  557.   DS(K1;J1;-J2;TAP,(DS(K2;-J1;J3;TAP,(
  558.   DIB(K1,K2,K3,J1,-J1,J3,-J3,J2,-J2)  ))))
  559.     + CONTR(K1,K2,K3)
  560.  
  561. Id,Anti,TAP
  562.  
  563. Id,DIB(K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~)=
  564.    VE3(K1,K4,K9,*,MU,Q,*,L4,P,*,L9,-R)*
  565.    VE3(K2,K5,K6,*,NU,T,*,L5,-P,*,L6,V)*
  566.    VE3(K3,K7,K8,*,AL,K,*,L7,-V,*,L8,R)*
  567.    PROP(K4,K5,*,L4,P,*,L5,P)*
  568.    PROP(K6,K7,*,L6,V,*,L7,V)*
  569.    PROP(K8,K9,*,L8,R,*,L9,R)
  570. B EP,TIPI2
  571. Id,Compo,<X>,VE4,VE3,PROP
  572. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  573. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  574.        AA(MU,P0,L2,Q,L1,P)
  575. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  576. Id,P0(MU~)=0.
  577. Al,Dotpr,P0(MU~)=0.
  578. Id,Commu,NOM
  579. Id,NOM(P,M~)*NOM(R,M0~)*NOM(V,SM~)=1.
  580. Al,NOM(P,M~)*NOM(Q~,M0~)=F2(Q)
  581. Al,NOM(P,M~)=F1(M)
  582. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  583. *yep
  584. Id,R(MU~)=P(MU)+Q(MU)
  585. Id,V(MU~)=P(MU)+Q(MU)+K(MU)
  586. Id,U(MU~)=P(MU)+K(MU)
  587. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  588. Id,RDR=PDP+2.*PDQ
  589. Al,VDV=PDP-2.*PDT
  590. Al,PDR=PDP+PDQ
  591. Al,PDV=PDP-PDT
  592. Al,VDR=PDP+2.*PDQ+PDK-QDT
  593. Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4
  594. Id,VDK=PDK
  595. Al,VDT=PDT
  596. Al,VDQ=PDQ
  597. Al,RDK=PDK
  598. Al,RDT=PDT
  599. Al,RDQ=PDQ
  600. Al,N=4
  601. Al,C2MS2=2*C**2-1
  602. *yep
  603. Id,P(MU~)*P(NU~)*P(AL~)=D3(MU,NU,AL,Q)*DEL*TIPI2/EP/6.
  604.      +D3(MU,NU,AL,K)*DEL*TIPI2/EP/12.
  605. Id,P(MU~)*PDP=Q(MU)*DEL*TIPI2/EP+K(MU)*DEL*TIPI2/EP/2.
  606. Al,PDP=-DEL*TIPI2/EP
  607. Id,P(MU~)*P(NU~)=-0.25*D(MU,NU)*DEL*TIPI2/EP
  608. Id,P(MU~)*PDK=-0.25*K(MU)*DEL*TIPI2/EP
  609. Id,P(MU~)*PDQ=-0.25*Q(MU)*DEL*TIPI2/EP
  610. Id,P(MU~)*PDT=-0.25*DEL*TIPI2/EP*T(MU)
  611. Id,P(MU~)*F2(R)=0.5*DEL*TIPI2/EP*Q(MU)
  612. Id,P(MU~)*F2(U)=0.5*DEL*TIPI2/EP*K(MU)
  613. Id,P(MU~)*F2(V)=0.5*DEL*TIPI2/EP*(Q(MU)+K(MU))
  614. Id,F2(Q~)=-DEL*TIPI2/EP
  615. *yep
  616. Id,T(MU~)=-K(MU)-Q(MU)
  617. Al,TDT=QDQ+KDK+2.*QDK
  618. Id,Dotpr,T(MU~)=-K(MU)-Q(MU)
  619. Id,D3(MU~,NU~,AL~,Q~)=D(MU,NU)*Q(AL)+D(MU,AL)*Q(NU)+D(NU,AL)*Q(MU)
  620. Id,Multi,S**2=1.-C**2
  621. Keep 'TADP'
  622. Nprint 'TADP'
  623. *next
  624. SVERT{~,,~}
  625. Z 'TADP'='TADP'(AL,P,BE,Q,GA,K)
  626. Id,CONTR(K1~,K2~,K3~)=CONT(K1,K2,K3,/,"K)
  627.    *VE3(K1,K2,K3,*,AL,P,*,BE,Q,*,GA,K)/EP
  628. Id,Compo,<SS>,CONT,<X>,VE3
  629. Id,CONT(S~)=S
  630. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P)
  631. CVERT{~,~,}
  632. SCVERT{~,~,}
  633. Id,C2MS2=2*C**2-1
  634. E1EZF{,,~,~,~}
  635. B EP,TIPI2
  636. Id,Count,1,EP,-2,E1F,-2,EZF,-2
  637. Id,Multi,S**2=1-C**2
  638. Al,Q(MU~)=-P(MU)-K(MU)
  639. P output
  640. *yep
  641. Id,DEL=-1
  642. *next
  643. P input
  644. ENDBLOCK
  645. P input
  646. Z IAOP(MU,Q,NU,T,AL,K)=VERT("A,"P_,"P)
  647. WORK{IAOP}
  648. Z IAXY(MU,Q,NU,T,AL,K)=VERT("A,"Y_,"Y)
  649. WORK{IAXY}
  650. Z IFOP(MU,Q,NU,T,AL,K)=VERT("F,"P_,"P)
  651. WORK{IFOP}
  652. Z IFXY(MU,Q,NU,T,AL,K)=VERT("F,"Y_,"Y)
  653. WORK{IFXY}
  654. Z IGPQ(MU,Q,NU,T,AL,K)=VERT("G,"P,"R_)
  655. WORK{IGPQ}
  656. Z IGRX(MU,Q,NU,T,AL,K)=VERT("G,"R,"Y_)
  657. WORK{IGRX}
  658. Z IGTX(MU,Q,NU,T,AL,K)=VERT("G,"T,"Y_)
  659. WORK{IGTX}
  660. Z IHOR(MU,Q,NU,T,AL,K)=VERT("G_,"P_,"R)
  661. WORK{IHOR}
  662. Z IHOT(MU,Q,NU,T,AL,K)=VERT("G_,"P_,"T)
  663. WORK{IHOT}
  664. Z IHQY(MU,Q,NU,T,AL,K)=VERT("G_,"R_,"Y)
  665. WORK{IHQY}
  666. Z IOPZ(MU,Q,NU,T,AL,K)=VERT("P_,"P,"Z)
  667. WORK{IOPZ}
  668. Z IOPW(MU,Q,NU,T,AL,K)=VERT("P_,"P,"W)
  669. WORK{IOPW}
  670. Z IORV(MU,Q,NU,T,AL,K)=VERT("P_,"R,"U_)
  671. WORK{IORV}
  672. Z IOTV(MU,Q,NU,T,AL,K)=VERT("P_,"T,"U_)
  673. WORK{IOTV}
  674. Z IPQU(MU,Q,NU,T,AL,K)=VERT("P,"R_,"U)
  675. WORK{IPQU}
  676. Z IPSU(MU,Q,NU,T,AL,K)=VERT("P,"T_,"U)
  677. WORK{IPSU}
  678. Z IQRZ(MU,Q,NU,T,AL,K)=VERT("R_,"R,"Z)
  679. WORK{IQRZ}
  680. Z IQTZ(MU,Q,NU,T,AL,K)=VERT("R_,"T,"Z)
  681. WORK{IQTZ}
  682. Z IQVY(MU,Q,NU,T,AL,K)=VERT("R_,"U_,"Y)
  683. WORK{IQVY}
  684. Z IRUX(MU,Q,NU,T,AL,K)=VERT("R,"U,"Y_)
  685. WORK{IRUX}
  686. Z ISVY(MU,Q,NU,T,AL,K)=VERT("T_,"U_,"Y)
  687. WORK{ISVY}
  688. Z ITUX(MU,Q,NU,T,AL,K)=VERT("T,"U,"Y_)
  689. WORK{ITUX}
  690. Z IWXY(MU,Q,NU,T,AL,K)=VERT("W,"Y_,"Y)
  691. WORK{IWXY}
  692. Z IXYZ(MU,Q,NU,T,AL,K)=VERT("Y_,"Y,"Z)
  693. WORK{IXYZ}
  694. *end
  695.  
  696. C RO-parameter 5. Two-loop self-energy diagrams.
  697.  
  698. C TWO-LOOP SELF-ENERGY DIAGRAMS.
  699. C THE DIAGRAMS ARE DIVIDED IN 8 TOPOLOGY CLASSES.
  700. C EACH CLASS IS WORKED OUT IN TERMS OF THE F211 ETC.
  701. C SUBSEQUENTLY THE F211 ETC ARE EXPANDED IN TERMS OF THE
  702. C  HIGGS MASS SM.
  703. C CDC CPU time: 111.85 sec.
  704.  
  705. Common A0A0,W0A0,W0W0,WPWM
  706.  
  707. S PM=1,M,M0,SM,N,C,S,EP,AH
  708. Oldnew i=I
  709. P ninput
  710. Read Roblocks.e
  711. VERT{,,,~,~}
  712. X NUM(K1,K2)=1.-0.5*DK(K1,K2)
  713. X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3)
  714.      +2/3*DK(K1,K2)*DK(K1,K3)
  715. X KUM(K1)=1-DK("Z,K1)
  716. C X KUM(K1)=1-DK(4,K1)
  717. X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5)
  718. F FP3,FP2,FP1,FQ2,FQ1,FK1
  719. *fix
  720. P ninput
  721. BLOCK WORK{}
  722. P ninput
  723. Id,Compo,<X>,VE4,VE3,PROP
  724. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  725. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  726.        AA(MU,P0,L2,Q,L1,P)
  727. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  728. Id,Commu,NOM
  729. Id,NOM(P,M~)*NOM(P,S~)*NOM(P,C~)=FP3(M,S,C)
  730. Al,NOM(P,M~)*NOM(P,S~)=FP2(M,S)
  731. Al,NOM(P,M~)=FP1(M)
  732. Al,NOM(Q,M~)*NOM(Q,S~)=FQ2(M,S)
  733. Al,NOM(Q,M~)=FQ1(M)
  734. Al,NOM(K,M~)=FK1(M)
  735. *yep
  736. Id,QDP=0.5*KDK-0.5*PDP-0.5*QDQ
  737. Al,QDK=-0.5*PDP+0.5*KDK+0.5*QDQ
  738. Al,PDK=-0.5*QDQ+0.5*KDK+0.5*PDP
  739. Id,Multi,S**2=1-C**2
  740. Al,C2MS2=2*C**2-1
  741. *yep
  742. C AT MOST FQ2, FK1, NOT FQ3 OR FK2
  743. C AT MOST QDQ**2, KDK**2.
  744. Id,QDQ**2*FQ2(M~,M0~)=1.-(M**2+M0**2)*FQ1(M0)+M**4*FQ2(M,M0)
  745. Al,KDK**2*FK1(M~)=PDP+QDQ-M**2+M**4*FK1(M)
  746. Al,QDQ**2*FQ1(M~)=QDQ-M**2+M**4*FQ1(M)
  747. C NOW NO MORE QDQ**2 OR KDK**2.
  748. Id,QDQ*FQ2(M~,M0~)=FQ1(M0)-M**2*FQ2(M,M0)
  749. Al,QDQ*FQ1(M~)=1.-M**2*FQ1(M)
  750. Al,QDQ*FK1(M~)=PDP*FK1(M)+1.-M**2*FK1(M)
  751. Al,KDK*FK1(M~)=1.-M**2*FK1(M)
  752. Id,PDP**2*FP3(M~,M0~,S~)=FP1(S)-(M**2+M0**2)*FP2(M0,S)
  753.        +M**4*FP3(M,M0,S)
  754. Al,PDP**2*FP2(M~,M0~)=1.-(M**2+M0**2)*FP1(M0)+M**4*FP2(M,M0)
  755. Al,PDP**2*FP1(M~)=PDP-M**2+M**4*FP1(M)
  756. Id,PDP*FP3(M~,M0~,S~)=FP2(M0,S)-M**2*FP3(M,M0,S)
  757. Al,PDP*FP2(M~,M0~)=FP1(M0)-M**2*FP2(M,M0)
  758. Al,PDP*FP1(M~)=1.-M**2*FP1(M)
  759. Id,FQ2(M~,M0~)=FP2(M,M0)
  760. Al,FQ1(M~)=FP1(M)
  761. Al,FK1(M~)=FP1(M)
  762. Id,Commu,FP3,FP2,FP1
  763. *yep
  764. Id,FP3(M~,S~,C~)*FP2(M0~,SM~)=F32(M,S,C,M0,SM)
  765. Al,FP3(M~,S~,C~)*FP1(M0~)*FP1(SM~)=F311(M,S,C,M0,SM)
  766. Al,FP3(M~,S~,C~)*FP1(M0~)=F31(M,S,C,M0)
  767. Al,FP3(M~,S~,C~)=0
  768. Id,FP2(M~,S~)*FP2(M0~,C~)*FP1(SM~)=F221(M,S,M0,C,SM)
  769. Al,FP2(M~,S~)*FP2(M0~,C~)=F22(M,S,M0,C)
  770. Al,FP2(M~,S~)*FP1(M0~)*FP1(C~)=F211(M,S,M0,C)
  771. Al,FP2(M~,S~)*FP1(M0~)=F21(M,S,M0)
  772. Al,FP2(M~,S~)=0
  773. Id,FP1(M~)*FP1(S~)*FP1(C~)=F111(M,S,C)
  774. Al,FP1(M~)*FP1(S~)=F11(M,S)
  775. Al,FP1(M~)=0
  776. *yep
  777. Id,F311(M~,S~,C~,M0~,SM~)=F311(M,S,C,M0,SM)*YYYY(C,SM)
  778. Al,F31(M~,S~,C~,M0~)=F31(M,S,C,M0)*XXXX(C,M0)
  779. Id,YYYY(SM,SM)=1./ATEL9**2
  780. Al,YYYY(M~,SM)=1.
  781. Al,YYYY(SM,M~)=1./ATEL9**2
  782. Al,YYYY(S~,C~)=1.
  783. Al,XXXX(SM,SM)=1.
  784. Al,XXXX(M~,SM)=ATEL9**2
  785. Al,XXXX(SM,M~)=1./ATEL9**2
  786. Al,XXXX(C~,S~)=1.
  787. Id,F221(M~,M0~,C~,S~,SM~)=F221(M,M0,C,S,SM)/ATEL9**2
  788. Al,F21(M~,M0~,SM)=F21(M,M0,SM)*ATEL9**2
  789. Al,F111(M~,M0~,SM)=F111(M,M0,SM)*ATEL9**2
  790. Id,Count,1,ATEL9,1,SM,1
  791. Id,ATEL9=1
  792. Al,Multi,ATEL9**-1=1
  793. C Nprint A0A0,W0A0,W0W0,WPWM
  794. ENDBLOCK
  795. BLOCK TOPO{}
  796. Id,TOPA(I1~,I2~)=
  797.    DS(I1;J1;J4;Sym;J1;J4;TAP,(
  798.      DS(J3;J2;-J1;TAP,(
  799.        DS(-J2;-J5;I2;TAP,(
  800.    DC("T,THI,-1,J1,J2,J3,J4,J5)*
  801.    DIA(I1,I2,J1,-J1,J2,-J2,J3,-J3,J4,-J4,J5,-J5) )) )) ))
  802.  
  803. Id,Anti,TAP
  804.  
  805. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  806.    VE3(I1,K1,K7,*,MU,P0,*,L1,P,*,L7,-P)*
  807.    VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)*
  808.    VE3(K4,I2,K0,*,L4,Q,*,NU,-P0,*,L0,-Q)*
  809.    VE3(K6,K8,K9,*,L6,-K,*,L8,P,*,L9,Q)*
  810.    PROP(K1,K2,*,L1,P,*,L2,P)*
  811.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  812.    PROP(K5,K6,*,L5,K,*,L6,K)*
  813.    PROP(K7,K8,*,L7,P,*,L8,P)*
  814.    PROP(K9,K0,*,L9,Q,*,L0,Q)*D(MU,NU)/N
  815. ENDBLOCK
  816. Z A0A0=TOPA("A,"A)
  817. TOPO{}
  818. WORK{}
  819. *next
  820. Z W0A0=TOPA("W,"A)
  821. TOPO{}
  822. WORK{}
  823. *next
  824. Z W0W0=TOPA("W,"W)
  825. TOPO{}
  826. WORK{}
  827. *next
  828. Z WPWM=TOPA("U,"U_)
  829. TOPO{}
  830. WORK{}
  831. *next
  832. BLOCK TOP1{}
  833. Id,TOPB(I1~,I2~)=
  834.    DS(I1;-J1;-J2;TAP,(
  835.      DS(J2;-J3;-J4;Sym;-J3;-J4;TAP,(
  836.        DS(J3;J4;-J5;TAP,(
  837.    DC("T,THI,-1,J1,J2,J3,J4,J5)*
  838.    DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,-J3,J3,J4,-J4) )) )) ))
  839.  
  840. Id,Anti,TAP
  841.  
  842. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  843.    VE3(I1,K1,K3,*,MU,P0,*,L1,P,*,L3,-P)*
  844.    VE3(K2,I2,K6,*,L2,-P,*,NU,-P0,*,L6,P)*
  845.    VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)*
  846.    VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)*
  847.    PROP(K1,K2,*,L1,P,*,L2,P)*
  848.    PROP(K3,K4,*,L3,P,*,L4,P)*
  849.    PROP(K5,K6,*,L5,P,*,L6,P)*
  850.    PROP(K7,K8,*,L7,K,*,L8,K)*
  851.    PROP(K9,K0,*,L9,Q,*,L0,Q)*D(MU,NU)/N
  852. ENDBLOCK
  853. Z A0A0=A0A0+TOPB("A,"A)
  854. TOP1{}
  855. WORK{}
  856. *next
  857. Z W0A0=W0A0+TOPB("W,"A)
  858. TOP1{}
  859. WORK{}
  860. *next
  861. Z W0W0=W0W0+TOPB("W,"W)
  862. TOP1{}
  863. WORK{}
  864. *next
  865. Z WPWM=WPWM+TOPB("U,"U_)
  866. TOP1{}
  867. WORK{}
  868. *next
  869. BLOCK TOP2{}
  870. Id,TOPC(I1~,I2~)=
  871.    DS(I1;-J1;-J2;I2;Sym;J1;J2;TAP,(
  872.      DS(J1;-J3;-J4;Sym;J3;J4;TAP,(
  873.      DC("T,THI,-1,J1,J2,J3,J4)*
  874.      DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3,J4,-J4) )) ))
  875.  
  876. Id,Anti,TAP
  877.  
  878. C    DS(J1,1,8,(DS(J2,J1,8,(
  879. C    DC(QN(I1),QN(I2),QH(J1),QH(J2))*(NUM(J1,J2))*
  880. C    DS(J3,1,8,(DS(J4,J3,8,(
  881. C    DC(QG(J1),QH(J3),QH(J4))*(NUM(J3,J4)*ZUM(J1,J2,J3,J4,3))*
  882. C    DIA(I1,I2,CHH(J1),CHG(J1),CHH(J2),CHG(J2),
  883. C        CHH(J3),CHG(J3),CHG(J4),CHH(J4) )  )))) ))))
  884. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  885.    VE4(I1,K1,K3,I2,*,MU,*,L1,*,L3,*,NU)*
  886.    VE3(K2,K5,K8,*,L2,P,*,L5,-K,*,L8,Q)*
  887.    VE3(K4,K6,K7,*,L4,-P,*,L6,K,*,L7,-Q)*
  888.    PROP(K1,K2,*,L1,P,*,L2,P)*
  889.    PROP(K3,K4,*,L3,P,*,L4,P)*
  890.    PROP(K5,K6,*,L5,K,*,L6,K)*
  891.    PROP(K7,K8,*,L7,Q,*,L8,Q)*D(MU,NU)/N
  892. ENDBLOCK
  893. Z A0A0=A0A0+TOPC("A,"A)
  894. TOP2{}
  895. WORK{}
  896. *next
  897. Z W0A0=W0A0+TOPC("W,"A)
  898. TOP2{}
  899. WORK{}
  900. *next
  901. Z W0W0=W0W0+TOPC("W,"W)
  902. TOP2{}
  903. WORK{}
  904. *next
  905. Z WPWM=WPWM+TOPC("U,"U_)
  906. TOP2{}
  907. WORK{}
  908. *next
  909. BLOCK TOP3{}
  910. Id,TOPD(I1~,I2~)=
  911.   DS(I1;-J1;-J2;I2;Sym;J1;J2,TAP,(
  912.    DS(J1;J2;-J3;J3;Sym;J3;-J3,TAP,(
  913.    DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3) )) ))
  914.  
  915. Id,Anti,TAP
  916.  
  917. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)=
  918.    VE4(I1,K1,K3,I2,*,MU,*,L1,*,L3,*,NU)*
  919.    VE4(K2,K4,K5,K6,*,L2,*,L4,*,L5,*,L6)*
  920.    PROP(K1,K2,*,L1,P,*,L2,P)*
  921.    PROP(K3,K4,*,L3,P,*,L4,P)*
  922.    PROP(K5,K6,*,L5,Q,*,L6,Q)*D(MU,NU)/N
  923. ENDBLOCK
  924. Z A0A0=A0A0+TOPD("A,"A)
  925. TOP3{}
  926. WORK{}
  927. *next
  928. Z W0A0=W0A0+TOPD("W,"A)
  929. TOP3{}
  930. WORK{}
  931. *next
  932. Z W0W0=W0W0+TOPD("W,"W)
  933. TOP3{}
  934. WORK{}
  935. *next
  936. Z WPWM=WPWM+TOPD("U,"U_)
  937. TOP3{}
  938. WORK{}
  939. *next
  940. BLOCK TOP4{}
  941. Id,TOPE(I1~,I2~)=
  942.     DS(I1;-J1;-J2;TAP,(
  943.       DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,(
  944.      DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) ))
  945.  
  946. Id,Anti,TAP
  947.  
  948. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  949.    VE3(I1,K1,K5,*,MU,P0,*,L1,-P,*,L5,P)*
  950.    VE3(K2,I2,K8,*,L2,P,*,NU,-P0,*,L8,-P)*
  951.    VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)*
  952.    PROP(K1,K2,*,L1,P,*,L2,P)*
  953.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  954.    PROP(K5,K6,*,L5,P,*,L6,P)*
  955.    PROP(K7,K8,*,L7,P,*,L8,P)*D(MU,NU)/N
  956. ENDBLOCK
  957. Z A0A0=A0A0+TOPE("A,"A)
  958. TOP4{}
  959. WORK{}
  960. *next
  961. Z W0A0=W0A0+TOPE("W,"A)
  962. TOP4{}
  963. WORK{}
  964. *next
  965. Z W0W0=W0W0+TOPE("W,"W)
  966. TOP4{}
  967. WORK{}
  968. *next
  969. Z WPWM=WPWM+TOPE("U,"U_)
  970. TOP4{}
  971. WORK{}
  972. *next
  973. BLOCK TOP5{}
  974. Id,TOPF(I1~,I2~)=
  975.     DS(I1;-J1;-J2;TAP,(
  976.       DS(J3;J2;J4;Sym;J3;J4,TAP,(
  977.    DC("T,THI,-1,J1,J2,J3,J4)*
  978.    DIA(I1,I2,-J1,J1,J3,-J3,-J2,J2,J4,-J4) )) ))
  979.  
  980. Id,Anti,TAP
  981.  
  982. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  983.    VE3(I1,K1,K5,*,MU,P0,*,L1,P,*,L5,-P)*
  984.    VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)*
  985.    VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)*
  986.    PROP(K1,K2,*,L1,P,*,L2,P)*
  987.    PROP(K3,K4,*,L3,K,*,L4,K)*
  988.    PROP(K5,K6,*,L5,P,*,L6,P)*
  989.    PROP(K7,K8,*,L7,Q,*,L8,Q)*D(MU,NU)/N
  990. ENDBLOCK
  991. Z A0A0=A0A0+2*TOPF("A,"A)
  992. TOP5{}
  993. WORK{}
  994. *next
  995. Z W0A0=W0A0+TOPF("W,"A)+TOPF("A,"W)
  996. TOP5{}
  997. WORK{}
  998. *next
  999. Z W0W0=W0W0+2*TOPF("W,"W)
  1000. TOP5{}
  1001. WORK{}
  1002. *next
  1003. Z WPWM=WPWM+TOPF("U,"U_)+TOPF("U_,"U)
  1004. TOP5{}
  1005. WORK{}
  1006. *next
  1007. BLOCK TOP6{}
  1008. Id,TOPH(I1~,I2~)=
  1009.     DS(I1;-J1;-J2;-J3;Sym;-J1;-J2;-J3,TAP,(
  1010.     DC("T,THI,-1,J1,J2,J3)*
  1011.     DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3) ))
  1012.  
  1013. Id,Anti,TAP
  1014.  
  1015. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)=
  1016.    VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)*
  1017.    VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)*
  1018.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1019.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1020.    PROP(K5,K6,*,L5,K,*,L6,K)*D(MU,NU)/N
  1021. ENDBLOCK
  1022. Z A0A0=A0A0+TOPH("A,"A)
  1023. TOP6{}
  1024. WORK{}
  1025. Print A0A0
  1026. *next
  1027. Z W0A0=W0A0+TOPH("W,"A)
  1028. TOP6{}
  1029. WORK{}
  1030. Print W0A0
  1031. *next
  1032. Z W0W0=W0W0+TOPH("W,"W)
  1033. TOP6{}
  1034. WORK{}
  1035. Print W0W0
  1036. *next
  1037. Z WPWM=WPWM+TOPH("U,"U_)
  1038. TOP6{}
  1039. WORK{}
  1040. Print WPWM
  1041. *next
  1042. Z A0A0=A0A0
  1043. Z W0A0=W0A0
  1044. Z W0W0=W0W0
  1045. Z WPWM=WPWM
  1046. *yep
  1047. P input
  1048. Id,F22(M~,M0~,S~,C~)=F221(M,M0,S,C,AH)
  1049. Al,F31(M~,M0~,S~,C~)=F311(M,M0,S,C,AH)
  1050. Al,F21(M~,M0~,S~)=F211(M,M0,S,AH)
  1051. Id,F221(M~,M~,M0~,M0~,SM~)=FF221(M,M,M0,M0,SM)
  1052. Al,F221(M~,M~,C~,S~,SM~)=DIF(C,S)*F211(M,M,S,SM)
  1053.                               -DIF(C,S)*F211(M,M,C,SM)
  1054. Al,F221(C~,S~,M0~,M~,SM~)=DIF(C,S)*F211(M0,M,S,SM)
  1055.                                -DIF(C,S)*F211(M0,M,C,SM)
  1056. Id,FF221(M~,M~,C~,C~,S~)=F221(M,M,C,C,S)
  1057. Al,F311(M~,M~,M~,C~,S~)=FF311(M,M,M,C,S)
  1058. Al,F311(M~,SM~,M0~,C~,S~)=DIF(M,M0)*F211(SM,M0,C,S)
  1059.                                    -DIF(M,M0)*F211(M,SM,C,S)
  1060. Id,FF311(M~,M~,M~,C~,S~)=F311(M,M,M,C,S)
  1061. Al,F211(M~,M~,C~,S~)=FF211(M,M,C,S)
  1062. Al,F211(C~,S~,M~,M0~)=DIF(C,S)*F111(S,M,M0)
  1063.                               -DIF(C,S)*F111(C,M,M0)
  1064. Id,FF211(M~,M~,C~,S~)=F211(M,M,C,S)
  1065. Id,F111(M~,C~,AH)=F11(M,C)
  1066. Al,F111(M~,C~,S~)=(EP-EP**2-1)*(M**2*F211(M,M,C,S)
  1067.                  +C**2*F211(C,C,M,S)+S**2*F211(S,S,M,C))
  1068. Id,F11(PM,M~)=0
  1069. Al,F11(M~,PM)=0
  1070. Id,Symme,F211,3,4,F311,4,5,F111,1,2,3
  1071. Id,Symme,F211,1,2,F311,1,2,3,F11,1,2
  1072. Id,Asymm,DIF,1,2
  1073. *yep
  1074. Id,DIF(M,SM)=-1./SM**2-M**2/SM**4-M**4/SM**6
  1075. Al,DIF(M0,SM)=-1./SM**2-M0**2/SM**4-M0**4/SM**6
  1076. Al,DIF(PM,M~)=-1./M**2
  1077. Al,DIF(M,M0)=-C**2/M**2/S**2
  1078. Id,Multi,M0**2=M**2/C**2
  1079. Al,Multi,M0**-2=C**2/M**2
  1080. Id,F221(M~,M0~,S~,C~,AH)=F22(M,M0,S,C)
  1081. Al,F311(M~,M0~,S~,C~,AH)=F31(M,M0,S,C)
  1082. Al,F211(M~,M0~,S~,AH)=F21(M,M0,S)
  1083. Id,EP**2*N=4.*EP**2
  1084. Al,N=4+EP
  1085. Al,EP**2*N**-1=0.25*EP**2
  1086. Al,EP*N**-1=EP/4.-EP**2/16.
  1087. Al,N**-1=1/4-EP/16+EP**2/64
  1088. Id,EP**2*F22(M~,M0~,S~,C~)=-4.*PI**4
  1089. Al,EP**2*F31(M~,M0~,S~,C~)=0.
  1090. Al,EP**2*F21(M~,M0~,S~)=4.*PI**4*S**2
  1091. Al,EP**2*F11(M~,M0~)=-4.*PI**4*M**2*M0**2
  1092. Al,EP**2*F221(M~,M0~,S~,C~,SM~)=0.
  1093. Al,EP**2*F311(M~,M0~,S~,C~,SM~)=0.
  1094. Al,EP**2*F211(M~,M0~,S~,C~)=-2.*PI**4
  1095. Id,EP*F3(M~,S~,C~)=0.
  1096. Al,EP**2*F3(M~,S~,C~)=0
  1097. Al,EP*F2(M~,C~)=-2.*I*PI**2
  1098. Al,EP**2*F2(M~,C~)=0.
  1099. Id,Multi,M0**2=M**2/C**2
  1100. *yep
  1101. Id,Multi,C**2=1-S**2
  1102. *yep
  1103. Id,Multi,S**2=1-C**2
  1104. Id,C**2*F211(M~,M0~,PM,SM~)=(1-S**2)*F211(M,M0,PM,SM)
  1105. Al,C**2*F3(PM,M~,M0~)=(1-S**2)*F3(PM,M,M0)
  1106. Al,C**2*F11(PM,M~)=(1-S**2)*F11(PM,M)
  1107. *yep
  1108. F21F22{}
  1109. Id,F22(M~,M~,M0~,M0~)=F(2,M)*F(2,M0)
  1110. Al,F21(M~,M~,M0~)=F(2,M)*F(1,M0)
  1111. Al,F31(M~,M~,M~,M0~)=F(3,M)*F(1,M0)
  1112. Al,F11(M~,M0~)=F(1,M)*F(1,M0)
  1113. Id,F(1,PM)=0
  1114. F1t5{}
  1115. Id,EP=0
  1116. B EP,I,PI2,TIPI2
  1117. Id,Count,1,SM,1
  1118. Id,LG(SM,M~)=LG(SM)-LG(M)
  1119. Al,LG(M0,M~)=LG(M0)-LG(M)
  1120. Al,LG(M,M0~)=LG(M)-LG(M0)
  1121. Id,Multi,M0**2=M**2/C**2
  1122. Al,PI**4=-0.25*TIPI2**2
  1123. Id,Commu,LG
  1124. *yep
  1125. Id,C**-6*S**-4=1/C**6/S**2+1/C**4/S**4
  1126. Id,C**-6*S**-2=1/C**6+1/C**4/S**2
  1127. Id,C**-2*S**-2=1/C**2+1/S**2
  1128. Al,C**-2*S**-4=1/C**2+1/S**2+1/S**4
  1129. Al,C**-4*S**-2=1/C**4+1/C**2+1/S**2
  1130. Al,C**-4*S**-4=1/C**4+2/C**2+2/S**2+1/S**4
  1131. Id,Multi,C**2=1-S**2
  1132. Id,Multi,S**2=1-C**2
  1133. *begin
  1134. Write comm2lp
  1135. *end
  1136.  
  1137. C RO-parameter 6. One-loop subtractions. RO-parameter result.
  1138.  
  1139. C ONE-LOOP SUBTRACTIONS AND RO-PARAMETER CALCULATION.
  1140. C NOT CONSIDERED ARE TADPOLE DIAGRAMS WITH INSERTED CORRECTIONS.
  1141. C ALTHOUGH THEY ARE IMPORTANT FOR GAUGE INVARIANCE OF THE WW LINES,
  1142. C THEY ARE NOT OF ANY CONSEQUENCE TO THE RO-PARAMETER.
  1143. C BELOW THEY ARE MADE INACTIVE.
  1144. C ENTER RESULT FROM TWO-LOOP SELF-ENERGY DIAGRAMS.
  1145. C THESE ARE THE FILES A0A0, W0A0, W0W0 AND WPWM.
  1146. C CDC CPU time 28.15 SEC.
  1147.  
  1148. Oldnew i=I
  1149. Enter comm2lp
  1150. Common SWA,SPM,SWW,SAA
  1151. P ninput
  1152. Read Roblocks.e
  1153. VERT{,,,~,~}
  1154. SVERT{,,}
  1155. X NUM(K1,K2)=1-0.5*DK(K1,K2)
  1156. *fix
  1157. P ninput
  1158. BLOCK WORK{TADP}
  1159. P ninput
  1160. B ET,EP,I,PI2,DEL,TIPI2
  1161. Id,Compo,<X>,VE4,VE3,PROP
  1162. Id,Compo,<SS>,CONT
  1163. Id,Adiso,CONT(S~)*CONT(C~)=S/EP+C/EP
  1164. Al,CONT(S~)=S/EP
  1165. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1166. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1167.        AA(MU,P0,L2,Q,L1,P)
  1168. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1169. Id,Commu,NOM
  1170. Id,NOM(P,M~)*NOM(P,M0~)*NOM(P,SM~)=F3(M,M0,SM)
  1171. Al,NOM(P,M~)*NOM(P,M0~)=F2(M,M0)
  1172. Al,NOM(P,M~)=F(1,M)
  1173. Al,ZERO**2=0
  1174. *yep
  1175. Id,F(1,PM)=0
  1176. Al,PM=0
  1177. Id,PDP**2*F3(M~,M0~,SM~)=F(1,SM)-(M**2+M0**2)*F2(M0,SM)
  1178.     +M**4*F3(M,M0,SM)
  1179. Al,PDP*F3(M~,M0~,SM~)=F2(M0,SM)-M**2*F3(M,M0,SM)
  1180. Al,PDP*F2(M~,M0~)=F(1,M0)-M**2*F2(M,M0)
  1181. Id,F(1,PM)=0
  1182. Al,PM=0
  1183. Id,F3(M~,M0~,SM)=1/ATEL9**2*F3(M,M0,SM)
  1184. Al,F(1,SM)=ATEL9**2*F(1,SM)
  1185. Id,Count,-1,ATEL9,1,SM,1,E1,2,E2,2,ET,2,EZF,2
  1186. Id,Multi,M0**2=M**2/C**2
  1187. Al,ATEL9=1
  1188. Al,Multi,ATEL9**-1=1
  1189. Id,Multi,S**2=1.-C**2
  1190. *yep
  1191. Id,Symme,F2,1,2,F3,1,2,3
  1192. Id,F3(M~,M~,M~)=F(3,M)
  1193. Al,F3(M~,M~,SM~)=F3(SM,M,M)
  1194. Id,F3(SM~,M0~,M~)=DIF(M0,SM)*(F2(SM,M)-F2(M0,M))
  1195. Id,F2(M~,M~)=F(2,M)
  1196. Al,F2(M~,M0~)=DIF(M0,M)*(F(1,M)-F(1,M0))
  1197. Id,F(1,PM)=0
  1198. Al,PM=0
  1199. Id,Asymm,DIF,1,2
  1200. Id,DIF(PM,M~)=-1/M**2
  1201. Al,DIF(M,M0)=-C**2/M**2/S**2
  1202. Al,DIF(M~,SM)=-(1+M**2/SM**2+M**4/SM**4+M**6/SM**6)/SM**2
  1203. Id,F(1,SM)=ATEL9**2*F(1,SM)
  1204. Al,F(3,SM)=F(3,SM)/ATEL9**2
  1205. Id,Count,-1,ATEL9,1,SM,1,E1,2,E2,2,ET,2,EZF,2
  1206. Id,Numer,ATEL9,1.
  1207. F1t5{}
  1208. Id,Once,PI**2=-I*TIPI2/2
  1209. Id,N**-1=0.25-EP/16+EP**2/64
  1210. Al,N=4+EP
  1211. Id,EP=0
  1212. Id,Multi,M0**2=M**2/C**2
  1213. Id,Multi,M0**-1=C**2/M**2
  1214. Id,Multi,C**2=1.-S**2
  1215. Id,Multi,S**2=1.-C**2
  1216. *yep
  1217. CVERT{,,~}
  1218. SCVERT{,,~}
  1219. Id,ZERO=0.
  1220. Id,Count,1,SM,1,E1,2,E2,2,ET,2,EZF,2
  1221. Id,C2MS2=2*C**2-1
  1222. E1EZF{,,~,,}
  1223. Id,PI**6=-PI2*TIPI2**2/4
  1224. Id,Commu,LG
  1225. Id,EP=0
  1226. Id,Count,1,SM,1,ET,2
  1227. Id,C**-2*S**-4=1/S**4+1/S**2+1/C**2
  1228. Al,C**-2*S**-2=1/S**2+1/C**2
  1229. P input
  1230. ENDBLOCK
  1231. BLOCK SELF{}
  1232. P ninput
  1233. Id,SELF(I1~,I2~)=
  1234.     DS(I1;J1;J2;Sym;J1;J2,TAP,(DIB(I1,J1,-J1,J2,-J2,I2) ))
  1235.   + DS(I1;J3;-J3;I2;Sym;J3;-J3,TAP,(DIC(I1,J3,-J3,I2) ))
  1236.   + DS(I1;J4;-J5,TAP,(DS("N;J5;-J6,TAP,(DID(I1,I2,"N,J4,-J5,J5,-J6,J6,-J4) ))))
  1237.   + DS(I1;J7;-J8;I2;Sym;J7;-J8,TAP,(DIE(I1,I2,"N,J7,-J7,J8,-J8) ))
  1238.  
  1239. Id,Anti,TAP
  1240.  
  1241. Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)=
  1242.    VE3(I1,K1,K3,*,MU,P0,*,L1,-P,*,L3,P)*
  1243.    VE3(K2,I2,K4,*,L2,P,*,NU,-P0,*,L4,-P)*
  1244.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1245.    PROP(K3,K4,*,L3,P,*,L4,P)
  1246.    *D(MU,NU)/N
  1247.   *CONT(I1,K1,K3,/,"K)*CONT(K2,I2,K4,/,"K)
  1248. Id,DIC(I1~,K1~,K2~,I2~)=
  1249.    VE4(I1,K1,K2,I2,*,MU,*,L1,*,L2,*,NU)*
  1250.    PROP(K1,K2,*,L1,P,*,L2,P)
  1251.     *D(MU,NU)/N
  1252.    *CONT(I1,K1,K2,I2,/,"K)
  1253. Al,DID(I1~,I2~,I3~,K1~,K2~,K3~,K4~,K5~,K6~)=
  1254.    VE3(I1,K1,K2,*,MU,P0,*,L1,P,*,L2,-P)*
  1255.    VE3(I3,K3,K4,*,AL,K,*,L3,P,*,L4,-P)*
  1256.    VE3(I2,K5,K6,*,NU,-P0,*,L5,P,*,L6,-P)*
  1257.    PROP(K6,K1,*,L6,P,*,L1,P)*
  1258.    PROP(K2,K3,*,L2,P,*,L3,P)*
  1259.    PROP(K4,K5,*,L4,P,*,L5,P)
  1260.    *D(MU,NU)/N   /EP
  1261. Al,DIE(I1~,I2~,I3~,K1~,K2~,K3~,K4~)=
  1262.    VE4(I1,K1,K4,I2,*,MU,*,L1,*,L4,*,NU)*
  1263.    VE3(I3,K2,K3,*,AL,K,*,L2,P,*,L3,-P)*
  1264.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1265.    PROP(K3,K4,*,L3,P,*,L4,P)
  1266.    *D(MU,NU)/N   /EP
  1267. ENDBLOCK
  1268. Z SWA=SELF("W,"A)
  1269. SELF{}
  1270. WORK{SWA}
  1271. *next
  1272. Z SPM=SELF("U,"U_)
  1273. SELF{}
  1274. WORK{SPM}
  1275. *next
  1276. P input
  1277. Z SWW=SELF("W,"W)
  1278. SELF{}
  1279. WORK{SWW}
  1280. *next
  1281. P input
  1282. Z SAA=SELF("A,"A)
  1283. SELF{}
  1284. WORK{SAA}
  1285. *next
  1286. S EP,TIPI2,N,PM,M,M0,SM,C,S
  1287. F LG
  1288. B EP,I,PI2,TIPI2
  1289. Z SAA=SAA
  1290. Z SWA=SWA-4*M**2*S/C*E1F*TIPI2/EP**2
  1291. Z SWW=SWW-M**2*TIPI2/EP**2*(-E1F/C**4+43/12*ET/C**2
  1292.        -55/6*E1F/C**2-E1F**2/C**2/TIPI2+8*E1F)
  1293. Z SPM=SPM-M**2*TIPI2/EP**2*(-E1F/C**2+43/12*ET
  1294.        -7/6*E1F-E1F**2/TIPI2)
  1295. E1EZF{~,~,,,}
  1296. Id,EP=0
  1297. Id,Count,1,SM,1
  1298. Id,Commu,LG
  1299. Id,C**-2*S**-2=1/S**2+1/C**2
  1300. Id,LG(M~,SM)=LG(M)-LG(SM)
  1301. Al,LG(M~,M0)=LG(M)-LG(M0)
  1302. Al,LG(M0~,M)=LG(M0)-LG(M)
  1303. Id,Commu,LG
  1304. *next
  1305. S EP,TIPI2,N,PM,M,M0,SM,C,S
  1306. B EP,I,PI2,TIPI2
  1307. F LG
  1308. Z RWPWM=WPWM-SPM
  1309. Z RW0W0=W0W0-SWW
  1310. Id,C**-2*S**-2=1/S**2+1/C**2
  1311. Id,LG(M)=LG(M,SM)+LG(SM)
  1312. Al,LG(M0)=LG(M0,SM)+LG(SM)
  1313. Id,Commu,LG
  1314. Id,LG(M~,SM)*LG(SM)=LG(SM)*LG(M,SM)
  1315. *next
  1316. S EP,TIPI2,N,PM,M,M0,SM,C,S
  1317. B M,SM,C,S
  1318. F LG
  1319. Z RO=-(WPWM-C**2*W0W0-SPM+C**2*SWW)/TIPI2**2/PI**4/64/M**2
  1320. Id,Multi,TIPI2**-1=0.5/PI**2/I
  1321. Id,Commu,LG
  1322. Id,C**-2*S**-2=1/S**2+1/C**2
  1323. Id,LG(M)=LG(M,SM)+LG(SM)
  1324. Al,LG(M0)=LG(M0,SM)+LG(SM)
  1325. Id,Commu,LG
  1326. Id,LG(M~,SM)*LG(SM)=LG(SM)*LG(M,SM)
  1327. *yep
  1328. Id,C**-2=1+S**2/C**2
  1329. *begin
  1330. Write common
  1331. *end
  1332.  
  1333. C RO-parameter 7. Two-loop self-energy diagrams. A-A wave-function.
  1334.  
  1335. Oldnew i=I
  1336. P ninput
  1337. Read Roblocks.e
  1338. Common AAWF
  1339. VERT{,,,~,~}
  1340. C P input
  1341. X NUM(K1,K2)=1.-0.5*DK(K1,K2)
  1342. X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3)
  1343.      +2/3*DK(K1,K2)*DK(K1,K3)
  1344. X KUM(K1)=1-DK(4,K1)
  1345. X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5)
  1346. S PM=1,EI=2,NP1,TRN
  1347. V QL,PX,QX
  1348. *fix
  1349. Z AAWF=0
  1350. Nprint AAWF
  1351. *next
  1352. BLOCK WORK{AAWFA}
  1353. C P ninput
  1354. PROJ{,,~,}
  1355. F21F51{}
  1356. Id,Count,1,SM,1
  1357. *yep
  1358. Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4
  1359. F1t5{}
  1360. Id,EP=0
  1361. *yep
  1362. NEXP{}
  1363. Id,EP=0
  1364. B EP,I,PI2,TIPI2,LE2
  1365. Id,Count,1,SM,1
  1366. Id,LG(SM,M~)=LG(SM)-LG(M)
  1367. Al,LG(M0,M~)=LG(M0)-LG(M)
  1368. Al,LG(M,M0~)=LG(M)-LG(M0)
  1369. Id,Multi,M0**2=M**2/C**2
  1370. Al,PI**4=-0.25*TIPI2**2
  1371. Id,Commu,LG
  1372. Keep 'AAWFA'
  1373. *next
  1374. Z AAWF=AAWF+'AAWFA'
  1375. Nprint AAWF
  1376. B EP,I,PI2,TIPI2,LE2
  1377. ENDBLOCK
  1378. BLOCK TOPO{}
  1379. Id,TOPA(I1~,I2~)=
  1380.    DS(I1;J1;J2;Sym;J1;J2;TAP,(
  1381.      DS(-J1;J5;"Z;TAP,(
  1382.        DS(-J5;I2;-J4;TAP,(
  1383.    DIA(I1,I2,J1,-J1,J5,-J5,"Z,"Z,J2,-J2,J4,-J4) )) )) ))
  1384. Id,Anti,TAP
  1385.  
  1386. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  1387.    VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)*
  1388.    VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)*
  1389.    VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)*
  1390.    VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)*
  1391.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1392.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1393.    PROP(K5,K6,*,L5,K,*,L6,K)*
  1394.    PROP(K7,K8,*,L7,PL,*,L8,PL)*
  1395.    PROP(K9,K0,*,L9,QL,*,L0,QL)*XX
  1396. Id,Compo,<X>,VE4,VE3,PROP
  1397. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1398. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1399.        AA(MU,P0,L2,Q,L1,P)
  1400. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1401. Id,Commu,NOM
  1402. Id,PDLE=PDLE*E
  1403. Al,QDLE=QDLE*E
  1404. Al,KDLE=KDLE*E
  1405. Al,PLDLE=PLDLE*E
  1406. Al,QLDLE=QLDLE*E
  1407. Al,LEDLE=E**2*LEDLE
  1408. Al,LE(MU~)=LE(MU)*E
  1409. Id,PLDPL=PXDPX+2*PXDLE*E*(1-X)+LEDLE*E**2/3
  1410. Al,Dotpr,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E
  1411. Al,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E
  1412. Id,QLDQL=QXDQX-2*QXDLE*E*(1-X)+LEDLE*E**2/3
  1413. Al,Dotpr,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E
  1414. Al,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E
  1415. Id,PDP=PXDPX-2*X*PXDLE*E+LEDLE*E**2/3
  1416. Al,Dotpr,P(MU~)=PX(MU)-X*LE(MU)*E
  1417. Al,P(MU~)=PX(MU)-X*LE(MU)*E
  1418. Id,QDQ=QXDQX+2*X*QXDLE*E+LEDLE*E**2/3
  1419. Al,Dotpr,Q(MU~)=QX(MU)+X*LE(MU)*E
  1420. Al,Q(MU~)=QX(MU)+X*LE(MU)*E
  1421. Id,PXDPX=PDP
  1422. Al,Dotpr,PX(MU~)=P(MU)
  1423. Al,PX(MU~)=P(MU)
  1424. Id,QXDQX=QDQ
  1425. Al,Dotpr,QX(MU~)=Q(MU)
  1426. Al,QX(MU~)=Q(MU)
  1427. *yep
  1428. Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-1/3*LEDLE*FP(3,M)*E**2
  1429. Id,Adiso,NOM(Q,M~)*NOM(QL,M~)=FQ(2,M)-4*QDLE*(X-Y)*FQ(3,M)*E
  1430.    -2/3*LEDLE*FQ(3,M)*E**2+2*QDLE**2*FQ(4,M)*E**2
  1431. Al,NOM(K,M~)=FK(1,M)
  1432. Id,E**1=0
  1433. Al,X**N~=1/(N+1)
  1434. Al,Y**N~=1/(N+1)
  1435. Al,XX*E**2=1
  1436. Al,XX=0
  1437. ENDBLOCK
  1438. Z AAWFA=TOPA("A,"A)
  1439. TOPO{}
  1440. WORK{AAWFA}
  1441. *next
  1442. BDELETE TOPO
  1443. BLOCK TOPO{}
  1444. Id,TOPB(I1~,I2~)=
  1445.    DS(I1;-J1;-J2;TAP,(
  1446.      DS(J2;"Z;-J4;TAP,( DC("P,TAP,-1,"Z,J4)*
  1447.        DS(J1;I2;J5,TAP,(
  1448.    DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,"Z,"Z,J4,-J4) ))) )))
  1449.  
  1450. Id,Anti,TAP
  1451.  
  1452. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  1453.    VE3(I1,K1,K3,*,MU,-LE,*,L1,PL,*,L3,-P)*
  1454.    VE3(K2,I2,K6,*,L2,-PL,*,NU,LE,*,L6,P)*
  1455.    VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)*
  1456.    VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)*
  1457.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1458.    PROP(K3,K4,*,L3,P,*,L4,P)*
  1459.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1460.    PROP(K7,K8,*,L7,K,*,L8,K)*
  1461.    PROP(K9,K0,*,L9,Q,*,L0,Q)*XX
  1462. Id,Compo,<X>,VE4,VE3,PROP
  1463. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1464. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1465.        AA(MU,P0,L2,Q,L1,P)
  1466. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1467. Id,Commu,NOM
  1468. Id,PDLE=PDLE*E
  1469. Al,QDLE=QDLE*E
  1470. Al,KDLE=KDLE*E
  1471. Al,PLDLE=PLDLE*E
  1472. Al,QLDLE=QLDLE*E
  1473. Al,LEDLE=E**2*LEDLE
  1474. Al,LE(MU~)=LE(MU)*E
  1475. Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  1476. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1477. Al,PL(MU~)=P(MU)+LE(MU)*E
  1478. *yep
  1479. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  1480.    FP(3,M)-2*PDLE*FP(4,M)*E
  1481.    -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  1482. Al,NOM(Q,M~)=FQ(1,M)
  1483. Al,NOM(K,M~)=FK(1,M)
  1484. Id,E**1=0
  1485. Al,XX*E**2=1
  1486. Al,XX=0
  1487. ENDBLOCK
  1488. Z AAWFB=TOPB("A,"A)
  1489. TOPO{}
  1490. WORK{AAWFB}
  1491. *next
  1492. BDELETE TOPO
  1493. BLOCK TOPO{}
  1494. Id,TOPE(I1~,I2~)=
  1495.     DS(I1;-J1;-J2;TAP,(
  1496.       DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,(
  1497.      DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) ))
  1498.  
  1499. Id,Anti,TAP
  1500.  
  1501. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  1502.    VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)*
  1503.    VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)*
  1504.    VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)*
  1505.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1506.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1507.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1508.    PROP(K7,K8,*,L7,P,*,L8,P)*XX
  1509. Id,Compo,<X>,VE4,VE3,PROP
  1510. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1511. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1512.        AA(MU,P0,L2,Q,L1,P)
  1513. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1514. Id,Commu,NOM
  1515. Id,PDLE=PDLE*E
  1516. Al,QDLE=QDLE*E
  1517. Al,KDLE=KDLE*E
  1518. Al,PLDLE=PLDLE*E
  1519. Al,QLDLE=QLDLE*E
  1520. Al,LEDLE=E**2*LEDLE
  1521. Al,LE(MU~)=LE(MU)*E
  1522. Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  1523. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1524. Al,PL(MU~)=P(MU)+LE(MU)*E
  1525. *yep
  1526. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  1527.    FP(3,M)-2*PDLE*FP(4,M)*E
  1528.    -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  1529. Al,NOM(Q,M~)=FQ(1,M)
  1530. Id,E**1=0
  1531. Al,XX*E**2=1
  1532. Al,XX=0
  1533. ENDBLOCK
  1534. Z AAWFE=TOPE("A,"A)
  1535. TOPO{}
  1536. WORK{AAWFE}
  1537. *next
  1538. BDELETE TOPO
  1539. BLOCK TOPO{}
  1540. Id,TOPF(I1~,I2~)=
  1541.     DS(I1;-J1;-J2;TAP,(
  1542.       DS("Z;J2;J4;TAP,( DC("P,TAP,-1,"Z,J4)*
  1543.    DIA(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J4,-J4) )) ))
  1544.  
  1545. Id,Anti,TAP
  1546.  
  1547. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  1548.    VE3(I1,K1,K5,*,MU,-LE,*,L1,PL,*,L5,-P)*
  1549.    VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)*
  1550.    VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)*
  1551.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1552.    PROP(K3,K4,*,L3,K,*,L4,K)*
  1553.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1554.    PROP(K7,K8,*,L7,Q,*,L8,Q)*XX
  1555. Id,Compo,<X>,VE4,VE3,PROP
  1556. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1557. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1558.        AA(MU,P0,L2,Q,L1,P)
  1559. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1560. Id,Commu,NOM
  1561. Id,PDLE=PDLE*E
  1562. Al,QDLE=QDLE*E
  1563. Al,KDLE=KDLE*E
  1564. Al,PLDLE=PLDLE*E
  1565. Al,QLDLE=QLDLE*E
  1566. Al,LEDLE=E**2*LEDLE
  1567. Al,LE(MU~)=LE(MU)*E
  1568. Id,PLDPL=PDP+2*PDLE+LEDLE*E**2
  1569. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1570. Al,PL(MU~)=P(MU)+LE(MU)*E
  1571. *yep
  1572. Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*FP(3,M)*E
  1573.    -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M)
  1574. Al,NOM(Q,M~)=FQ(1,M)
  1575. Al,NOM(K,M~)=FK(1,M)
  1576. Id,E**1=0
  1577. Al,XX*E**2=1
  1578. Al,XX=0
  1579. ENDBLOCK
  1580. Z AAWFF=2*TOPF("A,"A)
  1581. TOPO{}
  1582. WORK{AAWFF}
  1583. *next
  1584. BDELETE TOPO
  1585. BLOCK TOPO{}
  1586. Id,TOPH(I1~,I2~)=
  1587.     DS(I1;-J1;-J2;"Z;Sym;-J1;-J2;"Z,TAP,(
  1588.     DIA(I1,I2,-J1,J1,-J2,J2,"Z,"Z) ))
  1589.  
  1590. Id,Anti,TAP
  1591.  
  1592. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)=
  1593.    VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)*
  1594.    VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)*
  1595.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1596.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1597.    PROP(K5,K6,*,L5,K,*,L6,K)*XX
  1598. Id,Compo,<X>,VE4,VE3,PROP
  1599. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1600. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1601.        AA(MU,P0,L2,Q,L1,P)
  1602. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1603. Id,Commu,NOM
  1604. *yep
  1605. Id,NOM(PL,M~)=FP(1,M)-2*PDLE*FP(2,M)*E
  1606.    -LEDLE*E**2*FP(2,M)+4*PDLE**2*E**2*FP(3,M)
  1607. Al,NOM(Q,M~)=FQ(1,M)
  1608. Al,NOM(K,M~)=FK(1,M)
  1609. Id,E**1=0
  1610. Al,XX*E**2=1
  1611. Al,XX=0
  1612. ENDBLOCK
  1613. Z AAWFH=TOPH("A,"A)
  1614. TOPO{}
  1615. WORK{AAWFH}
  1616. Print AAWF
  1617. *begin
  1618. Write aawcomm
  1619. *end
  1620.  
  1621. C RO-parameter 8. Two-loop self-energy diagrams. A-W wave-function.
  1622.  
  1623. Oldnew i=I
  1624. Common AWWF
  1625. P ninput
  1626. Read Roblocks.e
  1627. VERT{,,,~,~}
  1628. S EI=2,NP1,TRN
  1629. V QL,PX,QX
  1630. X KROM(K1,K2)=DK(K1,5)*DK(K2,7)+DK(K1,7)*DK(K2,5)
  1631. X NUM(K1,K2)=1.-0.5*DK(K1,K2)
  1632. X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3)
  1633.      +2/3*DK(K1,K2)*DK(K1,K3)
  1634. X KUM(K1)=1-DK(4,K1)
  1635. X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5)
  1636. *fix
  1637. Z AWWF=0
  1638. Nprint AWWF
  1639. *next
  1640. BLOCK WORK{AWWFA}
  1641. P ninput
  1642. PROJ{,,~,}
  1643. F21F51{}
  1644. Id,Count,1,SM,1
  1645. *yep
  1646. Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4
  1647. F1t5{}
  1648. Id,EP=0
  1649. *yep
  1650. NEXP{}
  1651. Id,EP=0
  1652. B EP,I,PI2,TIPI2,LE2
  1653. Id,Count,1,SM,1
  1654. Id,LG(SM,M~)=LG(SM)-LG(M)
  1655. Al,LG(M0,M~)=LG(M0)-LG(M)
  1656. Al,LG(M,M0~)=LG(M)-LG(M0)
  1657. Id,Multi,M0**2=M**2/C**2
  1658. Al,Multi,M0**-2=C**2/M**2
  1659. Al,Multi,PI**4=-0.25*TIPI2**2
  1660. Id,Commu,LG
  1661. Keep 'AWWFA'
  1662. *next
  1663. Z AWWF=AWWF+'AWWFA'
  1664. Nprint AWWF
  1665. B EP,I,PI2,TIPI2,LE2
  1666. ENDBLOCK
  1667. BLOCK TOPO{}
  1668. Id,TOPA(I1~,I2~)=
  1669.    DS(I1;J1;J2;Sym;J1;J2;TAP,(
  1670.      DS(-J1;J5;"Z;TAP,(
  1671.        DS(-J5;I2;-J4;TAP,(
  1672.    DIA(I1,I2,J1,-J1,J5,-J5,"Z,"Z,J2,-J2,J4,-J4) )) )) ))
  1673. Id,Anti,TAP
  1674.  
  1675. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  1676.    VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)*
  1677.    VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)*
  1678.    VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)*
  1679.    VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)*
  1680.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1681.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1682.    PROP(K5,K6,*,L5,K,*,L6,K)*
  1683.    PROP(K7,K8,*,L7,PL,*,L8,PL)*
  1684.    PROP(K9,K0,*,L9,QL,*,L0,QL)*XX
  1685. Id,Compo,<X>,VE4,VE3,PROP
  1686. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1687. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1688.        AA(MU,P0,L2,Q,L1,P)
  1689. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1690. Id,Commu,NOM
  1691. Id,PDLE=PDLE*E
  1692. Al,QDLE=QDLE*E
  1693. Al,KDLE=KDLE*E
  1694. Al,PLDLE=PLDLE*E
  1695. Al,QLDLE=QLDLE*E
  1696. Al,LEDLE=E**2*LEDLE
  1697. Al,LE(MU~)=LE(MU)*E
  1698. Id,PLDPL=PXDPX+2*PXDLE*E*(1-X)+LEDLE*E**2/3
  1699. Al,Dotpr,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E
  1700. Al,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E
  1701. Id,QLDQL=QXDQX-2*QXDLE*E*(1-X)+LEDLE*E**2/3
  1702. Al,Dotpr,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E
  1703. Al,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E
  1704. Id,PDP=PXDPX-2*X*PXDLE*E+LEDLE*E**2/3
  1705. Al,Dotpr,P(MU~)=PX(MU)-X*LE(MU)*E
  1706. Al,P(MU~)=PX(MU)-X*LE(MU)*E
  1707. Id,QDQ=QXDQX+2*X*QXDLE*E+LEDLE*E**2/3
  1708. Al,Dotpr,Q(MU~)=QX(MU)+X*LE(MU)*E
  1709. Al,Q(MU~)=QX(MU)+X*LE(MU)*E
  1710. Id,PXDPX=PDP
  1711. Al,Dotpr,PX(MU~)=P(MU)
  1712. Al,PX(MU~)=P(MU)
  1713. Id,QXDQX=QDQ
  1714. Al,Dotpr,QX(MU~)=Q(MU)
  1715. Al,QX(MU~)=Q(MU)
  1716. *yep
  1717. Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-1/3*LEDLE*FP(3,M)*E**2
  1718. Id,Adiso,NOM(Q,M~)*NOM(QL,M~)=FQ(2,M)-4*QDLE*(X-Y)*FQ(3,M)*E
  1719.    -2/3*LEDLE*FQ(3,M)*E**2+2*QDLE**2*FQ(4,M)*E**2
  1720. Al,NOM(K,M~)=FK(1,M)
  1721. Id,E**1=0
  1722. Al,X**N~=1/(N+1)
  1723. Al,Y**N~=1/(N+1)
  1724. Al,XX*E**2=1
  1725. Al,XX=0
  1726. ENDBLOCK
  1727. Z AWWFA=TOPA("A,"W)
  1728. TOPO{}
  1729. WORK{AWWFA}
  1730. *next
  1731. BDELETE TOPO
  1732. BLOCK TOPO{}
  1733. Id,TOPAP(I1~,I2~)=
  1734.    DS(I1;J1;J2;Sym;J1;J2;TAP,(
  1735.      DS(-J1;J3;"Z;TAP,(
  1736.        DS("Z;I2;-J4;TAP,(
  1737.    DIA(I1,I2,J1,-J1,"Z,"Z,J3,-J3,J2,-J2,J4,-J4) )) )) ))
  1738. Id,Anti,TAP
  1739.  
  1740. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  1741.    VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)*
  1742.    VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)*
  1743.    VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)*
  1744.    VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)*
  1745.    PROP(K1,K2,*,L1,P,*,L2,P)*
  1746.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1747.    PROP(K5,K6,*,L5,K,*,L6,K)*
  1748.    PROP(K7,K8,*,L7,PL,*,L8,PL)*
  1749.    PROP(K9,K0,*,L9,QL,*,L0,QL)*XX
  1750. Id,Compo,<X>,VE4,VE3,PROP
  1751. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1752. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1753.        AA(MU,P0,L2,Q,L1,P)
  1754. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1755. Id,Commu,NOM
  1756. Id,PDLE=PDLE*E
  1757. Al,QDLE=QDLE*E
  1758. Al,KDLE=KDLE*E
  1759. Al,PLDLE=PLDLE*E
  1760. Al,QLDLE=QLDLE*E
  1761. Al,LEDLE=E**2*LEDLE
  1762. Al,LE(MU~)=LE(MU)*E
  1763. Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  1764. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1765. Al,PL(MU~)=P(MU)+LE(MU)*E
  1766. Id,QLDQL=QDQ-2*QDLE*E+LEDLE*E**2
  1767. Al,Dotpr,QL(MU~)=Q(MU)-LE(MU)*E
  1768. Al,QL(MU~)=Q(MU)-LE(MU)*E
  1769. *yep
  1770. Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*E*FP(3,M)
  1771.    -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M)
  1772. Id,NOM(QL,M~)=FQ(1,M)+2*QDLE*E*FQ(2,M)-LEDLE*E**2*FQ(2,M)
  1773.    +4*QDLE**2*E**2*FQ(3,M)
  1774. Al,NOM(K,M~)=FK(1,M)
  1775. Al,NOM(Q,M~)=FQ(1,M)
  1776. Id,E**1=0
  1777. Al,XX*E**2=1
  1778. Al,XX=0
  1779. Id,Adiso,FQ(1,SM)*FQ(N~,M0)=DIFF**-N*FQ(1,SM)*(-1)**N
  1780.    *ATEL9
  1781. Id,DIFF**N~=SM**N*SM**N*(1-N*M0**2/SM**2)
  1782. Id,Count,1,SM,1,P,1,Q,1,K,1,ATEL9,2
  1783. Id,Numer,ATEL9,1.
  1784. ENDBLOCK
  1785. Z AWWFA=TOPAP("A,"W)
  1786. TOPO{}
  1787. WORK{AWWFA}
  1788. *next
  1789. BDELETE TOPO
  1790. BLOCK TOPO{}
  1791. Id,TOPB(I1~,I2~)=
  1792.    DS(I1;-J1;-J2;TAP,(
  1793.      DS(J2;"Z;-J4;TAP,( DC("P,TAP,-1,"Z,J4)*
  1794.        DS(J1;I2;J5,TAP,(
  1795.    DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,"Z,"Z,J4,-J4) ))) )))
  1796.  
  1797. Id,Anti,TAP
  1798.  
  1799. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)=
  1800.    VE3(I1,K1,K3,*,MU,-LE,*,L1,PL,*,L3,-P)*
  1801.    VE3(K2,I2,K6,*,L2,-PL,*,NU,LE,*,L6,P)*
  1802.    VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)*
  1803.    VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)*
  1804.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1805.    PROP(K3,K4,*,L3,P,*,L4,P)*
  1806.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1807.    PROP(K7,K8,*,L7,K,*,L8,K)*
  1808.    PROP(K9,K0,*,L9,Q,*,L0,Q)*XX
  1809. Id,Compo,<X>,VE4,VE3,PROP
  1810. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1811. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1812.        AA(MU,P0,L2,Q,L1,P)
  1813. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1814. Id,Commu,NOM
  1815. Id,PDLE=PDLE*E
  1816. Al,QDLE=QDLE*E
  1817. Al,KDLE=KDLE*E
  1818. Al,PLDLE=PLDLE*E
  1819. Al,QLDLE=QLDLE*E
  1820. Al,LEDLE=E**2*LEDLE
  1821. Al,LE(MU~)=LE(MU)*E
  1822. Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  1823. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1824. Al,PL(MU~)=P(MU)+LE(MU)*E
  1825. *yep
  1826. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  1827.    FP(3,M)-2*PDLE*FP(4,M)*E
  1828.    -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  1829. Al,NOM(Q,M~)=FQ(1,M)
  1830. Al,NOM(K,M~)=FK(1,M)
  1831. Id,E**1=0
  1832. Al,XX*E**2=1
  1833. Al,XX=0
  1834. ENDBLOCK
  1835. Z AWWFB=TOPB("A,"W)
  1836. TOPO{}
  1837. WORK{AWWFB}
  1838. *next
  1839. BDELETE TOPO
  1840. BLOCK TOPO{}
  1841. Id,TOPE(I1~,I2~)=
  1842.     DS(I1;-J1;-J2;TAP,(
  1843.       DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,(
  1844.      DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) ))
  1845.  
  1846. Id,Anti,TAP
  1847.  
  1848. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  1849.    VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)*
  1850.    VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)*
  1851.    VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)*
  1852.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1853.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1854.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1855.    PROP(K7,K8,*,L7,P,*,L8,P)*XX
  1856. Id,Compo,<X>,VE4,VE3,PROP
  1857. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1858. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1859.        AA(MU,P0,L2,Q,L1,P)
  1860. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1861. Id,Commu,NOM
  1862. Id,PDLE=PDLE*E
  1863. Al,QDLE=QDLE*E
  1864. Al,KDLE=KDLE*E
  1865. Al,PLDLE=PLDLE*E
  1866. Al,QLDLE=QLDLE*E
  1867. Al,LEDLE=E**2*LEDLE
  1868. Al,LE(MU~)=LE(MU)*E
  1869. Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  1870. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1871. Al,PL(MU~)=P(MU)+LE(MU)*E
  1872. *yep
  1873. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  1874.    FP(3,M)-2*PDLE*FP(4,M)*E
  1875.    -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  1876. Al,NOM(Q,M~)=FQ(1,M)
  1877. Id,E**1=0
  1878. Al,XX*E**2=1
  1879. Al,XX=0
  1880. ENDBLOCK
  1881. Z AWWFE=TOPE("A,"W)
  1882. TOPO{}
  1883. WORK{AWWFE}
  1884. *next
  1885. BDELETE TOPO
  1886. BLOCK TOPO{}
  1887. Id,TOPF(I1~,I2~)=
  1888.     DS(I1;-J1;-J2;TAP,(
  1889.       DS("Z;J2;J4;TAP,( DC("P,TAP,-1,"Z,J4)*
  1890.    DIA(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J4,-J4) )) ))
  1891.  
  1892. Id,Anti,TAP
  1893.  
  1894. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  1895.    VE3(I1,K1,K5,*,MU,-LE,*,L1,PL,*,L5,-P)*
  1896.    VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)*
  1897.    VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)*
  1898.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1899.    PROP(K3,K4,*,L3,K,*,L4,K)*
  1900.    PROP(K5,K6,*,L5,P,*,L6,P)*
  1901.    PROP(K7,K8,*,L7,Q,*,L8,Q)*XX
  1902. Id,Compo,<X>,VE4,VE3,PROP
  1903. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1904. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1905.        AA(MU,P0,L2,Q,L1,P)
  1906. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1907. Id,Commu,NOM
  1908. Id,PDLE=PDLE*E
  1909. Al,QDLE=QDLE*E
  1910. Al,KDLE=KDLE*E
  1911. Al,PLDLE=PLDLE*E
  1912. Al,QLDLE=QLDLE*E
  1913. Al,LEDLE=E**2*LEDLE
  1914. Al,LE(MU~)=LE(MU)*E
  1915. Id,PLDPL=PDP+2*PDLE+LEDLE*E**2
  1916. Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E
  1917. Al,PL(MU~)=P(MU)+LE(MU)*E
  1918. *yep
  1919. Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*FP(3,M)*E
  1920.    -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M)
  1921. Al,NOM(Q,M~)=FQ(1,M)
  1922. Al,NOM(K,M~)=FK(1,M)
  1923. Id,E**1=0
  1924. Al,XX*E**2=1
  1925. Al,XX=0
  1926. ENDBLOCK
  1927. Z AWWFF=TOPF("A,"W)+TOPF("W,"A)
  1928. TOPO{}
  1929. WORK{AWWFF}
  1930. *next
  1931. BDELETE TOPO
  1932. BLOCK TOPO{}
  1933. Id,TOPFP(I1~,I2~)=
  1934.     DS(I2;-J1;"Z;TAP,(
  1935.       DS(J1;I1;-J3;-J4;TAP,(
  1936.    DIA(I1,I2,-J1,J1,J3,-J3,"Z,"Z,J4,-J4) )) ))
  1937.  
  1938. Id,Anti,TAP
  1939.  
  1940. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  1941.    VE3(I2,K1,K5,*,NU,-LE,*,L1,QL,*,L5,-Q)*
  1942.    VE4(K2,I1,K4,K8,*,L2,*,MU,*,L4,*,L8)*
  1943.    VE3(K3,K6,K7,*,L3,-K,*,L6,Q,*,L7,P)*
  1944.    PROP(K1,K2,*,L1,QL,*,L2,QL)*
  1945.    PROP(K3,K4,*,L3,K,*,L4,K)*
  1946.    PROP(K5,K6,*,L5,Q,*,L6,Q)*
  1947.    PROP(K7,K8,*,L7,P,*,L8,P)*XX
  1948. Id,Compo,<X>,VE4,VE3,PROP
  1949. Id,VE4(AA~,L1~,L2~,L4~)=AA(L1,L2,L3,L4)
  1950. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  1951.        AA(MU,P0,L2,Q,L1,P)
  1952. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  1953. Id,Commu,NOM
  1954. Id,PDLE=PDLE*E
  1955. Al,QDLE=QDLE*E
  1956. Al,KDLE=KDLE*E
  1957. Al,PLDLE=PLDLE*E
  1958. Al,QLDLE=QLDLE*E
  1959. Al,LEDLE=E**2*LEDLE
  1960. Al,LE(MU~)=LE(MU)*E
  1961. Id,QLDQL=QDQ+2*QDLE+LEDLE*E**2
  1962. Al,Dotpr,QL(MU~)=Q(MU)+LE(MU)*E
  1963. Al,QL(MU~)=Q(MU)+LE(MU)*E
  1964. *yep
  1965. Id,NOM(QL,M~)=FQ(1,M)-2*QDLE*E*FQ(2,M)
  1966.    -LEDLE*E**2*FQ(2,M)+4*QDLE**2*E**2*FQ(3,M)
  1967. Al,NOM(Q,M~)=FQ(1,M)
  1968. Al,NOM(P,M~)=FP(1,M)
  1969. Al,NOM(K,M~)=FK(1,M)
  1970. Id,E**1=0
  1971. Al,XX*E**2=1
  1972. Al,XX=0
  1973. Id,Adiso,FQ(1,SM)*FQ(N~,M0)=DIFF**-N*FQ(1,SM)*(-1)**N
  1974.    *ATEL9
  1975. Id,DIFF**N~=SM**N*SM**N*(1-N*M0**2/SM**2)
  1976. Id,Count,1,SM,1,P,1,Q,1,K,1,ATEL9,2
  1977. Id,Numer,ATEL9,1.
  1978. ENDBLOCK
  1979. Z AWWFF=TOPFP("A,"W)
  1980. TOPO{}
  1981. WORK{AWWFF}
  1982. *next
  1983. BDELETE TOPO
  1984. BLOCK TOPO{}
  1985. Id,TOPH(I1~,I2~)=
  1986.     DS(I1;-J1;-J2;"Z;Sym;-J1;-J2;"Z,TAP,(
  1987.     DIA(I1,I2,-J1,J1,-J2,J2,"Z,"Z) ))
  1988.  
  1989. Id,Anti,TAP
  1990.  
  1991. Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)=
  1992.    VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)*
  1993.    VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)*
  1994.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  1995.    PROP(K3,K4,*,L3,Q,*,L4,Q)*
  1996.    PROP(K5,K6,*,L5,K,*,L6,K)*XX
  1997. Id,Compo,<X>,VE4,VE3,PROP
  1998. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  1999. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  2000.        AA(MU,P0,L2,Q,L1,P)
  2001. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  2002. Id,Commu,NOM
  2003. *yep
  2004. Id,NOM(PL,M~)=FP(1,M)-2*PDLE*FP(2,M)*E
  2005.    -LEDLE*E**2*FP(2,M)+4*PDLE**2*E**2*FP(3,M)
  2006. Al,NOM(Q,M~)=FQ(1,M)
  2007. Al,NOM(K,M~)=FK(1,M)
  2008. Id,E**1=0
  2009. Al,XX*E**2=1
  2010. Al,XX=0
  2011. ENDBLOCK
  2012. Z AWWFH=TOPH("A,"W)
  2013. TOPO{}
  2014. WORK{AWWFH}
  2015. Print AWWF
  2016. *begin
  2017. Write awwcomm
  2018. *end
  2019.  
  2020. C RO-parameter 9. Subtractions for A-A and A-W wave-functions.
  2021.  
  2022. C SUBTRACTIONS, A-A AND A-W WAVEFUNCTIONS.
  2023. C ENTER RESULTS FROM TWO-LOOP CALCULATIONS, AAWF AND AWWF.
  2024. C DCDC CPU time 14.7 SEC.
  2025.  
  2026. Oldnew i=I
  2027. Enter aawcomm
  2028. Enter awwcomm
  2029. P ninput
  2030. Read Roblocks.e
  2031. VERT{,,~,~,~}
  2032. SVERT{,,~}
  2033. X NUM(K1,K2)=1-0.5*DK(K1,K2)
  2034. *fix
  2035. BLOCK WORK{}
  2036. B E1,EZF,ET,EP,I,PI2,TIPI2,LE2
  2037. Id,Compo,<X>,VE4,VE3,PROP
  2038. Id,Compo,<SS>,CONT
  2039. Id,Adiso,CONT(S~)*CONT(C~)=S/EP+C/EP
  2040. Al,CONT(S~)=S/EP
  2041. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  2042. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  2043.        AA(MU,P0,L2,Q,L1,P)
  2044. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  2045. Id,Commu,NOM
  2046. Id,ZERO**2=0
  2047. Id,PDLE=PDLE*E
  2048. Al,LEDLE=LEDLE*E**2
  2049. Al,PDPL=PDP+PDLE*E
  2050. Al,PLDLE=PDLE*E+LEDLE*E**2
  2051. Al,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  2052. Al,LE(MU~)=LE(MU)*E
  2053. Al,PL(MU~)=P(MU)+LE(MU)*E
  2054. *yep
  2055. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  2056.    FP(3,M)-2*PDLE*FP(4,M)*E
  2057.    -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  2058. Al,Adiso,NOM(P,M~)*NOM(PL,M~)=
  2059.    FP(2,M)-2*PDLE*FP(3,M)*E
  2060.    -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M)
  2061. Id,E**1=0
  2062. Al,XX*E**2=1
  2063. Al,XX=0
  2064. PROJ{,,~,~}
  2065. Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4
  2066. F1t5{}
  2067. *yep
  2068. CVERT{,~,~}
  2069. SCVERT{,~,~}
  2070. Id,ZERO=0.
  2071. Id,Count,1,SM,1,E1,2,E2,2,ET,2,EZF,2
  2072. Id,C2MS2=1-2*S**2
  2073. E1EZF{,,~,~,~}
  2074. Id,Count,1,SM,1,ET,2,E1F,2,EZF,2
  2075. Id,EP=0
  2076. *yep
  2077. E1EZF{~,~,,,}
  2078. Id,Count,1,SM,1
  2079. Id,EP=0
  2080. *yep
  2081. NEXP{}
  2082. Id,EP=0
  2083. B EP,I,PI2,TIPI2,LE2
  2084. Id,C**-2*S**-4=1/S**4+1/S**2+1/C**2
  2085. Al,C**-2*S**-2=1/S**2+1/C**2
  2086. Id,LG(SM,M~)=LG(SM)-LG(M)
  2087. Al,LG(M0,M~)=LG(M0)-LG(M)
  2088. Al,LG(M,M0~)=LG(M)-LG(M0)
  2089. Id,Multi,M0**2=M**2/C**2
  2090. Al,PI**4=-0.25*TIPI2**2
  2091. Al,PI**2=-0.5*TIPI2*I
  2092. Id,Commu,LG
  2093. Id,C**2=1-S**2
  2094. ENDBLOCK
  2095. BLOCK SELF{}
  2096. Id,SELF(I1~,I2~)=
  2097.     DS(I1;J1;J2;Sym;J1;J2,TAP,(
  2098.     DIB(I1,J1,-J1,J2,-J2,I2) ))
  2099.   + DS(I1;J4;-J5;TAP,(
  2100.       DS("N;J5;-J6;TAP,(
  2101.     DID(I1,I2,"N,J4,-J5,J5,-J6,J6,-J4) )) ))
  2102.  
  2103. Id,Anti,TAP
  2104.  
  2105. Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)=
  2106.    VE3(I1,K1,K3,*,MU,LE,*,L1,-PL,*,L3,P)*
  2107.    VE3(K2,I2,K4,*,L2,PL,*,NU,-LE,*,L4,-P)*
  2108.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  2109.    PROP(K3,K4,*,L3,P,*,L4,P)
  2110.    *XX
  2111.   *CONT(I1,K1,K3,/,"K)*CONT(K2,I2,K4,/,"K)
  2112. Al,DID(I1~,I2~,I3~,K1~,K2~,K3~,K4~,K5~,K6~)=
  2113.    VE3(I1,K1,K2,*,MU,-LE,*,L1,PL,*,L2,-P)*
  2114.    VE3(I3,K3,K4,*,AL,K,*,L3,P,*,L4,-P)*
  2115.    VE3(I2,K5,K6,*,NU,LE,*,L5,P,*,L6,-PL)*
  2116.    PROP(K6,K1,*,L6,PL,*,L1,PL)*
  2117.    PROP(K2,K3,*,L2,P,*,L3,P)*
  2118.    PROP(K4,K5,*,L4,P,*,L5,P)
  2119.    *XX  /EP
  2120. ENDBLOCK
  2121. P input
  2122. Z AAWFC=SELF("A,"A)
  2123. P ninput
  2124. SELF{}
  2125. WORK{}
  2126. Keep AAWFC
  2127. *next
  2128. P input
  2129. Z AWWFC=SELF("A,"W)
  2130. P ninput
  2131. SELF{}
  2132. WORK{}
  2133. Keep AAWFC,AWWFC
  2134. *next
  2135. P input
  2136. B EP,I,PI2,TIPI2,LE2
  2137. Z TAAWF=AAWF-AAWFC
  2138. Z TAWWF=AWWF-AWWFC
  2139. *end
  2140.  
  2141. C RO-parameter 10. Tadpoles in A-A wave-function.
  2142.  
  2143. C A-A TWO-LOOP WAVE-FUNCTION. TADPOLE INSERTIONS.
  2144. C THERE ARE MORE DIAGRAMS INVOLVING TADPOLES, NAMELY
  2145. C WITH ONE 4-VERTEX AND ONE 3-VERTEX WHERE ONE OF THE
  2146. C LINES OF THE 4-VERTEX CONNECTS TO A TADPOLE.
  2147. C THESE DIAGRAMS CANCEL OUT IF ONE SUBTRACTS THE COUNTERDIAGRAMS
  2148. C CONTAINING THE SAME TYPE OF DIAGRAMS, BUT THEY WERE COMPUTED
  2149. C TO SEE IF WITH THIS ADDITION THE TWO-LOOP DIAGRAMS WHERE
  2150. C GAUGE INVARIANT BY THEMSELVES, WHICH MUST BE.
  2151. C CDC CPU TIME 2.5 SEC.
  2152.  
  2153. Oldnew i=I
  2154. P ninput
  2155. Read Roblocks.e
  2156. C P input
  2157. VERT{,,~,,}
  2158. F FSC
  2159. S NP1,TRN
  2160. *fix
  2161. Z A0A0=0
  2162. Keep A0A0
  2163. Nprint A0A0
  2164. *next
  2165. P ninput
  2166. BLOCK WORK{A0A0A}
  2167. P ninput
  2168. Id,Compo,<X>,VE4,VE3,PROP
  2169. Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4)
  2170. Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=
  2171.        AA(MU,P0,L2,Q,L1,P)
  2172. Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q)
  2173. Id,Commu,NOM
  2174. Id,PDLE=PDLE*E
  2175. Al,LEDLE=E**2*LEDLE
  2176. Al,LE(MU~)=LE(MU)*E
  2177. Al,PDPL=PDP+PDLE*E
  2178. Al,PLDLE=PDLE*E+LEDLE*E**2
  2179. Al,PLDPL=PDP+2*PDLE*E+LEDLE*E**2
  2180. Al,PL(MU~)=P(MU)+LE(MU)*E
  2181. *yep
  2182. Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)=
  2183.   FP(3,M)-2*PDLE*FP(4,M)*E
  2184.   -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M)
  2185. Id,E**1=0
  2186. Al,XX*E**2=1
  2187. Al,XX=0
  2188. PROJ{,,~,~}
  2189. Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4
  2190. F1t5{}
  2191. Id,EP=0
  2192. *yep
  2193. NEXP{}
  2194. Id,EP=0
  2195. B EP,I,PI2,TIPI2,LE2,TADPO,TADGH
  2196. Id,Count,1,SM,1,ET,2
  2197. Id,LG(SM,M~)=LG(SM)-LG(M)
  2198. Al,LG(M0,M~)=LG(M0)-LG(M)
  2199. Al,LG(M,M0~)=LG(M)-LG(M0)
  2200. Id,Multi,M0**2=M**2/C**2
  2201. Al,PI**4=-0.25*TIPI2**2
  2202. Id,Commu,LG
  2203. Keep A0A0,'A0A0A'
  2204. *next
  2205. Z A0A0=A0A0+'A0A0A'
  2206. Nprint A0A0
  2207. Keep A0A0
  2208. B EP,I,PI2,TIPI2,LE2,TADPO,TADGH
  2209. ENDBLOCK
  2210. BLOCK TOPO{}
  2211. P ninput
  2212. Id,TOPE(I1~,I2~)=
  2213.     DS(I1;-J1;-J2;TAP,(
  2214.       DS(J1;I2;-J3;TAP,( DC("F,TFE,0,J1)*
  2215.      DIB(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J3,-J3) )) ))
  2216.  
  2217. Id,Anti,TAP
  2218.  
  2219. Id,DIB(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  2220.    VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)*
  2221.    VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)*
  2222.    VE3(K6,K7,"Z,*,L6,-P,*,L7,P,*,L9,P0)/SM**2*
  2223.    M*SM**2*ET/EP*(-1)*
  2224.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  2225.    PROP(K5,K6,*,L5,P,*,L6,P)*
  2226.    PROP(K7,K8,*,L7,P,*,L8,P)*XX*TADPO
  2227. ENDBLOCK
  2228. P input
  2229. Z A0A0E=TOPE("A,"A)
  2230. TOPO{}
  2231. WORK{A0A0E}
  2232. C PRINT OUTPUT
  2233. C PRINT A0A0
  2234. *yep
  2235. E1EZF{~,~,,~,~}
  2236. Id,EP=0
  2237. Id,Count,1,SM,1,ET,2
  2238. Id,PI**2=-0.5*I*TIPI2
  2239. *next
  2240. BLOCK TOPOP{}
  2241. P ninput
  2242. Id,TOPE(I1~,I2~)=
  2243.     DS(I1;-J1;-J2;TAP,(
  2244.       DS(J1;I2;-J3;TAP,( -DC("F_,TFE,0,J1)*
  2245.      DIB(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J3,-J3) )) ))
  2246.  
  2247. Id,Anti,TAP
  2248.  
  2249. Id,DIB(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)=
  2250.    VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)*
  2251.    VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)*
  2252.    VE3(K6,K7,"Z,*,L6,-P,*,L7,P,*,L9,P0)/SM**2*
  2253.    M*SM**2*ET/EP*(-1)*
  2254.    PROP(K1,K2,*,L1,PL,*,L2,PL)*
  2255.    PROP(K5,K6,*,L5,P,*,L6,P)*
  2256.    PROP(K7,K8,*,L7,P,*,L8,P)*XX*TADGH
  2257. ENDBLOCK
  2258. Z A0A0E=TOPE("A,"A)
  2259. TOPOP{}
  2260. WORK{A0A0E}
  2261. C PRINT OUTPUT
  2262. Print A0A0
  2263. *yep
  2264. E1EZF{~,~,,~,~}
  2265. Id,EP=0
  2266. Id,Count,1,SM,1,ET,2
  2267. Id,PI**2=-0.5*I*TIPI2
  2268. C PRINT OUTPUT
  2269. *yep
  2270. Id,TADGH=TADPO
  2271. *end
  2272.  
  2273. C RO-parameter 11. Diagrams with tadpole insertions.
  2274.  
  2275. C DIAGRAMS WITH ONE 4-VERTEX WITH TADPOLE AND ONE 3-VERTEX.
  2276. C A-A WAVE-FUNCTION.
  2277. C REST REFERS TO THE RESULT OF THE PREVIOUS PROGRAM,
  2278. C SELF-ENERGY DIAGRAMS WITH TADPOLE INSERTION,
  2279. C AND THE D(MU,NU) PART OF THE A-A WAVE-FUNCTION CALCULATION.
  2280. C CDC CPU time 1 SEC.
  2281.  
  2282. P ninput
  2283. Read Roblocks.e
  2284. C P input
  2285. Oldnew,i=I
  2286. I MU=N,NU=N
  2287. S M,SM,LE2
  2288. B EP,TIPI2
  2289. F LG,F
  2290. V LE
  2291. Z XX=4*0.5*S**2*M*LE2*(-EP/N*F(3,M)-4/N*M**2*F(4,M))
  2292.     *(-M*ET/EP)
  2293.    + REST
  2294. Id,N**-1=1/4-EP/16+EP**2/64
  2295. F1t5{}
  2296. E1EZF{~,~,,~,~}
  2297. Id,EP=0
  2298. Al,PI**2=-0.5*I*TIPI2
  2299. Id,Count,2,SM,1,REST,2
  2300. P output
  2301. *yep
  2302. Id,REST=TIPI2**2*SM**2/M**2*S**2*LE2*(
  2303.      (1/16 + 21/16)/EP -1/6 - 37/48
  2304.     +(1/16 + 5/8)*LG(M)
  2305.     +11/16*LG(SM) )
  2306. *end
  2307.  
  2308. C RO-parameter 12. Counter-term Lagrangian for the standard model.
  2309.  
  2310. C COUNTERLAGRANGIAN. TWO SCHOONSCHIP PROGRAMS, THE FIRST
  2311. C TO PRODUCE THE REGULAR ONE-LOOP COUNTERTERMS, THE SECOND
  2312. C TO PRODUCE THE QUADRATIC TERMS ARISING FROM THE ONE-LOOP
  2313. C COUNTERTERMS.
  2314. C CDC CPU time 10 SEC.
  2315.  
  2316. Common DELL
  2317. *fix
  2318. P brackets
  2319. S X,M,SM,AL,BET,C,S,E=3
  2320. S GG,AM,AN,AMN,AMM
  2321.     ,F3,F3M,FP,FMP,FM,FMM
  2322.     ,WMNP,WMMP,WMP,WNP
  2323.     ,WMNM,WMMM,WMM,WNM
  2324.     ,WMN0,WMM0,WM0,WN0,Z,ZM
  2325. B GG,AM,AN,AMN,AMM
  2326.     ,F3,F3M,FP,FMP,FM,FMM
  2327.     ,WMNP,WMMP,WMP,WNP
  2328.     ,WMNM,WMMM,WMM,WNM
  2329.     ,WMN0,WMM0,WM0,WN0,Z,ZM
  2330. Z DELL = (HAND + WMMP*WMMM - M*WMMP*FM - M*WMMM*FP
  2331.          + M**2*FM*FP + 0.5*WMM0**2 - M/C*WMM0*F3
  2332.          + 0.5*M**2/C**2*F3**2 + 0.5*AMM**2 )*X
  2333. Id  HAND =
  2334.       - WMNP*WMNM - M**2*WMP*WMM - 0.5*WMN0**2 - 0.5*M**2*C**-2
  2335.       *WM0**2 - 0.5*AMN**2 - FMP*FMM - M**2*FP*FM - 0.5*F3M**2
  2336.       - 0.5*M**2*C**-2*F3**2 - 0.5*ZM**2 - 0.5*SM**2*Z**2
  2337.    + GG*(-I*C*(WMN0*(WNP*WMM-WNM*WMP) - WM0*(WNP*WMNM-WNM*WMNP)
  2338.        + WN0*(WMP*WMNM-WMM*WMNP))
  2339.        - I*S*(AMN*(WNP*WMM-WNM*WMP) - AM*(WNP*WMNM-WNM*WMNP)
  2340.        + AN*(WMP*WMNM-WMM*WMNP))
  2341.      + GG*{-0.5*WMP*WMM*WNP*WNM + 0.5*WMP**2*WNM**2
  2342.        + C**2*WM0*(WMP*WN0*WNM-WM0*WNP*WNM)
  2343.        + S**2*AM*WNM*(WMP*AN-AM*WNP)
  2344.        + S*C*AM*(WN0*(WMP*WNM+WNP*WMM) - 2.*WM0*WNP*WNM)   } )
  2345.    + GG*(-AL*M*Z*(Z**2+F3**2+2.*FP*FM)
  2346.      + GG*{-0.125*AL*(Z**4+F3**4+4.*FP**2*FM**2+4.*F3**2*FP*FM
  2347.          + 4.*Z**2*FP*FM + 2.*F3**2*Z**2)   }
  2348.        - M*Z*WMP*WMM - 0.5*M*C**-2*Z*WM0**2
  2349.        - 0.5*I*(WMP*(F3*FMM-FM*F3M) - WMM*(F3*FMP-FP*F3M))
  2350.        + 0.5*(WMP*(Z*FMM-FM*ZM) + WMM*(Z*FMP-FP*ZM))
  2351.        + 0.5*C**-1*(WM0*(Z*F3M-F3*ZM))
  2352.        - I*S**2*C**-1*M*WM0*(WMP*FM-WMM*FP)
  2353.        + I*S*M*AM*(WMP*FM-WMM*FP)
  2354.        - I*(0.5*C**-1 - C)*WM0*(FP*FMM-FM*FMP)
  2355.        + I*S*AM*(FP*FMM-FM*FMP)
  2356.      + GG*{-0.25*WMP*WMM*(Z**2+F3**2+2.*FP*FM)
  2357.       - 0.125*C**-2*WM0**2*(Z**2+F3**2 + 2.*(2.*S**2-1.)**2*FP*FM)
  2358.       - S**2*AM**2*FP*FM
  2359.        - 0.5*S**2*C**-1*WM0*F3*(WMP*FM+WMM*FP)
  2360.        - 0.5*I*S**2/C*WM0*Z*(WMP*FM-WMM*FP)
  2361.        + 0.5*S*AM*F3*(WMP*FM+WMM*FP)
  2362.        + 0.5*I*S*AM*Z*(WMP*FM-WMM*FP)
  2363.        - S/C*(2.*C**2-1)*WM0*AM*FP*FM     } )
  2364. Id,WMNP=WMNP*(1+E*EC)
  2365. Al,WMMP=WMMP*(1+E*EC)
  2366. Al,WMNM=WMNM*(1+E*EC)
  2367. Al,WMMM=WMMM*(1+E*EC)
  2368. Al,WMP=WMP*(1+E*EC)
  2369. Al,WNP=WNP*(1+E*EC)
  2370. Al,WMM=WMM*(1+E*EC)
  2371. Al,WNM=WNM*(1+E*EC)
  2372. Al,WMN0=WMN0*(1+E*E0) + E*E0A*AMN
  2373. Al,WMM0=WMM0*(1+E*E0) + E*E0A*AMM
  2374. Al,WM0=WM0*(1+E*E0) + E*E0A*AM
  2375. Al,WN0=WN0*(1+E*E0) + E*E0A*AN
  2376. Al,AMN=AMN*(1+E*EA) + E*EA0*WMN0
  2377. Al,AMM=AMM*(1+E*EA) + E*EA0*WMM0
  2378. Al,AM=AM*(1+E*EA) + E*EA0*WM0
  2379. Al,AN=AN*(1+E*EA) + E*EA0*WN0
  2380. Id,FMP=FMP*(1+E*EFC)
  2381. Al,FP=FP*(1+E*EFC)
  2382. Al,FMM=FMM*(1+E*EFC)
  2383. Al,FM=FM*(1+E*EFC)
  2384. Al,F3M=F3M*(1+E*EF3)
  2385. Al,F3=F3*(1+E*EF3)
  2386. Al,ZM=ZM*(1+E*EZ)
  2387. Al,Z=Z*(1+E*EZ)+E*ETP
  2388. Id,EFC=EZ
  2389. Al,EF3=EZ
  2390. *yep
  2391. Id,GG=GG*(1+E*EG)
  2392. Al,AL=AL*(1+E*EAL)
  2393. Al,C=C*(1+E*ECO)
  2394. Al,Multi,C**-1=C**-1*(1-E*ECO)
  2395. Al,S=S*(1-E*ECO*C**2/S**2)
  2396. Al,Multi,S**-1=S**-1*(1+E*ECO*C**2/S**2)
  2397. Al,M=M*(1+E*EM)
  2398. Al,SM=SM*(1+E*ESM)
  2399. Nprint DELL
  2400. *next
  2401. B GG,AM,AN,AMN,AMM
  2402.     ,F3,F3M,FP,FMP,FM,FMM
  2403.     ,WMNP,WMMP,WMP,WNP
  2404.     ,WMNM,WMMM,WMM,WNM
  2405.     ,WMN0,WMM0,WM0,WN0,Z,ZM
  2406. Z DELP=DELL
  2407. Id,Multi,E**2=0
  2408. Id,X*E=1
  2409. Id,EAL=2*ESM-2*EM
  2410. Al,ETP=M*ET*GG**-1
  2411. Al,AL=0.25*SM**2/M**2
  2412. C E1=EM+0.5*ET, E2=EM-ESM
  2413. Id,EM=E1-0.5*ET
  2414. Al,ESM=E1-E2-0.5*ET
  2415. *yep
  2416. C PRINT OUTPUT
  2417. Id,Multi,S**2=1-C**2
  2418. Id  WMP**2*WNM**2=WNP**2*WMM**2
  2419. Id  WM0*WN0*WMM*WNP=WM0*WN0*WNM*WMP
  2420. Al  WM0*AN*WMM*WNP=WN0*AM*WNM*WMP
  2421. Al  WM0*AN*WMP*WNM=WN0*AM*WNP*WMM
  2422. Al  AM*AN*WMM*WNP=AM*AN*WNM*WMP
  2423. Al  WN0*AN*WMP*WMM=WM0*AM*WNP*WNM
  2424. Al  WN0**2*WMP*WMM=WM0**2*WNP*WNM
  2425. Al  AN**2*WMP*WMM=AM**2*WNP*WNM
  2426. Oldnew,G=GAM,WNM=VN,WMM=VM,WMMM=VMM,WMNM=VMN
  2427. Oldnew,WNP=UN,WMP=UM,WMMP=UMM,WMNP=UMN
  2428. Oldnew,FMM=HM,FM=H,FMP=GM,FP=G,F3=F,F3M=FM
  2429. B GG,AM,AN,AMN,AMM,F,FM,G,GM,H,HM,UMN,UMM
  2430.  ,UM,UN,VMN,VMM,VM,VN,WMN0,WMM0,WM0,WN0,Z,ZM
  2431. *yep
  2432. Id,EC=19/12
  2433. Al,E0=1/6+1.5*C**2-1/12/C**2
  2434. Al,E0A=-2*C*S
  2435. Al,EA=1.5*S**2
  2436. Al,EA0=5*S*C+S/C/6
  2437. Al,EZ=0.5+0.25/C**2+EZF
  2438. Al,EG=-43/12
  2439. Al,ECO=-S**2*(43-42*S**2)/12/C**2
  2440.  
  2441. C AL,E1=0.5/C**2-31/12+E1F
  2442. C AL,E2=-25/12+0.75/C**2-1.5*M**2/SM**2
  2443. C       -0.75*M**2/C**4/SM**2-0.75*SM**2/M**2
  2444. C       +E2F
  2445. C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2
  2446. C     +0.75*SM**2/M**2
  2447. C     +ETF
  2448. C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2
  2449. C     -3*SM**2/M**2/8
  2450. C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8
  2451.  
  2452. Al,AL=0.25*SM**2/M**2
  2453. Id,Multi,S**2=1-C**2
  2454. *begin
  2455. C COUNTER LAGRANGIAN, QUADRATIC TERMS.
  2456. Oldnew,GAM=G
  2457. Names DELL
  2458. S X,M,SM,AL,BET,C,S,E=3
  2459. S GG,AM,AN,AMN,AMM
  2460.     ,F3,F3M,FP,FMP,FM,FMM
  2461.     ,WMNP,WMMP,WMP,WNP
  2462.     ,WMNM,WMMM,WMM,WNM
  2463.     ,WMN0,WMM0,WM0,WN0,Z,ZM
  2464. B GG,AM,AN,AMN,AMM
  2465.     ,F3,F3M,FP,FMP,FM,FMM
  2466.     ,WMNP,WMMP,WMP,WNP
  2467.     ,WMNM,WMMM,WMM,WNM
  2468.     ,WMN0,WMM0,WM0,WN0,Z,ZM
  2469. Z DEPP=DELL
  2470. Id,X*E**2=1
  2471. Al,E**1=0
  2472. Id,EAL=2*ESM-2*EM
  2473. Al,ETP=M*ET*GG**-1
  2474. Al,AL=0.25*SM**2/M**2
  2475. C E1=EM+0.5*ET, E2=EM-ESM
  2476. Id,EM=E1-0.5*ET
  2477. Al,ESM=E1-E2-0.5*ET
  2478. *yep
  2479. C PRINT OUTPUT
  2480. Id,Multi,S**2=1-C**2
  2481. Id  WMP**2*WNM**2=WNP**2*WMM**2
  2482. Id  WM0*WN0*WMM*WNP=WM0*WN0*WNM*WMP
  2483. Al  WM0*AN*WMM*WNP=WN0*AM*WNM*WMP
  2484. Al  WM0*AN*WMP*WNM=WN0*AM*WNP*WMM
  2485. Al  AM*AN*WMM*WNP=AM*AN*WNM*WMP
  2486. Al  WN0*AN*WMP*WMM=WM0*AM*WNP*WNM
  2487. Al  WN0**2*WMP*WMM=WM0**2*WNP*WNM
  2488. Al  AN**2*WMP*WMM=AM**2*WNP*WNM
  2489. Oldnew,G=GAM,WNM=VN,WMM=VM,WMMM=VMM,WMNM=VMN
  2490. Oldnew,WNP=UN,WMP=UM,WMMP=UMM,WMNP=UMN
  2491. Oldnew,FMM=HM,FM=H,FMP=GM,FP=G,F3=F,F3M=FM
  2492. B GG,AM,AN,AMN,AMM,F,FM,G,GM,H,HM,UMN,UMM
  2493.  ,UM,UN,VMN,VMM,VM,VN,WMN0,WMM0,WM0,WN0,Z,ZM
  2494. Id,F=0
  2495. Al,FM=0
  2496. Al,Z=0
  2497. Al,ZM=0
  2498. Al,G=0
  2499. Al,GM=0
  2500. Al,H=0
  2501. Al,HM=0
  2502. Al,GG=0
  2503. Al,Multi,GG**-1=0
  2504. *yep
  2505. Id,EC=19/12
  2506. Al,E0=1/6+1.5*C**2-1/12/C**2
  2507. Al,E0A=-2*C*S
  2508. Al,EA=1.5*S**2
  2509. Al,EA0=5*S*C+S/C/6
  2510. Al,EZ=0.5+0.25/C**2+EZF
  2511. Al,EG=-43/12
  2512. Al,ECO=-S**2*(43-42*S**2)/12/C**2
  2513. Al,E1=0.5/C**2-31/12+E1F
  2514. Al,E2=-25/12+0.75/C**2-1.5*M**2/SM**2
  2515.       -0.75*M**2/C**4/SM**2-0.75*SM**2/M**2
  2516.       +E2F
  2517. C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2
  2518. C     +0.75*SM**2/M**2
  2519. C     +ETF
  2520. C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2
  2521. C     -3*SM**2/M**2/8
  2522. C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8
  2523. Al,AL=0.25*SM**2/M**2
  2524. C ID,COUNT,1,SM,1,E1F,2,E2F,2,EZF,2,ET,2,X,2
  2525. Id,Multi,S**2=1-C**2
  2526. *end
  2527.  
  2528. C RO-parameter 13. Counter terms for the Ghost Lagrangian, standard model.
  2529.  
  2530. C GHOST COUNTER-LAGRANGIAN.
  2531. C LAGRANGIAN WITH COUNTERTERMS GENERATED BY RENORMALIZED GAUGE
  2532. C TRANSFORMATIONS.
  2533. C INSTRUCTIONS FOR DIAGONILIZATION ARE GIVEN NEAR THE *END CARD.
  2534. C FERMIONS DO NOT CONTRIBUTE TO GHOST INFINITIES.
  2535. C A SECOND PROGRAM INDICATES AND CHECKS THE IDENTITIES
  2536. C RESULTING FROM THIS REQUIREMENT.
  2537.  
  2538. S XX,M,MP,LP,LPP,LNPP,LNP,LM,LMP,LNMP,LNM,L0,L0P,LN0P,LN0
  2539.   ,LA,LAP,LNA,LNAP
  2540. S  E=2
  2541. Oldnew,G=GAM,DF=DFREZ
  2542. B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN
  2543.   ,X,XN,Y,YN,Z
  2544. Z GHOST=XX*( XN*DUN + M*X*DG
  2545.           +ON*DVN+M*O*DH
  2546.           +QN*DWN+M*Q*DF/C
  2547.           +SN*DAN)
  2548. Id,DUN=(1-E*EC)*(I*BP*LPP*(CP*WNP+SP*ANP)
  2549.         -I*BP*(CP*L0P+SP*LAP)*UNP-LNPP)
  2550. Al,DVN=(1-E*EC)*(-I*BP*LMP*(CP*WNP+SP*ANP)
  2551.         +I*BP*(CP*L0P+SP*LAP)*VNP-LNMP)
  2552. Al,DWN=(1-E*E0)*(-I*BP*CP*LPP*VNP
  2553.                  +I*BP*CP*LMP*UNP-LN0P)
  2554.         - E*E0A*(-I*GG*S*LP*VN+I*GG*S*LM*UN-LNA)
  2555. Al,DAN=(1-E*EA)*(-I*BP*SP*LPP*VNP
  2556.                  +I*BP*SP*LMP*UNP-LNAP)
  2557.         - E*EA0*(-I*GG*C*LP*VN+I*GG*C*LM*UN-LN0)
  2558. Al,DG=(1-E*EZ)*(0.5*I*BP*LPP*FP
  2559.                 -0.5*I*BP*((2*CP**2-1)*L0P/CP+2*SP*LAP)*GP
  2560.                 -0.5*BP*ZP*LPP-MP*LPP)
  2561. Al,DH=(1-E*EZ)*(-0.5*I*BP*LMP*FP
  2562.                 +0.5*BP*I*((2*CP**2-1)*L0P/CP+2*SP*LAP)*HP
  2563.                 -0.5*BP*ZP*LMP-MP*LMP)
  2564. Al,DF=(1-E*EZ)*(-0.5*I*BP*(LPP*HP-LMP*GP)
  2565.                 -0.5*BP*L0P*ZP/CP-MP*L0P/CP)
  2566. Al,DZ=(1-E*EZ)*(0.5*BP*(LPP*HP*LMP*GP)+0.5*BP*FP*L0P/CP)
  2567. Id,BP=GG*(1+E*EG)
  2568. Al,MP=M*(1+E*EM)
  2569. Al,LPP=LP*(1+E*ELC)
  2570. Al,LMP=LM*(1+E*ELC)
  2571. Al,CP=C*(1+E*ECO)
  2572. Al,Multi,CP**-1=(1-E*ECO)/C
  2573. Al,SP=S*(1-E*ECO*C**2/S**2)
  2574. Al,WNP=(1+E*E0)*WN+E*E0A*AN
  2575. Al,ANP=(1+E*EA)*AN+E*EA0*WN
  2576. Al,L0P=(1+E*EL0)*L0+E*EL0A*LA
  2577. Al,LAP=(1+E*ELA)*LA+E*ELA0*L0
  2578. Al,LN0P=(1+E*EL0)*LN0+E*EL0A*LNA
  2579. Al,LNAP=(1+E*ELA)*LNA+E*ELA0*LN0
  2580. Al,LNPP=(1+E*ELC)*LNP
  2581. Al,LNMP=(1+E*ELC)*LNM
  2582. Id,ZP=(1+E*EZ)*Z+E*M*ET/GG
  2583. Al,GP=(1+E*EZ)*G
  2584. Al,HP=(1+E*EZ)*H
  2585. Al,FP=(1+E*EZ)*F
  2586. Al,UNP=(1+E*EC)*UN
  2587. Al,VNP=(1+E*EC)*VN
  2588. Id,XX*E=1
  2589. Id,L0=R
  2590. Al,LN0=RN
  2591. Al,LA=T
  2592. Al,LNA=TN
  2593. Al,LP=Y
  2594. Al,LNP=YN
  2595. Al,LM=P
  2596. Al,LNM=PN
  2597. Id,EM=E1-0.5*ET
  2598. Al,ESM=E1-E2-0.5*ET
  2599. Id,Multi,S**2=1-C**2
  2600. Keep GHOST
  2601. *next
  2602. B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN
  2603.   ,X,XN,Y,YN,Z
  2604. Z GHO=GHOST
  2605. Id,EC=19/12
  2606. Al,E0=1/6+1.5*C**2-1/12/C**2
  2607. Al,E0A=-2*C*S
  2608. Al,EA=1.5*S**2
  2609. Al,EA0=5*S*C+S/C/6
  2610. Al,EZ=0.5+0.25/C**2+EZF
  2611. Al,ELC=31/12
  2612. Al,EL0=1/6+5*C**2/2-1/12/C**2
  2613. Al,ELA=2.5*S**2
  2614. Al,EL0A=-C*S
  2615. Al,ELA0=6*S*C+S/C/6
  2616. Al,EG=-43/12
  2617. Al,ECO=-S**2*(43-42*S**2)/12/C**2
  2618. C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2
  2619. C     +0.75*SM**2/M**2
  2620. C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2
  2621. C     -3*SM**2/M**2/8
  2622. C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8
  2623. Id,Multi,S**2=1-C**2
  2624. C PRINT OUTPUT
  2625. C *YEP
  2626. C PRINT INPUT
  2627. C C THE FOLLOWING DIAGOLINIZES THE QUADRATIC PART.
  2628. C ID,R=(1-S**2*EP)*R+C*S*T*EP
  2629. C AL,RN=(1-S**2*EP)*RN+C*S*TN*EP
  2630. C AL,T=-C*S*R*EP+(1-S**2*EP)*T
  2631. C AL,TN=-C*S*EP*RN+(1-S**2*EP)*TN
  2632. C AL,SN=SN+EP*SN-2*C*S*EP*QN
  2633. C AL,Q=Q+2*S**2*EP*Q
  2634. C AL,QN=QN+2*S**2*EP*QN
  2635. C ID,XX*EP=1
  2636. C ID,EP=0
  2637. C ID,MULTI,S**2=1-C**2
  2638. C PRINT OUTPUT
  2639. C *YEP
  2640. C C THE FOLLOWING REMOVES THE DIVERGENCIES OF THE QUADRATIC PART
  2641. C C BUT NOT OF THE MASS TERMS.
  2642. C ID,Q=Q*(1-EP)
  2643. C AL,QN=QN*(1-EP)
  2644. C AL,O=O*(1-EP)
  2645. C AL,ON=ON*(1-EP)
  2646. C AL,SN=SN*(1-EP)
  2647. C AL,X=X*(1-EP)
  2648. C AL,XN=XN*(1-EP)
  2649. C ID,XX*EP=1
  2650. C ID,EP=0
  2651. C ID,MULTI,S**2=1-C**2
  2652. Keep GHOST
  2653. *next
  2654. B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN
  2655.   ,X,XN,Y,YN,Z
  2656. Z GHO=GHOST
  2657. Id,XX=0
  2658. *yep
  2659. C REQUIRING NO INFINITIES IN QUADRATIC PART.
  2660. Id,ELC=EC
  2661. Al,ELA=EA
  2662. Al,ELA0=EA0
  2663. Al,EL0A=E0A
  2664. Al,EL0=E0
  2665. P output
  2666. *yep
  2667. C REQUIRING NO INFINITIES IN VERTICES.
  2668. Id,EG=-EC
  2669. Al,E0A=0
  2670. Al,ECO=E0-EC
  2671. Al,E1=-EC+EZ
  2672. Al,EA0=2*C*EC/S-2*C*E0/S
  2673. Al,EA=-C**2*EC/S**2+C**2*E0/S**2+EC
  2674. *end
  2675.  
  2676. C RO-parameter 14. Rationalization.
  2677.  
  2678. C RATIONALIZATION.
  2679. P ninput
  2680. S EI=2,N,M,M0,SM
  2681. V P,Q,K
  2682. B A1,A2,A3,A4,B1,B2,B3,B4,B5
  2683. Z  XX= (A1*PDP + A2*PDP**2 + A3*PDP**3)
  2684.       *(B1*FP(1,M) + B2*FP(2,M) + B3*FP(3,M) + B4*FP(4,M) )
  2685.       *(1+T)
  2686. Id,T*PDP**K1~*FP(L1~,M~)=T*(-1)**K1*M**K1*M**K1*
  2687.   DS(IX,0,K1+(L1-1-K1)*DT(K1-L1+1),(M**-IX*M**-IX*FP(L1-IX,M)),
  2688.           (-(K1-IX+1)/IX) )
  2689.    +T*EI*(-1)**K1*(-1)**L1*M**K1*M**K1/M**L1/M**L1*
  2690.    DT(K1-L1)*DB(K1-1,K1-L1)* DS(IX2,0,K1-L1,
  2691.      (PDP**IX2/M**IX2/M**IX2),(-(K1-L1-IX2+1)/(K1-IX2)) )
  2692. Id,T*PDP**2=T*QDQ**2+T*KDK**2+T*2*QDQ*KDK+T*4/N*QDQ*KDK
  2693. Al,T*PDP=T*QDQ+T*KDK
  2694. Id,PDP**3*FP(1,M~)=EI*QDQ**2+EI*KDK**2+2*EI*QDQ*KDK+4/N*EI*QDQ*KDK
  2695.    -M**2*EI*QDQ-M**2*EI*KDK+EI*M**4-M**6*FP(1,M)
  2696. Al,PDP**3*FP(2,M~)=EI*KDK+EI*QDQ-2*EI*M**2
  2697.     +3*M**4*FP(1,M)-M**6*FP(2,M)
  2698. Id,2,PDP**2*FP(1,M~)=EI*QDQ+EI*KDK-EI*M**2+M**4*FP(1,M)
  2699. Id,3,PDP**N~*FP(4,M~)=PDP**N/PDP*FP(3,M)
  2700.     -PDP**N/PDP*M**2*FP(4,M)
  2701. Id,3,PDP**N~*FP(3,M~)=PDP**N/PDP*FP(2,M)
  2702.    -PDP**N/PDP*M**2*FP(3,M)
  2703. Id,PDP**2*FP(2,M~)=EI-2*M**2*FP(1,M)+M**4*FP(2,M)
  2704. Al,PDP*FP(2,M~)=FP(1,M)-M**2*FP(2,M)
  2705. Al,PDP*FP(1,M~)=EI-M**2*FP(1,M)
  2706. Id,FP(N~,M~)=AFP**N
  2707. P output
  2708. *yep
  2709. Id,T=-1
  2710. C Id,NUMER,T,-1.
  2711. *begin
  2712. C
  2713. C RATIONALIZATION.
  2714. C XA=X+A, XB=X+B, BA=B-A.
  2715. C EXPONENT OF XB POSITIVE, EXPONENT OF XA NEGATIVE.
  2716. C
  2717. Z XX=A1*XB**3*XA**-5 + A2*XB**3*XA**-4
  2718.    + A3*XB**3*XA**-1 + A4*XB**4*XA**-2
  2719.    + A5*XB**7*XA**-10 + A6*XB**10*XA**-5
  2720.    - A1*XBP**3*XAP**-5 - A2*XBP**3*XAP**-4
  2721.    - A3*XBP**3*XAP**-1 - A4*XBP**4*XAP**-2
  2722.    - A5*XBP**7*XAP**-10 - A6*XBP**10*XAP**-5
  2723. B A1,A2,A3,A4,A5,A6
  2724. Id,XB**M~*XA**N~=BA**M*XA**N*DS(M0,0,-1-N,(BA**-M0*XA**M0),
  2725.                                  ((M-M0+1)/M0) )
  2726.    + BA**M*BA**N*EI*DT(M+N)*DB(M-1,M+N)*DS(M1,0,M+N,
  2727.                     (XB**M1*BA**-M1),((M+N-M1+1)/(M-M1)) )
  2728. Id,XBP=XAP+BAP
  2729. *yep
  2730. Id,XAP=XBP-BAP
  2731. C ID,RATIO,XAP,XBP,BAP
  2732. P output
  2733. *yep
  2734. Id,XBP=XB
  2735. Al,BAP=BA
  2736. Al,Multi,XAP**-1=XA**-1
  2737. Id,EI=1
  2738. C Id,NUMER,EI,1.
  2739. *end
  2740.  
  2741. C RO-parameter 15. Epsilon expansion and projection operators.
  2742.  
  2743. S N,TRN,NP1,EP=3
  2744. Z TR1M1=2*N-N**2-N**3
  2745. Z X1=N**2*(N+1)*TRN
  2746. Z X2=N*(N+1)*TRN
  2747. Z X3=(N+1)*TRN
  2748. Z X4=N**3*TRN
  2749. Z X5=N**2*TRN
  2750. Z X6=N*TRN
  2751. Z X7=TRN
  2752. Z X8=1/N
  2753. Z X9=1/N**2
  2754. Z X0=N/OMN
  2755. Id,TRN=-1/72*(1.-R+R**2)
  2756. Id,N=4+EP
  2757. Al,R=54/72*EP+13/72*EP**2
  2758. Al,Multi,N**-1=(1-EP/4+EP**2/16)/4
  2759. Al,OMN**-1=-1/3*(1-EP/3+EP**2/9)
  2760. *next
  2761. C PROJECTION OPERATORS AND EP-EXPANSION.
  2762. S N,TRN,NP1,EP=3
  2763. I MU=N,NU=N,AL=N,BE=N,MUP=N,NUP=N
  2764. Z XX=(EE*D(MU,NU)*D(AL,BE)+FF*D(MU,AL)*D(NU,BE)
  2765.         +GG*D(MU,BE)*D(NU,AL) ) *FACT
  2766. Z YY=A1*AN/N + A2*AN**2/N**2 +A3*AOMN*N/OMN
  2767. C PROJECTION OPERATOR FOR EE AND FF+GG PARTS.
  2768. Id,FACT=TRN*(2*D(MU,NU)*D(AL,BE)-N*D(MU,AL)*D(NU,BE)
  2769.              -N*D(MU,BE)*D(NU,AL))*FGPRT
  2770.        +TRN*(-NP1*D(MU,NU)*D(AL,BE)+D(MU,AL)*D(NU,BE)
  2771.              +D(MU,BE)*D(NU,AL) )*EPART
  2772. Id,N**2*NP1*TRN =  - 10./9. + 1./18.*EP - 7./324.*EP**2
  2773. Al,N*NP1*TRN =  - 5./18. + 1./12.*EP - 17./648.*EP**2
  2774. Al,NP1*TRN =  - 5./72. + 11./288.*EP - 167./10368.*EP**2
  2775. Al,N**3*TRN =  - 8./9. - 1./162.*EP**2
  2776. Al,N**2*TRN =  - 2./9. + 1./18.*EP - 5./324.*EP**2
  2777. Al,N*TRN =  - 1./18. + 1./36.*EP - 7./648.*EP**2
  2778. Al,TRN =  - 1./72. + 1./96.*EP - 55./10368.*EP**2
  2779. Al,N*OMN** - 1 =  - 4/3 + EP/9 - EP**2/27
  2780. Al,N = 4 + EP
  2781. Al,N**-2 = 1/16 - EP/32 + 3*EP**2/256
  2782. Al,N**-1 = 1/4 - EP/16 + EP**2/64
  2783. Id,AN=4+EP
  2784. Al,AOMN=(-3-EP)*(1/4-EP/16+EP**2/64)
  2785. *end
  2786.  
  2787. C RO-parameter 16. Differentiating F111.
  2788.  
  2789. P stat
  2790. F LG
  2791. S SM,M,M0
  2792. X F1(M)=2*I*PI**2*M**2*(1/EP-0.5+0.5*LG(M)
  2793.    +EP*(1/4-LG(M)/4+LG(M)*LG(M)/8+PI**2/48))
  2794. X F2(M)=2*I*PI**2*(-1/EP-0.5*LG(M)
  2795.     -EP*(PI**2/48+LG(M)*LG(M)/8))
  2796. X F3(M)=I*PI**2/2/M**2+I*EP*PI**2/2/M**2/2*LG(M)
  2797. X F4(M)=I*PI**2/6/M**4
  2798.    -1/12*I*EP*PI**2/M**4*(1-LG(M))
  2799. X F5(M)=I*PI**2/M**6*(1/12-EP/16+EP*LG(M)/24)
  2800. X FX211(M,M0,SM)=
  2801.    +PI**4*(-1./2.-3.*SM**(-4)*M**2*M0**2-1./4.*SM**(-4)*M**4-9./4.*
  2802.    SM**(-4)*M0**4-SM**(-2)*M**2-SM**(-2)*M0**2-2.*EP**(-2)+EP**(-1)
  2803.    )
  2804.    +PI**6*(1./12.+2./3.*SM**(-4)*M**2*M0**2+1./3.*SM**(-4)*M0**4+1.
  2805.    /3.*SM**(-2)*M0**2)
  2806.    +LG(SM)*PI**4*(-4.*SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M**4-5./2.
  2807.    *SM**(-4)*M0**4-SM**(-2)*M**2-SM**(-2)*M0**2)
  2808.    +LG(SM)*LG(SM)*PI**4*(1./2.+2.*SM**(-4)*M**2*M0**2+SM**(-4)*M0**
  2809.    4+SM**(-2)*M0**2)
  2810.    -1./2.*LG(SM)*LG(M)*PI**4
  2811.    +LG(SM)*LG(M0)*PI**4*(-2.*SM**(-4)*M**2*M0**2-SM**(-4)*M0**4-SM*
  2812.    *(-2)*M0**2)
  2813.    +LG(M)*PI**4*(1.+3.*SM**(-4)*M**2*M0**2+1./2.*SM**(-4)*M**4+SM**
  2814.    (-2)*M**2-2.*EP**(-1))
  2815.    +LG(M)*LG(SM)*PI**4*(-1./2.-2.*SM**(-4)*M**2*M0**2-SM**(-4)*M0**
  2816.    4-SM**(-2)*M0**2)
  2817.    -1./2.*LG(M)*LG(M)*PI**4
  2818.    +LG(M)*LG(M0)*PI**4*(2.*SM**(-4)*M**2*M0**2+SM**(-4)*M0**4+SM**(
  2819.    -2)*M0**2)
  2820.    +LG(M0)*PI**4*(SM**(-4)*M**2*M0**2+5./2.*SM**(-4)*M0**4+SM**(-2)
  2821.    *M0**2)
  2822. X FX112(M,M0,SM)=
  2823.    +PI**4*(-1./2.+3.*SM**(-6)*M**2*M0**4+3.*SM**(-6)*M**4*M0**2+1./
  2824.    9.*SM**(-6)*M**6+1./9.*SM**(-6)*M0**6+SM**(-4)*M**2*M0**2+1./4.*
  2825.    SM**(-4)*M**4+1./4.*SM**(-4)*M0**4+SM**(-2)*M**2+SM**(-2)*M0**2-
  2826.    2.*EP**(-2)+EP**(-1))
  2827.    +PI**6*(-1./4.-2./3.*SM**(-6)*M**2*M0**4-2./3.*SM**(-6)*M**4*M0*
  2828.    *2-1./3.*SM**(-4)*M**2*M0**2)
  2829.    +LG(SM)*PI**4*(1.+5.*SM**(-6)*M**2*M0**4+5.*SM**(-6)*M**4*M0**2+
  2830.    1./3.*SM**(-6)*M**6+1./3.*SM**(-6)*M0**6+2.*SM**(-4)*M**2*M0**2+
  2831.    1./2.*SM**(-4)*M**4+1./2.*SM**(-4)*M0**4+SM**(-2)*M**2+SM**(-2)*
  2832.    M0**2-2.*EP**(-1))
  2833.    +LG(SM)*LG(SM)*PI**4*(-1.-2.*SM**(-6)*M**2*M0**4-2.*SM**(-6)*M**
  2834.    4*M0**2-SM**(-4)*M**2*M0**2)
  2835.    +LG(SM)*LG(M0)*PI**4*(2.*SM**(-6)*M**2*M0**4+2.*SM**(-6)*M**4*M0
  2836.    **2+SM**(-4)*M**2*M0**2)
  2837.    +LG(M)*PI**4*(-SM**(-6)*M**2*M0**4-4.*SM**(-6)*M**4*M0**2-1./3.*
  2838.    SM**(-6)*M**6-SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M**4-SM**(-2)*M
  2839.    **2)
  2840.    +LG(M)*LG(SM)*PI**4*(2.*SM**(-6)*M**2*M0**4+2.*SM**(-6)*M**4*M0*
  2841.    *2+SM**(-4)*M**2*M0**2)
  2842.    +LG(M)*LG(M0)*PI**4*(-2.*SM**(-6)*M**2*M0**4-2.*SM**(-6)*M**4*M0
  2843.    **2-SM**(-4)*M**2*M0**2)
  2844.    +LG(M0)*PI**4*(-4.*SM**(-6)*M**2*M0**4-SM**(-6)*M**4*M0**2-1./3.
  2845.    *SM**(-6)*M0**6-SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M0**4-SM**(-2
  2846.    )*M0**2)
  2847. X FX111(M,M0,SM)=
  2848.    +PI**4*(7./2.*SM**2+2.*SM**2*EP**(-2)-3.*SM**2*EP**(-1)+9./4.*SM
  2849.    **(-4)*M**2*M0**4+9./4.*SM**(-4)*M**4*M0**2+5./36.*SM**(-4)*M**6
  2850.    +5./36.*SM**(-4)*M0**6+SM**(-2)*M**2*M0**2+3./4.*SM**(-2)*M**4+3
  2851.    ./4.*SM**(-2)*M0**4+5./2.*M**2+2.*M**2*EP**(-2)-3.*M**2*EP**(-1)
  2852.    +5./2.*M0**2+2.*M0**2*EP**(-2)-3.*M0**2*EP**(-1))
  2853.    +PI**6*(1./4.*SM**2-1./3.*SM**(-4)*M**2*M0**4-1./3.*SM**(-4)*M**
  2854.    4*M0**2-1./3.*SM**(-2)*M**2*M0**2-1./12.*M**2-1./12.*M0**2)
  2855.    +LG(SM)*PI**4*(-3.*SM**2+2.*SM**2*EP**(-1)+3./2.*SM**(-4)*M**2*M
  2856.    0**4+3./2.*SM**(-4)*M**4*M0**2+1./6.*SM**(-4)*M**6+1./6.*SM**(-4
  2857.    )*M0**6+1./2.*SM**(-2)*M**4+1./2.*SM**(-2)*M0**4-M**2-M0**2)
  2858.    +LG(SM)*LG(SM)*PI**4*(SM**2-SM**(-4)*M**2*M0**4-SM**(-4)*M**4*M0
  2859.    **2-SM**(-2)*M**2*M0**2-1./2.*M**2-1./2.*M0**2)
  2860.    +LG(SM)*LG(M)*PI**4*(2.*SM**(-4)*M**2*M0**4+SM**(-4)*M**4*M0**2+
  2861.    SM**(-2)*M**2*M0**2+1./2.*M**2)
  2862.    +LG(SM)*LG(M0)*PI**4*(-SM**(-4)*M**2*M0**4+1./2.*M0**2)
  2863.    +LG(M)*PI**4*(-3./2.*SM**(-4)*M**4*M0**2-1./6.*SM**(-4)*M**6-1./
  2864.    2.*SM**(-2)*M**4-2.*M**2+2.*M**2*EP**(-1))
  2865.    +LG(M)*LG(SM)*PI**4*(-SM**(-4)*M**2*M0**4+1./2.*M**2)
  2866.    +LG(M)*LG(M)*PI**4*(1./2.*M**2)
  2867.    +LG(M)*LG(M0)*PI**4*(SM**(-4)*M**2*M0**4)
  2868.    +LG(M0)*PI**4*(-3./2.*SM**(-4)*M**2*M0**4-1./6.*SM**(-4)*M0**6-1
  2869.    ./2.*SM**(-2)*M0**4-2.*M0**2+2.*M0**2*EP**(-1))
  2870.    +LG(M0)*LG(SM)*PI**4*(2.*SM**(-4)*M**2*M0**4+SM**(-4)*M**4*M0**2
  2871.    +SM**(-2)*M**2*M0**2+1./2.*M0**2)
  2872.    +LG(M0)*LG(M)*PI**4*(-2.*SM**(-4)*M**2*M0**4-SM**(-4)*M**4*M0**2
  2873.    -SM**(-2)*M**2*M0**2)
  2874.    +LG(M0)*LG(M0)*PI**4*(1./2.*M0**2)
  2875. *fix
  2876. BLOCK DIFF{}
  2877. B PI
  2878. Id,I=i
  2879. Id,DM*M**N~=N*M**N/M**2/2+M**N*DM
  2880. Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0
  2881. Al,DSM*SM**N~=N*SM**N/SM**2/2+SM**N*DSM
  2882. Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM
  2883. Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0
  2884. Al,Adiso,DSM*LG(SM)*LG(SM)=2*LG(SM)/SM**2+LG(SM)*LG(SM)*DSM
  2885. Al,DM*LG(M)=1/M**2+LG(M)*DM
  2886. Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0
  2887. Al,DSM*LG(SM)=1/SM**2+LG(SM)*DSM
  2888. Id,DM*XX=0
  2889. Al,DM0*XX=0
  2890. Al,DSM*XX=0
  2891. Al,XX=1
  2892. Id,Commu,LG
  2893. Id,EP=0
  2894. ENDBLOCK
  2895. Z CH1=FX211(M,M0,SM)+DM*FX111(M,M0,SM)*XX
  2896. Z CH2=FX112(M,M0,SM)+DSM*FX111(M,M0,SM)*XX
  2897. Z CH3=FX211(M0,M,SM)+DM0*FX111(M,M0,SM)*XX
  2898. Z CH4=-(1+EP)*FX211(M,M0,SM)+2*M02*DM0*FX211(M,M0,SM)*XX
  2899.   -FX112(M,M0,SM)+F2(M)*F2(SM)-MM0SM*DSM*FX211(M,M0,SM)*XX
  2900. DIFF{}
  2901. Id,M02=M0**2
  2902. Al,MM0SM=M**2-M0**2-SM**2
  2903. *end
  2904.  
  2905. C RO-parameter 17. Differentiating F211.
  2906.  
  2907. P stats
  2908. F LG
  2909. S M,M0,SM
  2910. *fix
  2911.  
  2912. B PI
  2913. Z F311(M,M0,SM)=-1/2*DM*FX211(M,M,M0,SM)*XX
  2914. Z F221(M,M0,SM)=-DM0*FX211(M,M,M0,SM)*XX
  2915. Z F211(M,M0,SM)=FX211(M,M,M0,SM)
  2916. Id,FX211(M~,M~,M0~,SM)=PI**4*(-2/EP**2+(1-2*LG(M))/EP
  2917.   -0.5+PI**2/12+LG(M)-LG(M)*LG(M)+0.5*LG(SM,M)*LG(SM,M)
  2918.   +(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4*LG(SM,M)*LG(SM,M)
  2919.   -(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4*LG(SM,M)*LG(M0,M)
  2920.   -(M**2*SM**2+M0**2*SM**2+4*M**2*M0**2+5/2*M0**4+0.5*M**4)
  2921.   /SM**4*LG(SM,M) + (M0**2*SM**2+M**2*M0**2+5/2*M0**4)/SM**4
  2922.   *LG(M0,M) - (M**2+M0**2)/SM**2
  2923.   - (1/4*M**4+3*M**2*M0**2+9/4*M0**4)/SM**4
  2924.   +PI**2/3*(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4  )
  2925. Id,LG(SM~,M)=LG(SM)-LG(M)
  2926. Id,DM*M**N~=N*M**N/M**2/2+M**N*DM
  2927. Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0
  2928. Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM
  2929. Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0
  2930. Al,DM*LG(M)=1/M**2+LG(M)*DM
  2931. Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0
  2932. Id,DM*XX=0
  2933. Al,DM0*XX=0
  2934. Al,XX=1
  2935. Id,Commu,LG
  2936. Keep F311,F221,F211
  2937. Punch F311,F221,F211
  2938. *next
  2939. B PI
  2940. Z F411(M,M0,SM)=-1/3*DM*F311(M,M0,SM)*XX
  2941. Z F321(M,M0,SM)=-1/2*DM*F221(M,M0,SM)*XX
  2942. Id,DM*M**N~=N*M**N/M**2/2+M**N*DM
  2943. Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0
  2944. Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM
  2945. Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0
  2946. Al,DM*LG(M)=1/M**2+LG(M)*DM
  2947. Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0
  2948. Id,DM*XX=0
  2949. Al,DM0*XX=0
  2950. Al,XX=1
  2951. Id,Commu,LG
  2952. Keep F311,F221,F411,F321,F211
  2953. Punch F411,F321
  2954. *next
  2955. B PI
  2956. Z F511(M,M0,SM)=-1/4*DM*F411(M,M0,SM)*XX
  2957. Z F421(M,M0,SM)=-1/3*DM*F321(M,M0,SM)*XX
  2958. Id,DM*M**N~=N*M**N/M**2/2+M**N*DM
  2959. Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0
  2960. Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM
  2961. Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0
  2962. Al,DM*LG(M)=1/M**2+LG(M)*DM
  2963. Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0
  2964. Id,DM*XX=0
  2965. Al,DM0*XX=0
  2966. Al,XX=1
  2967. Id,Commu,LG
  2968. Keep F311,F221,F411,F321,F421,F211,F511
  2969. Punch F421,F511
  2970. *next
  2971. B PI
  2972. Z FF211=F211(M,M,SM)
  2973. Z FF311=F311(M,M,SM)
  2974. Z FF411=F411(M,M,SM)
  2975. Z FF511=F511(M,M,SM)
  2976. Z FF221=F221(M,M,SM)
  2977. Z FF321=F321(M,M,SM)
  2978. Z FF421=F421(M,M,SM)
  2979. Id,Commu,LG
  2980. *end
  2981.  
  2982. C RO-parameter 18. Expansion of F211(SM,M1,M2) for large SM.
  2983.  
  2984. C A=M1**2/SM**2, B=M2**2/SM**2. LGA=LOG(A), LGB=LG(B).
  2985. C S2=PI**2/6. E=EXPANSION PARAMETER, COUNTS ORDER IN A,B. E**7=0.
  2986. C THE FORMULA USED IS:
  2987. C F(A,B)=-1/2*LOG(A)**2-SP((A-B)/A)
  2988. C + FAC1*( SP((B-A)/X1)-SP((A-B)/(1-X1))-SP(1-1/X1)+SP(-X1/(1-X1)) )
  2989. C + FAC2*(  SAME, BUT X1 REPLACED BY X2  )
  2990. C FAC1=(B-X1)/ROOT, FAC2=(X2-B)/ROOT
  2991. C X1=(1+B-A+ROOT)/2, X2=(1+B-A-ROOT)/2.
  2992. C ROOT=SQRT((A-B)**2+1-2*(A+B))
  2993. C X1,2 SOLUTION OF  X**2+(A-B-1)*X+B=0
  2994. C THUS X1*X2=B, (1-X1)*(1-X2)=A, X1+X2=1+B-A.
  2995. C NOTE THAT FAC1+FAC2=-1.
  2996. C FOR THIS EXPANSION THE EQUATION WAS REWRITTEN AS
  2997. C F(A,B)=-1/2*LOG(A)**2-SP((A-B)/A)+SP((A-B)*(1-X2)/A)
  2998. C +S2*(1-A-B)/ROOT
  2999. C + FAC1*(SP((B-A)*X2/B)-2*SP(-(1-X1)*X2/B)
  3000. C -1/2*LOG((1-X1)*X2/B)**2 )
  3001. C + FAC2*(-1/2*LOG(1-(B-A)*X1/B)**2-SP((A-B)*(1-X1)/A)
  3002. C +2*SP(-X2*(1-X1)/A)+1/2*LOG(X2*(1-X1)/A)**2 )
  3003. C THE TERMS LOG(A)**2 AND LOG(B)**2 CANCEL OUT.
  3004. C THE EXPRESSIONS BELOW REFER TO THE EXPANSION OF THE
  3005. C INDIVIDUAL TERMS, FOR INSTANCE EXP(2) REFERS TO THE
  3006. C EXPRESSION CONTAINING S2.
  3007. C
  3008. C THE FUNCTION F211 IS GIVEN BY
  3009. C F211=PI**4*(-2/EP**2+1/EP*(1-2*GA-2*LOG(SM**2)
  3010. C       -1/2-PI**2/12+GA-GA**2+(1-2*GA)*LOG(SM**2)
  3011. C       -LOG(SM**2)**2-F(A,B) )
  3012. C EP=N-4, GA=EULERS CONSTANT. GA MAY BE ABSORBED IN
  3013. C A REDIFINITION OF THE UNITS IN THE LOG, WHICH WAS
  3014. C ALREADY DONE WITH FACTORS LOG(PI). (READ LOG(PI*SM**2)
  3015. C EVERYWHERE).
  3016. C THE WORK WAS DIVIDED IN TWO PARTS. PART 1 = COMPUTING THE
  3017. C VARIOUS ARGUMENTS OF THE FUNCTIONS TO BE EXPANDED. THIS
  3018. C INCLUDED WORKING OUT THE ROOT, ALSO GIVEN HERE. GIVEN X1 AND
  3019. C X2 THE OTHER ARGUMENTS ARE COMPUTED ACCORDING TO THE CARDS
  3020. C BELOW MADE INACTIVE. PART 2 IS COMPUTING THE EXPRESSIONS.
  3021. C PRINT NINPUT
  3022. C
  3023. C C IN THIS PART X1, X2 ETC ARE COMPUTED TO ORDER E**7. THIS
  3024. C C IS NECESSARY TO OBTAIN THE ARGUMENTS OF THE VARIOUS FUNCTIONS
  3025. C C TO ORDER E**6.
  3026. C
  3027. C SCREEN
  3028. C N  R
  3029. C COMMON XX(0),XX1(0),XX2(0)
  3030. C S E=8,A,B
  3031. C X X(A)=E**2*(A**2+B**2-2*A*B)-2*E*(A+B)
  3032. C *FIX
  3033. C Z XX(0)=1.
  3034. C *NEXT
  3035. C DO K1=1,7
  3036. C Z XX('K1')=X(A)*XX('K1'-1)
  3037. C B E
  3038. C NPRINT XX('K1')
  3039. C *NEXT
  3040. C ENDDO
  3041. C Z WO=1+XX(1)/2-XX(2)/8+XX(3)/16-5*XX(4)/128
  3042. C      +7*XX(5)/256-21*XX(6)/1024
  3043. C   +33/2048*XX(7)
  3044. C Z WOI=1.-XX(1)/2+3*XX(2)/8-5*XX(3)/16+35*XX(4)/128
  3045. C       -63*XX(5)/256+231*XX(6)/1024
  3046. C      -429/2048*XX(7)
  3047. C B E
  3048. C KEEP WO,WOI
  3049. C *NEXT
  3050. C Z X1=0.5+0.5*B*E-0.5*A*E+0.5*WO
  3051. C Z X2=0.5+0.5*B*E-0.5*A*E-0.5*WO
  3052. C B E
  3053. C PUNCH X1,X2
  3054. C KEEP WO,WOI,X1,X2
  3055. C *NEXT
  3056. C B E
  3057. C Z OMX1A=1/A/E-X1/A/E
  3058. C Z X2B=X2/B/E
  3059. C Z BMX2A=B/A-X2/A/E
  3060. C PUNCH OMX1A,X2B,BMX2A
  3061. C B E
  3062. C KEEP X1,X2,WOI
  3063. C *NEXT
  3064. C S E=7
  3065. C Z FAC1=(B*E-X1)*WOI
  3066. C Z FAC2=(X2-B*E)*WOI
  3067. C B E
  3068. C PUNCH FAC1,FAC2
  3069. C *END
  3070.  
  3071. Common EXP(0),Exp(0)
  3072. S LOMX,LGA,LGB
  3073.  
  3074. C X X1=1-E*A-A*B*E**2-E**3*A*B**2-E**3*A**2*B
  3075. C    +E**4*(-A*B**3-3.*A**2*B**2-A**3*B)
  3076. C    +E**5*(-A*B**4-6.*A**2*B**3-6.*A**3*B**2-A**4*B)
  3077. C    +E**6*(-A*B**5-10.*A**2*B**4-20.*A**3*B**3-10.*A**4*B**2-A**5*B)
  3078. C    +E**7*(-A*B**6-15.*A**2*B**5-50.*A**3*B**4-50.*A**4*B**3-15.*A**
  3079. C    5*B**2-A**6*B)
  3080. C X X2=E*B+E**2*A*B+E**3*A*B**2+E**3*A**2*B
  3081. C    +E**4*(A*B**3+3.*A**2*B**2+A**3*B)
  3082. C    +E**5*(A*B**4+6.*A**2*B**3+6.*A**3*B**2+A**4*B)
  3083. C    +E**6*(A*B**5+10.*A**2*B**4+20.*A**3*B**3+10.*A**4*B**2+A**5*B)
  3084. C    +E**7*(A*B**6+15.*A**2*B**5+50.*A**3*B**4+50.*A**4*B**3+15.*A**5
  3085. C    *B**2+A**6*B)
  3086. C X OMX1A=1 + E*B
  3087. C    +E**2*(A*B+B**2)
  3088. C    +E**3*(3.*A*B**2+A**2*B+B**3)
  3089. C    +E**4*(6.*A*B**3+6.*A**2*B**2+A**3*B+B**4)
  3090. C    +E**5*(10.*A*B**4+20.*A**2*B**3+10.*A**3*B**2+A**4*B+B**5)
  3091. C    +E**6*(15.*A*B**5+50.*A**2*B**4+50.*A**3*B**3+15.*A**4*B**2+A**5
  3092. C    *B+B**6)
  3093. C X X2B=1+E*A
  3094. C    +E**2*(A*B+A**2)
  3095. C    +E**3*(A*B**2+3.*A**2*B+A**3)
  3096. C    +E**4*(A*B**3+6.*A**2*B**2+6.*A**3*B+A**4)
  3097. C    +E**5*(A*B**4+10.*A**2*B**3+20.*A**3*B**2+10.*A**4*B+A**5)
  3098. C    +E**6*(A*B**5+15.*A**2*B**4+50.*A**3*B**3+50.*A**4*B**2+15.*A**5
  3099. C    *B+A**6)
  3100. C X BMX2A=-B*E
  3101. C    +E**2*(-A*B-B**2)
  3102. C    +E**3*(-3.*A*B**2-A**2*B-B**3)
  3103. C    +E**4*(-6.*A*B**3-6.*A**2*B**2-A**3*B-B**4)
  3104. C    +E**5*(-10.*A*B**4-20.*A**2*B**3-10.*A**3*B**2-A**4*B-B**5)
  3105. C    +E**6*(-15.*A*B**5-50.*A**2*B**4-50.*A**3*B**3-15.*A**4*B**2-A**
  3106. C    5*B-B**6)
  3107. X FAC1=-1-A*B*E**2
  3108.    +E**3*(-2.*A*B**2-2.*A**2*B)
  3109.    +E**4*(-3.*A*B**3-9.*A**2*B**2-3.*A**3*B)
  3110.    +E**5*(-4.*A*B**4-24.*A**2*B**3-24.*A**3*B**2-4.*A**4*B)
  3111.    +E**6*(-5.*A*B**5-50.*A**2*B**4-100.*A**3*B**3-50.*A**4*B**2-5.*A
  3112.    **5*B)
  3113. X FAC2=E**2*A*B
  3114.    +E**3*(2.*A*B**2+2.*A**2*B)
  3115.    +E**4*(3.*A*B**3+9.*A**2*B**2+3.*A**3*B)
  3116.    +E**5*(4.*A*B**4+24.*A**2*B**3+24.*A**3*B**2+4.*A**4*B)
  3117.    +E**6*(5.*A*B**5+50.*A**2*B**4+100.*A**3*B**3+50.*A**4*B**2+5.*A
  3118.    **5*B)
  3119. X ARG1=E*B+A*B*E**2
  3120.    +E**3*(A*B**2+A**2*B)
  3121.    +E**4*(A*B**3+3.*A**2*B**2+A**3*B)
  3122.    +E**5*(A*B**4+6.*A**2*B**3+6.*A**3*B**2+A**4*B)
  3123.    +E**6*(A*B**5+10.*A**2*B**4+20.*A**3*B**3+10.*A**4*B**2+A**5*B)
  3124. X ARG3=-A*E+E*B
  3125.    +E**2*(A*B-A**2)
  3126.    +E**3*(A*B**2-A**3)
  3127.    +E**4*(A*B**3+2.*A**2*B**2-2.*A**3*B-A**4)
  3128.    +E**5*(A*B**4+5.*A**2*B**3-5.*A**4*B-A**5)
  3129.    +E**6*(A*B**5+9.*A**2*B**4+10.*A**3*B**3-10.*A**4*B**2-9.*A**5*B
  3130.    -A**6)
  3131. X ARG4=-A*E
  3132.    +E**2*(-A*B-A**2)
  3133.    +E**3*(-A*B**2-3.*A**2*B-A**3)
  3134.    +E**4*(-A*B**3-6.*A**2*B**2-6.*A**3*B-A**4)
  3135.    +E**5*(-A*B**4-10.*A**2*B**3-20.*A**3*B**2-10.*A**4*B-A**5)
  3136.    +E**6*(-A*B**5-15.*A**2*B**4-50.*A**3*B**3-50.*A**4*B**2-15.*A**
  3137.    5*B-A**6)
  3138. X ARG5=E*A+E*B
  3139.    +E**2*(3.*A*B+A**2+B**2)
  3140.    +E**3*(6.*A*B**2+6.*A**2*B+A**3+B**3)
  3141.    +E**4*(10.*A*B**3+20.*A**2*B**2+10.*A**3*B+A**4+B**4)
  3142.    +E**5*(15.*A*B**4+50.*A**2*B**3+50.*A**3*B**2+15.*A**4*B+A**5+B*
  3143.    *5)
  3144.    +E**6*(21.*A*B**5+105.*A**2*B**4+175.*A**3*B**3+105.*A**4*B**2+2
  3145.    1.*A**5*B+A**6+B**6)
  3146. X ARG6=-E*A+B*E
  3147.    +E**2*(-A*B+B**2)
  3148.    +E**3*(-A**2*B+B**3)
  3149.    +E**4*(2.*A*B**3-2.*A**2*B**2-A**3*B+B**4)
  3150.    +E**5*(5.*A*B**4-5.*A**3*B**2-A**4*B+B**5)
  3151.    +E**6*(9.*A*B**5+10.*A**2*B**4-10.*A**3*B**3-9.*A**4*B**2-A**5*B
  3152.    +B**6)
  3153. X ARG8=-B*E
  3154.    +E**2*(-A*B-B**2)
  3155.    +E**3*(-3.*A*B**2-A**2*B-B**3)
  3156.    +E**4*(-6.*A*B**3-6.*A**2*B**2-A**3*B-B**4)
  3157.    +E**5*(-10.*A*B**4-20.*A**2*B**3-10.*A**3*B**2-A**4*B-B**5)
  3158.    +E**6*(-15.*A*B**5-50.*A**2*B**4-50.*A**3*B**3-15.*A**4*B**2-A**
  3159.    5*B-B**6)
  3160. S E=7
  3161. *fix
  3162. C B E
  3163. C Z ARG1=X2
  3164. C Z ARG3=(B-A)*X2/B
  3165. C Z ARG4=1-X2B
  3166. C Z ARG5=OMX1A*X2B - 1
  3167. C Z ARG6=(B-A)*(1-X1)/A
  3168. C Z ARG7=(A-B)*E*OMX1A
  3169. C Z ARG8=BMX2A
  3170. C Punch ARG1,ARG3,ARG4,ARG5,ARG6,ARG8
  3171. C *end
  3172. Z SP(1)=-LOMX/X
  3173. Z XX2(1)=-ARG1
  3174. B E
  3175. Nprint SP,XX2
  3176. Keep SP,XX2
  3177. *next
  3178. DO K1=2,6
  3179. P input
  3180. Z SP('K1')=DIFX*SP('K1'-1)*YY/'K1'
  3181. Z XX2('K1')=-XX2('K1'-1)*ARG1
  3182. Id,DIFX*LOMX=-1/OMX+LOMX*DIFX
  3183. Id,DIFX*OMX**N~=-N*OMX**N/OMX+OMX**N*DIFX
  3184. Id,DIFX*X**N~=N*X**N/X+X**N*DIFX
  3185. Id,DIFX*YY=0
  3186. Al,YY=1
  3187. Id,X**N~*OMX**-1=DS(J1,1,-N,(X**-J1))+1/OMX
  3188. B E
  3189. Nprint SP,XX2
  3190. Keep SP,XX2
  3191. *next
  3192. ENDDO
  3193. DO K2=1,6
  3194. P input
  3195. Z SP('K2')=SP('K2')*X**'K2'
  3196. ENDDO
  3197. Id,X**N~*OMX**M~=XOMX**-M*X**N*X**M
  3198. Id,X=(A-B)/A
  3199. Al,XOMX=(A-B)/B
  3200. Id,LOMX=LGB-LGA
  3201. B LGA,LGB
  3202. Keep SP,XX2
  3203. Nprint SP
  3204. *next
  3205. B E,LGA,LGB
  3206. Z EXP(1)=DS(J3,1,6,(SP(J3)*XX2(J3)) )
  3207. *next
  3208. B E,S2
  3209. Z EXP(2)=S2*(FAC2-FAC1)
  3210. *next
  3211. B E
  3212. Z TOT(3)=0
  3213. Z TOT(4)=0
  3214. Z TOT(7)=0
  3215. Z TOT(8)=0
  3216. Z SP(3)=ARG3
  3217. Z SP(4)=ARG4
  3218. Z SP(7)=-ARG6
  3219. Z SP(8)=ARG8
  3220. Keep TOT,SP
  3221. Nprint TOT,SP
  3222. *next
  3223. DO K3=2,6
  3224. B E
  3225. Z TOT(3)=TOT(3)+SP(3)
  3226. Z TOT(4)=TOT(4)+SP(4)
  3227. Z TOT(7)=TOT(7)+SP(7)
  3228. Z TOT(8)=TOT(8)+SP(8)
  3229. Z SP(3)=SP(3)*ARG3*('K3'-1)**2/'K3'**2
  3230. Z SP(4)=SP(4)*ARG4*('K3'-1)**2/'K3'**2
  3231. Z SP(7)=-SP(7)*ARG6*('K3'-1)**2/'K3'**2
  3232. Z SP(8)=SP(8)*ARG8*('K3'-1)**2/'K3'**2
  3233. Keep TOT,SP
  3234. Nprint TOT,SP
  3235. *next
  3236. ENDDO
  3237. B E
  3238. Z EXP(3)=FAC1*(TOT(3)+SP(3))
  3239. Z EXP(4)=-2*FAC1*(TOT(4)+SP(4))
  3240. Z EXP(7)=-FAC2*(TOT(7)+SP(7))
  3241. Z EXP(8)=2*FAC2*(TOT(8)+SP(8))
  3242. *next
  3243. Z Exp(3)=EXP(3)
  3244. Z Exp(4)=EXP(4)
  3245. Z Exp(7)=EXP(7)
  3246. Delete EXP(3),EXP(4),EXP(7)
  3247. *next
  3248. B E,LGA,LGB
  3249. Z XX(5)=ARG5
  3250. Z XX(6)=ARG6
  3251. Z TOT(5)=0
  3252. Z TOT(6)=0
  3253. Keep XX,TOT
  3254. Nprint XX,TOT
  3255. *next
  3256. DO K5=2,6
  3257. Z TOT(5)=TOT(5)+XX(5)
  3258. Z TOT(6)=TOT(6)+XX(6)
  3259. Z XX(5)=-XX(5)*ARG5*('K5'-1)/'K5'
  3260. Z XX(6)=-XX(6)*ARG6*('K5'-1)/'K5'
  3261. B E
  3262. Keep TOT,XX
  3263. Nprint TOT,XX
  3264. *next
  3265. ENDDO
  3266. B E
  3267. Z TOT(5)=TOT(5)+XX(5)
  3268. Z TOT(6)=TOT(6)+XX(6)
  3269. Keep TOT
  3270. Nprint TOT
  3271. *next
  3272. Z TOT(15)=TOT(5)*TOT(5)
  3273. Z TOT(16)=TOT(6)*TOT(6)
  3274. Keep TOT
  3275. Nprint TOT
  3276. B E
  3277. *next
  3278. Z EXP(5)=-0.5*FAC1*(2*LGA*TOT(5)+TOT(15))
  3279. Z EXP(6)=-0.5*FAC2*(-2*LGA*LGB+2*ABLG*TOT(6)+TOT(16) )
  3280. Z EXP(9)=+0.5*FAC2*(2*LGB*TOT(5)+TOT(15))
  3281. Id,ABLG=LGA-LGB
  3282. B E,LGA,LGB
  3283. *next
  3284. Z EXP(3)=Exp(3)
  3285. Z EXP(4)=Exp(4)
  3286. Z EXP(7)=Exp(7)
  3287. Delete Exp(3),Exp(4),Exp(7)
  3288. *next
  3289. B E,LGA,LGB,S2
  3290. Z TOTAL=DS(J0,1,9,(EXP(J0)))
  3291. P outp
  3292. *yep
  3293. C Id,Numer,E,1.
  3294. Id,E=1
  3295. B S2,LGA,LGB
  3296. *end
  3297.  
  3298. C RO-parameter 19. Higher orders of F211(M,M0,SM) expansion for large SM.
  3299.  
  3300. C THE HIGHER ORDERS ARE MADE SUCH THAT THE RELATION
  3301. C -(N-3)*F211-2*M0**2*F221-F112+F2(M)*F2(M)+(M**2-M0**2-SM**2)*F212=0
  3302. C IS SATISFIED. START WITH THE COEFFICIENT OF LGA*LGB, ETC.
  3303. F LG
  3304. S M,M0,SM,LGA,LGB
  3305. C THIS IS F211/PI**4
  3306. X F211=-1./2.-A-3.*A*B-1./4.*A**2-B-9./4.*B**2
  3307.    -47/18*B**3-9*B**2*A-11/2*B*A**2-1/9*A**3
  3308.     -401/144*B**4-20*B**3*A-107/4*B**2*A**2-74/9*B*A**3-1/16*A**4
  3309.     -5197/1800*B**5-2296/63*B**4*A-177/2*B**3*A**2-569/9*B**2*A**3
  3310.      -797/72*B*A**4-1/25*A**5
  3311.    +LGA*(1.+A+3.*A*B+1./2.*A**2
  3312.     +5*B**2*A+7*B*A**2+1/3*A**3
  3313.     +7*B**3*A+51/2*B**2*A**2+35/3*B*A**3+1/4*A**4
  3314.     +9*B**4*A+62*B**3*A**2+224/3*B**2*A**3
  3315.      +101/6*B*A**4+1/5*A**5 )
  3316.    +LGA*LGB*(2.*A*B+B+B**2
  3317.     +B**3+6*B**2*A+3*B*A**2
  3318.     +B**4+12*B**3*A+18*B**2*A**2+4*B*A**3
  3319.     +B**5+20*B**4*A+60*B**3*A**2+40*B**2*A**3
  3320.      +5*B*A**4 )
  3321.    -1./2.*LGA**2
  3322.    +LGB*(A*B+B+5./2.*B**2
  3323.   +10/3*B**3+8*B**2*A+B*A**2
  3324.     +47/12*B**4+23*B**3*A+33/2*B**2*A**2+B*A**3
  3325.     +131/30*B**5+142/3*B**4*A+82*B**3*A**2+28*B**2*A**3
  3326.      +B*A**4 )
  3327.    +PI**2*(1./12.+2./3.*A*B+1./3.*B+1./3.*B**2
  3328.     +1/3*B**3+2*B**2*A+B*A**2
  3329.     +1/3*B**4+4*B**3*A+6*B**2*A**2+4/3*B*A**3
  3330.    +1/3*B**5+20/3*B**4*A+20*B**3*A**2+40/3*B**2*A**3
  3331.    +5/3*B*A**4 )
  3332.    -2.*EP**(-2)
  3333.    +EP**(-1)
  3334.    -2.*EP**(-1)*LGA
  3335.    +LG(SM)
  3336.    -2.*LG(SM)*LGA
  3337.    -2.*LG(SM)*EP**(-1)
  3338.    -LG(SM)*LG(SM)
  3339. C THIS IS F2(M)*F2(SM)/PI**4
  3340. X F22=-1./2.*LGA**2
  3341.    -1./6.*PI**2
  3342.    -4.*EP**(-2)
  3343.    -2.*EP**(-1)*LGA
  3344.    -2.*LG(SM)*LGA
  3345.    -4.*LG(SM)*EP**(-1)
  3346.    -2.*LG(SM)*LG(SM)
  3347. X FFF(A,B)=-A-A*B-3.*A*B**2-11./2.*A*B**3-74./9.*A*B**4-797./72.*A*B*
  3348.    *5-1./4.*A**2-3.*A**2*B-49./4.*A**2*B**2-35.*A**2*B**3-2851./36.
  3349.    *A**2*B**4-1./9.*A**3-11./2.*A**3*B-35.*A**3*B**2-2531./18.*A**3
  3350.    *B**3-1./16.*A**4-74./9.*A**4*B-2851./36.*A**4*B**2-1./25.*A**5-
  3351.    797./72.*A**5*B-1./36.*A**6-B-1./4.*B**2-1./9.*B**3-1./16.*B**4-
  3352.    1./25.*B**5-1./36.*B**6
  3353.    +LGA*(A+A*B+A*B**2+A*B**3+A*B**4+A*B**5+1./2.*A**2+4.*A**2*B+21.
  3354.    /2.*A**2*B**2+20.*A**2*B**3+65./2.*A**2*B**4+1./3.*A**3+8.*A**3*
  3355.    B+40.*A**3*B**2+370./3.*A**3*B**3+1./4.*A**4+38./3.*A**4*B+310./
  3356.    3.*A**4*B**2+1./5.*A**5+107./6.*A**5*B+1./6.*A**6)
  3357.    +LGA*LGB*(A*B+2.*A*B**2+3.*A*B**3+4.*A*B**4+5.*A*B**5+2.*A**2*B+
  3358.    9.*A**2*B**2+24.*A**2*B**3+50.*A**2*B**4+3.*A**3*B+24.*A**3*B**2
  3359.    +100.*A**3*B**3+4.*A**4*B+50.*A**4*B**2+5.*A**5*B)
  3360.    +LGB*(A*B+4.*A*B**2+8.*A*B**3+38./3.*A*B**4+107./6.*A*B**5+A**2*
  3361.    B+21./2.*A**2*B**2+40.*A**2*B**3+310./3.*A**2*B**4+A**3*B+20.*A*
  3362.    *3*B**2+370./3.*A**3*B**3+A**4*B+65./2.*A**4*B**2+A**5*B+B+1./2.
  3363.    *B**2+1./3.*B**3+1./4.*B**4+1./5.*B**5+1./6.*B**6)
  3364.    +S2*(1.+2.*A*B+4.*A*B**2+6.*A*B**3+8.*A*B**4+10.*A*B**5+4.*A**2*
  3365.    B+18.*A**2*B**2+48.*A**2*B**3+100.*A**2*B**4+6.*A**3*B+48.*A**3*
  3366.    B**2+200.*A**3*B**3+8.*A**4*B+100.*A**4*B**2+10.*A**5*B)+0.
  3367. *fix
  3368. B EP,LGA,LGB,PI,SM
  3369. Z F112=-2/EP**2+(1-2*LG(SM))/EP-1/2-PI**2/12+LG(SM)-LG(SM)*LG(SM)
  3370.        -FFF(A,B)
  3371. Z F221=-DM0*F211*XX
  3372. Z F212=DM*FFF(A,B)*XX
  3373. Z FF211=F211
  3374. Id,DM=DFA/SM**2
  3375. Al,DM0=DFB/SM**2
  3376. Al,EP=0
  3377. Id,DFB*B**N~=N*B**N/B+B**N*DFB
  3378. Al,DFA*A**N~=N*A**N/A+A**N*DFA
  3379. Id,DFB*LGB**2=2*LGB/B+LGB**2*DFB
  3380. Al,DFA*LGA**2=2*LGA/A+LGA**2*DFA
  3381. Al,DFB*LGB=1/B+LGB*DFB
  3382. Al,DFA*LGA=1/A+LGA*DFA
  3383. Id,DFB*XX=0
  3384. Al,DFA*XX=0
  3385. Al,XX=1
  3386. Id,Multi,M**2=A*SM**2
  3387. Al,Multi,M0**2=B*SM**2
  3388. Id,LG(M)=LGA+LG(SM)
  3389. Al,LG(M0)=LGB+LG(SM)
  3390. Id,Commu,LG
  3391. Id,S2=PI**2/6
  3392. Keep F112,F221,F212
  3393. *next
  3394. B EP,LGA,LGB,PI,SM
  3395. Z CH1=-(1+EP)*F211-2*M0**2*F221-F112+F22+(M**2-M0**2-SM**2)*F212
  3396. Id,Multi,M**2=A*SM**2
  3397. Al,Multi,M0**2=B*SM**2
  3398. Id,EP=0
  3399. Id,Commu,LG
  3400. *end
  3401.  
  3402. C RO-parameter 20. Expansion of F211(SM,SM,M) for large SM.
  3403.  
  3404. C S X=13,B=7
  3405. C *FIX
  3406. C Z XX(1)=X
  3407. C KEEP XX
  3408. C *NEXT
  3409. C DO K2=2,12
  3410. C Z XX(K2)=XX(K2-1)*X
  3411. C ID,X**2=B*X-B
  3412. C KEEP XX
  3413. C PUNCH XX(K2)
  3414. C *NEXT
  3415. C ENDDO
  3416. C *END
  3417.  
  3418. Common Exp,Expp
  3419. S B=7,LGB,ROOT,FACT
  3420. S X1=13,X2=13
  3421. X FB=1+B+B**2+B**3+B**4*B**5+B**6
  3422. D POW(N,X)=X,
  3423.      (-B+B*X),
  3424.      (-B*X-B**2+B**2*X),
  3425.      (+B**2-2.*B**2*X-B**3+B**3*X),
  3426.      (+B**2*X+2.*B**3-3.*B**3*X-B**4+B**4*X),
  3427.      (-B**3+3.*B**3*X+3.*B**4-4.*B**4*X-B**5+B**5*X),
  3428.      (-B**3*X-3.*B**4+6.*B**4*X+4.*B**5-5.*B**5*X-B**6+B**6*X),
  3429.      (+B**4-4.*B**4*X-6.*B**5+10.*B**5*X+5.*B**6-6.*B**6*X),
  3430.      (+B**4*X+4.*B**5-10.*B**5*X-10.*B**6+15.*B**6*X),
  3431.      (-B**5+5.*B**5*X+10.*B**6-20.*B**6*X),
  3432.      (-B**5*X-5.*B**6+15.*B**6*X),
  3433.      (+B**6-6.*B**6*X),
  3434.      B**6*X,0.
  3435. *fix
  3436. Z TOT=0.
  3437. Z TOTP=0.
  3438. Z SPE=-X1*FB
  3439. Z SPEP=X2-X2**2
  3440. Keep TOT,SPE,TOTP,SPEP
  3441. Nprint TOT,SPE,TOTP,SPEP
  3442. *next
  3443. DO K1=2,12
  3444. Z TOT=TOT+SPE
  3445. Z TOTP=TOTP+SPEP
  3446. Z SPE=-SPE*X1*FB*('K1'-1)**2/'K1'**2
  3447. Z SPEP=SPEP*(X2-X2**2)*('K1'-1)**2/'K1'**2
  3448. Nprint TOT,SPE,TOTP,SPEP
  3449. Keep TOT,SPE,TOTP,SPEP
  3450. *next
  3451. ENDDO
  3452. Z TOT=TOT+SPE
  3453. Z TOTP=TOTP+SPEP
  3454. Nprint TOT,TOTP
  3455. Keep TOT,TOTP
  3456. *next
  3457. N 20,R20
  3458. B LGB,ROOT,FACT
  3459. X SP(X)=X+X**2/4+X**3/9+X**4/16+X**5/25+X**6/36+X**7/49
  3460.      +X**8/64+X**9/81+X**10/100+X**11/121+X**12/144
  3461. X LGP(X)=-X-X**2/2-X**3/3-X**4/4-X**5/5-X**6/6-X**7/7
  3462.      -X**8/8-X**9/9-X**10/10-X**11/11-X**12/12
  3463. C TOT=SPENCE(-X1/(1-B)), TOTP=SPENCE(X2-X2**2).
  3464. C POWERS OF X1 AND X2 HAVE BEEN COMPUTED USING X**2=B*X-B.
  3465. Z EXP=FACT*(-TOT+TOTP+2*SP(X2)-S2
  3466.   +(LGP(B)+LGP(X2))*(LGB+LGP(X2))
  3467.   +0.5*LGP(X1)*LGP(X1)-0.5*LGP(B)*LGP(B) )
  3468.   +SP(B)+LGB*LGP(B)-S2
  3469. *yep
  3470. Id,X1**N~=POW(N,X1)
  3471. Al,X2**N~=POW(N,X2)
  3472. *yep
  3473. Id,X1=0.5*B+0.5*ROOT
  3474. Al,X2=0.5*B-0.5*ROOT
  3475. Al,FACT=B/ROOT-1
  3476. Id,ROOT=0.
  3477. Al,ROOT**-1=0
  3478. Keep EXP
  3479. Punch EXP
  3480. *next
  3481. B EP,LGB,PI
  3482. F LG
  3483. C COMPUTE NOW F211(SM,SM,M), WITH B=M**2/SM**2.
  3484. Z F211=PI**4*(-2/EP**2+(1-2*GA-2*LG(SM))/EP
  3485.    -1/2-PI**2/12+GA-GA**2+(1-2*GA)*LG(SM)-LG(SM)*LG(SM)
  3486.    -EXP )
  3487. Z Exp=EXP
  3488. C GA=EULERS CONSTANT, CAN BE ABSORBED INTO LOG DEFINITION.
  3489. Id,GA=0
  3490. Keep F211
  3491. *next
  3492. Z Expp=F211
  3493. *begin
  3494. Write Exp
  3495. Write Expp
  3496. *end
  3497.