home *** CD-ROM | disk | FTP | other *** search
/ Frozen Fish 1: Amiga / FrozenFish-Apr94.iso / bbs / alib / d5xx / d568 / schoonschip.lha / Schoonschip / SDocsAMI.LZH / SDocsAMI / Vectors.e < prev    next >
Text File  |  1991-06-14  |  40KB  |  1,188 lines
  1. C Vectors 1. Consequence of flagpole addition to vector boson masses.
  2. C Vectors 2. Vector-boson self-energies, infinite parts.
  3. C Vectors 3. Vector-boson self-energies. Comparison of various expressions.
  4. C Vectors 4. Photon-W0 ward identity.
  5. C Vectors 5. Neutral vector boson ward identity.
  6. C Vectors 6. Photon ward identity.
  7. C Vectors 7. Charged vector boson ward identity.
  8. C Vectors 8. Vector boson - vector boson scattering. Tree diagrams.
  9. C Vectors 9. Vector boson box diagram.
  10. C Vectors 10. Example of a gauge field theory. One loop poles.
  11. *end
  12.  
  13. C Vectors 1. Consequence of flagpole addition to vector boson masses.
  14.  
  15. C  CONSEQUENCE OF FLAGPOLE ADDITION TO VECTOR BOSON MASSES,
  16. C  AND NEUTRINo-ELECTRON SCATTERING CROSS SECTION AT ZERO ENERGY.
  17. C  WCM2S IS THE SHIFT IN THE SQUARE OF THE CHARGED VECTOR BOSON MASS.
  18. C  W0M2S SIMILARLY FOR THE NEUTRAL VECTOR BOSON.
  19. C  WSG, WSZ, WSP AND WSGZ ARE THE SELF ENERGY ADDITIONS FOR PHOTON,
  20. C  NEUTRAL W, CHARGED W, AND PHOTON-NEUTRAL W TRANSITION.
  21. P stat
  22. S  MC,M0,MP,MU,MD,MT,MN
  23. F  LOG
  24. F  SGV,SZV,SWPV,SGZV
  25. B   DDPI2,GG2,PI2
  26. Z  WSG(AK2)=COUPW*SGV(AK2,TO2,BO2,HN2,TM2)
  27. Z  WSZ(AK2)=COUPW*SZV(AK2,TO2,BO2,HN2,TM2)
  28. Z  WSP(AK2)=COUPW*SECWV(AK2,TO2,BO2,HN2,TM2)
  29. Z  WSGZ(AK2)=COUPW*SGZV(AK2,TO2,BO2,HN2,TM2)
  30. Id,SGV(AK2~,MU~,MD~,MN~,MT~) = AK2*SNT**2*(8.*B21(AK2,MT,MT)
  31.       - 4.*B0(AK2,MT,MT)) + 4.*SNT**2*AK2/3.*(8.*B21(AK2,MU,MU)
  32.       - 4.*B0(AK2,MU,MU)) + AK2*SNT**2/3.*(8.*B21(AK2,MD,MD)
  33.       - 4.*B0(AK2,MD,MD))
  34. Al,SZV(AK2~,MU~,MD~,MN~,MT~)=AK2/16./CST**2*((4.*SNT**2-1.)**2+1)*
  35.       (8.*B21(AK2,MT,MT)-4.*B0(AK2,MT,MT))
  36.       + AK2/8./CST**2*(8.*B21(AK2,MN,MN)-4.*B0(AK2,MN,MN))
  37.       + AK2*3./16./CST**2*((1.-8./3.*SNT**2)**2+1)*(8.*B21(AK2,MU,MU)
  38.       - 4.*B0(AK2,MU,MU)) + 3.*AK2/16./CST**2*((4./3.*SNT**2-1.)**2+1)*
  39.       (8.*B21(AK2,MD,MD)-4.*B0(AK2,MD,MD))
  40.       -0.5/CST**2*(MT*B0(AK2,MT,MT)+3.*MU*B0(AK2,MU,MU)+
  41.          3.*MD*B0(AK2,MD,MD)+MN*B0(AK2,MN,MN))
  42. Al,SECWV(AK2~,MU~,MD~,MN~,MT~)=2.*AK2*(B21(AK2,MN,MT)+B1(AK2,MN,MT))
  43.       - MN*B0(AK2,MN,MT) + (MT-MN)*
  44.          B1(AK2,MN,MT)+6.*AK2*(B21(AK2,MU,MD)+B1(AK2,MU,MD))
  45.       + 3.*(MD-MU)*B1(AK2,MU,MD)-3.*MU*B0(AK2,MU,MD)
  46. Al,SGZV(AK2~,MU~,MD~,MN~,MT~) = -AK2*SNT/CST*(4.*SNT**2-1.)*
  47.       (2.*B21(AK2,MT,MT)-B0(AK2,MT,MT))
  48.       + 2.*AK2*SNT/CST*(1.-8.*SNT**2/3.)*(2.*B21(AK2,MU,MU)
  49.       - B0(AK2,MU,MU)) - AK2*SNT/CST*(4.*SNT**2/3.-1.)*
  50.       (2.*B21(AK2,MD,MD)-B0(AK2,MD,MD))
  51. Id,COUPW=GG2/16./PI2
  52. Id,Multi,SNT**2=1.-CST**2
  53. Id,Multi,CST**2=1.-SNT**2
  54. Id,Multi,SNT**2=1.-CST**2
  55. Id,SNT**-2*CST**-2=1./SNT**2+1./CST**2
  56. Id,Multi,SNT**2=1.-CST**2
  57. Id,Multi,CST**2=1.-SNT**2
  58. Id,Multi,SNT**2=1.-CST**2
  59. Keeo WSG,WSZ,WSP,WSGZ
  60. *next
  61. B   DDPI2,GG2,PI2
  62. Z  DELMA=WSP(AK2)-MC*CST*WSGZ(AK2)/AK2/SNT-MC*WSG(AK2)/AK2
  63. Z  W0AD=MC*SNT/CST**3*WSGZ(AK2)/AK2
  64. Z  ELNEU=2.*WSZ(AK2)*CST**2/MC-2.*WSP(AK2)/MC
  65. Id,AK2=0.
  66. Al,B0(AK2,M1~,M2~)=B0(0,M1,M2)
  67. Al,B1(AK2,M1~,M2~)=B1(0,M1,M2)
  68. Al,B21(AK2,M1~,M2~)=B21(0,M1,M2)
  69. Id,B0(0,M1~,M1~)=DDPI2-LOG(M1)
  70. Al,B1(0,M1~,M1~)=-DDPI2/2+LOG(M1)/2.
  71. Al,B21(0,M1~,M1~)=DDPI2/3.-LOG(M1)/3.
  72. Al,B0(0,0,M1~)=DDPI2-LOG(M1)+1
  73. Al,B1(0,0,M1~)=-DDPI2/2.+LOG(M1)/2.-0.25
  74. Al,B21(0,0,M1~)=DDPI2/3.-LOG(M1)/3.+1./9.
  75. Id,B0(0,M1~,M2~)=DDPI2-LOG(M2)-F1(M1,M2)
  76. Al,B1(0,M1~,M2~)=-DDPI2/2.+LOG(M2)/2.+0.5*F2(M1,M2)
  77. Al,B21(0,M1~,M2~)=DDPI2/3.-LOG(M2)/3.-F3(M1,M2)/3.
  78. C  F1(M1,M2) = FUNCTION F1 OF  Y = M1**2/(M1**2-M2**2)
  79. C  1/Y = 1 - M2**2/M1**2
  80. Id,F1(M1~,M2~)=(1.-M2/M1)*(0.5+F2(M1,M2))
  81. Id,F2(M1~,M2~)=(1.-M2/M1)*(1./3.+F3(M1,M2))
  82. *yep
  83. Id,3,BO2**N~*F3(TO2,BO2)=(F3(TO2,BO2)*TO2+(TO2-BO2)/3.
  84.       -TO2*F2(TO2,BO2))*BO2**N/BO2
  85. Al,3,TM2**N~*F3(HN2,TM2)=(F3(HN2,TM2)*HN2+(HN2-TM2)/3.
  86.       -HN2*F2(HN2,TM2))*TM2**N/TM2
  87. Id,2,BO2**N~*F2(TO2,BO2)=(F2(TO2,BO2)*TO2+(TO2-BO2)/2.
  88.       -TO2*F1(TO2,BO2))*BO2**N/BO2
  89. Al,2,TM2**N~*F2(HN2,TM2)=(F2(HN2,TM2)*HN2+(HN2-TM2)/2.
  90.        -HN2*F1(HN2,TM2))*TM2**N/TM2
  91. *yep
  92. Id,Multi,SNT**2=1.-CST**2
  93. Id,Multi,CST**2=1.-SNT**2
  94. Id,Multi,SNT**2=1.-CST**2
  95. Id,SNT**-2*CST**-2=1./SNT**2+1./CST**2
  96. Id,Multi,SNT**2=1.-CST**2
  97. Id,Multi,CST**2=1.-SNT**2
  98. Id,Multi,SNT**2=1.-CST**2
  99. Keep WSG,WSP,WSGZ,WSZ,DELMA,W0AD
  100. *next
  101. F  AA0
  102. Z  WCM2S=DELMA-WSP(-MC)
  103. Z  W0M2S=DELMA/CST**2+W0AD-WSZ(-M0)
  104. Id,Multi,M0=MC/CST**2
  105. Al,Multi,M0**-1=CST**2/MC
  106. Id,B21(AK2~,M1~,M2~)=-(-AA0(M2)-M1*B0(AK2,M1,M2)
  107.       - 2.*(M1-M2-AK2)*B1(AK2,M1,M2) - 0.5*(M1+M2+AK2/3.))/3./AK2
  108. Id,B1(AK2~,M1~,M2~)=(0.5*AA0(M1)-0.5*AA0(M2)+0.5*(M1-M2-AK2)*
  109.        B0(AK2,M1,M2))/AK2
  110. Id,AA0(M1~)=-M1*DDPI2+M1*LOG(M1)-M1
  111. Id,Multi,M0=MC/CST**2
  112. Al,Multi,M0**-1=CST**2/MC
  113. *yep
  114. B  DDPI2,GG2,PI2
  115. Id,B0(AK2~,M1~,0)=B0(AK2,0,M1)
  116. Id,B0(AK2~,M1~,M2~)=DDPI2-LOG(M2)+B0R(AK2,M1,M2)
  117. Id,LOG(TO2)=LOG(TO2,BO2)+LOG(BO2)
  118. Al,LOG(HN2)=LOG(HN2,TM2)+LOG(TM2)
  119. Id,Multi,SNT**2=1.-CST**2
  120. Id,Multi,CST**2=1.-SNT**2
  121. Id,Multi,SNT**2=1.-CST**2
  122. Id,SNT**-2*CST**-2=1./SNT**2+1./CST**2
  123. Id,Multi,SNT**2=1.-CST**2
  124. Id,Multi,CST**2=1.-SNT**2
  125. Id,Multi,SNT**2=1.-CST**2
  126. Keep WCM2S,W0M2S
  127. *next
  128. B  GG2,PI2
  129. Z  CONTC=WCM2S-HAC
  130. Z  CONT0=W0M2S-HA0
  131. Id,HAC=GG2/16./PI2*(4.*MC/9.-0.5*(TO2-BO2)**2/MC
  132.       -1./6.*(TM2-HN2)**2/MC+3./4.*(TO2-BO2)
  133.       +1./4.*(HN2-TM2)
  134.       +(-2./3.*MC-TO2+0.5*TO2*(TO2-BO2)/MC)*LOG(TO2,BO2)
  135.       +(-1./3.*HN2+1./6.*HN2*(HN2-TM2)/MC)*LOG(HN2,TM2)
  136.       +3./2.*TO2*F1(TO2,BO2)+0.5*HN2*F1(HN2,TM2)
  137.       +(-MC+0.5*(TO2-BO2)**2/MC+0.5*(TO2+BO2))*B0R(-MC,TO2,BO2)
  138.    +(-1./3.*MC+1./6.*(HN2-TM2)**2/MC+1./6.*(HN2+TM2))*B0R(-MC,HN2,TM2))
  139. Al,HA0=GG2/PI2/CST**2*(MC/108./CST**2*(8.*CST**4-10.*CST**2+5.)
  140.       +1./64.*(3.*(TO2-BO2)+HN2-TM2)
  141.       +1./16.*(-1./6.*MC/CST**2-3./2.*TO2)*LOG(TO2,BO2)
  142.       +1./16.*(1./6.*MC/CST**2-0.5*HN2)*LOG(HN2,TM2)
  143.       +1./32.*(3.*TO2*F1(TO2,BO2)+HN2*F1(HN2,TM2))
  144.       +(MC/288./CST**2*(-32.*CST**4+40.*CST**2-17.)
  145.       +TO2/288.*(-64.*CST**4+80.*CST**2-7.))*B0R(-M0,TO2,TO2)
  146.       +(MC/288./CST**2*(-8.*CST**4+4.*CST**2-5.)
  147.       +BO2/288.*(-16.*CST**4+8.*CST**2+17.))*B0R(-M0,BO2,BO2)
  148.       +1./96.*(-MC/CST**2+HN2)*B0R(-M0,HN2,HN2)
  149.       +1./96.*(MC/CST**2*(-8.*CST**4+12.*CST**2-5.)
  150.       +TM2*(-16.*CST**4+24.*CST**2-7.))*B0R(-M0,TM2,TM2))
  151. Keep WCM2S,W0M2S
  152. *next
  153. Z  WHM2S=WCM2S
  154. Z  WH0MS=W0M2S
  155. C  LIMIT OF HIGH EQUAL MASSES OF THE FERMIONS.
  156. Id,B0R(AK2~,M1~,M2~)=-AK2/6./M2
  157. Id,BO2=TO2
  158. Al,TM2=HN2
  159. Id,M0=MC/CST**2
  160. Al,Multi,M0**-1=CST**2/MC
  161. Id,Multi,BO2**-1=TO2**-1
  162. Al,Multi,TM2**-1=HN2**-1
  163. Al,LOG(TM2)=LOG(HN2)
  164. Al,LOG(TO2,BO2)=0.
  165. Al,F1(HN2,TM2)=0.
  166. Al,F1(TO2,BO2)=0.
  167. Keep WCM2S,W0M2S
  168. *next
  169. B  GG2,PI2,MC,M0
  170. Z  WCM2L=WCM2S
  171. Id,B0R(AK2~,M1~,M2~)=LOG(M2,-AK2)+2.
  172. Id,LOG(M1~,M2~)=LOG(M1,MC)-LOG(M2,MC)
  173. Id,LOG(M1~)=LOG(M1,MC)+LOG(MC)
  174. Id,LOG(MC,MC)=0.
  175. Keep WCM2S,W0M2S,WCM2L
  176. *next
  177. B  GG2,PI2,MC,M0
  178. Z  W0M2L=W0M2S
  179. Id,B0R(AK2~,M1~,M2~)=LOG(M2,-AK2)+2.
  180. Id,LOG(M1~,M2~)=LOG(M1,M0)-LOG(M2,M0)
  181. Id,LOG(M1~)=LOG(M1,M0)+LOG(M0)
  182. Id,LOG(M0,M0)=0.
  183. Keep WCM2S,W0M2S,WCM2L,W0M2L
  184. *next
  185. N  10,R0
  186. B  GG2,PI2,MC
  187. S  LCST2
  188. Z  WCM2N=WCM2L/2./MC1
  189. Z  W0M2N=W0M2L/2./MC1*CST
  190. Id,GG2*PI2**-1=0.0390389874
  191. Id,LOG(M1~,M0)=LOG(M1,MC)+LCST2
  192. Id,LOG(TO2,MC)=-11.44717349
  193. Al,LOG(BO2,MC)=-11.44717349
  194. Al,LOG(TM2,MC)=-23.8328534
  195. Id,Numer,CST2,0.762,CST,0.8729261134,MC,5.852269263E9
  196.      ,MC1,7.650012588851E4,LCST2,-0.2718087233
  197. Keep WCM2S,W0M2S,WCM2L,W0M2L
  198. *next
  199. N
  200. B  GG2,PI2,MC
  201. Z  CHECC=WCM2L-HANDC
  202. Z  CHEC0=W0M2L-HAND0
  203. Id,HANDC=-GG2*MC*PI2**-1*(5./36.+1./48.*(2.*LOG(TO2,MC)
  204.       +LOG(BO2,MC)+LOG(TM2,MC)) )
  205. Al,HAND0=-GG2*MC*PI2**-1*CST2**-2*(1./108.*(40.*CST2**2-50.*CST2+25.)
  206.       +1./72.*(8.*CST2**2-10.*CST2+5.)*LOG(TO2,M0)
  207.       +1./72.*(2.*CST2**2-CST2+0.5)*LOG(BO2,M0)
  208.       +1./48.*(4.*CST2**2-6.*CST2+3.)*LOG(TM2,M0))
  209. Id,CST2=CST**2
  210. Al,Multi,CST2**-1=CST**-2
  211. Id,Numer,TO2,0.,BO2,0.,HN2,0.,TM2,0.
  212. Keep WCM2S,W0M2S
  213. *next
  214. B  GG2,PI2
  215. Z  WCM2H=WCM2S
  216. Z   W0M2H=W0M2S
  217. Id,F1(HN2,TM2)=F1(TM2,HN2)+LOG(HN2,TM2)
  218. Al,B0R(AK2~,HN2,TM2)=B0R(AK2,TM2,HN2)-LOG(HN2,TM2)
  219. Id,LOG(HN2,TM2)=-LOG(TM2,HN2)
  220. Id,B0R(AK2~,M1~,M2~)=-F1(M1,M2)-AK2*INV(M1,M2)*(F1(M1,M2)-F2(M1,M2))
  221. Id,LOG(M1~,M2~)=(1.-M2/M1)*F1(M1,M2)+1.-M2/M1
  222. *yep
  223. Id,F1(M1~,M2~)=0.5*ANV(M1,M2)/M1+1./3.*(ANV(M1,M2)/M1)**2
  224.       +1./4.*(ANV(M1,M2)/M1)**3
  225. Al,F2(M1~,M2~)=1./3.*ANV(M1,M2)/M1+1./4.*(ANV(M1,M2)/M1)**2
  226.       +1./5.*(ANV(M1,M2)/M1)**3
  227. Id,Adiso,INV(M1~,M2~)*ANV(M1~,M2~)=1.
  228. Id,ANV(M1~,M2~)=M1-M2
  229. Id,LOG(HN2,TM2)=-LOG(TM2,HN2)
  230. Id,LOG(M1~,M2~)=1.-M2/M1+0.5*(1.-2.*M2/M1+M2**2/M1**2)
  231. Id,M0=MC/CST**2
  232. Al,Multi,M0**-1=CST**2/MC
  233. P output
  234. *yep
  235. B  GG2,PI2,EQ2,EL2
  236. Id,BO2=TO2+EQ2
  237. Al,TM2=HN2+EL2
  238. Id,TO2=BO2-EQ2
  239. Al,HN2=TM2-EL2
  240. *end
  241.  
  242. C Vectors 2. Vector-boson self-energies, infinite parts.
  243.  
  244. C  SELF-ENERGIES, INFINITE PARTS.
  245. C  ALSO  DM2, DMU, DE, DSNT2 CONSIDERATIONS.
  246. P stat
  247. F  SGV,SZV,SWPV,SGZV
  248. B   DDPI2,GG2,PI2
  249. Z  WSG=COUPW*(SG
  250.       +SGV(UP2,DO2,ELM2)+SGV(CH2,ST2,UM2)+SGV(TO2,BO2,TM2))
  251. Z  WSZ=COUPW*(SZ
  252.       +SZV(UP2,DO2,ELM2)+SZV(CH2,ST2,UM2)+SZV(TO2,BO2,TM2))
  253. Z  WSP=COUPW*(SWP
  254.       +SWPV(UP2,DO2,ELM2)+SWPV(CH2,ST2,UM2)+SWPV(TO2,BO2,TM2))
  255. Z  WSGZ=COUPW*(SGZ
  256.       +SGZV(UP2,DO2,ELM2)+SGZV(CH2,ST2,UM2)+SGZV(TO2,BO2,TM2))
  257. Id,SG=SNT2*S*(12.*(CB21+0.5*CB1)-4.*CB0-2./3.)
  258. Al,SZ=(12.*CST2-4.+CSTM2)*S*(CB21-0.25*CB0)
  259.        + S*(HZB21+HZB1+0.25*HZB0)/CST2
  260.        + (W0M2-HM2)*(0.5*HZB1+0.25*HZB0)/CST2 + W0M2*HZB0/CST2
  261.        + WCM2*(2./CST2-4.)*CB0 - 2.*S*CST2/3.-4.*S*CB0*CST2
  262. Al,SGZ=CST*SNT*((12.-2./CST2)*S*(CB21-0.25*CB0)
  263.         - (4.*S+2.*WCM2/CST2)*CB0 - 2.*S/3.)
  264. Al,   SWP=(8.*CST2+1.)*(S*(CNB21+CNB1+0.25*CNB0)
  265.         + (W0M2-WCM2)*(0.5*CNB1+0.25*CNB0))
  266.        + 8.*SNT2*(S*(CPB21+CPB1+0.25*CPB0)-WCM2*(0.5*CPB1+0.25*CPB0))
  267.        + S*(CHB21+CHB1+0.25*CHB0)+(WCM2-HM2)*(0.5*CHB1+0.25*CHB0)
  268.        + CNB0*(WCM2*(CSTM2-3.)-4.*S*CST2) - CPB0*SNT2*4.*S
  269.        + WCM2*CHB0-2.*S/3.
  270. Id,SGV(UP2~,DO2~,TM2~)=-S*SNT2*(8.*B21-4.*B0+32.*B21/3.-16.*B0/3.
  271.       +8.*B21/3.-4.*B0/3.)
  272. Al,SZV(UP2~,DO2~,TM2~)=S*(-3.*((1.-8.*SNT**2/3.)**2+1.)*(8.*B21
  273.    -4.*B0)/16/CST**2 - 3.*((4.*SNT**2/3.-1.)**2+1.)
  274.      *(8.*B21-4.*B0)/16./CST**2) - 0.5*(3.*UP2*B0+3.*DO2*B0)/CST**2
  275.             +S*(-(8.*B21-4.*B0)/8./CST**2
  276.    - ((4.*SNT**2-1.)**2+1.)*(8.*B21-4.*B0)/16./CST**2)
  277.     - 0.5*(HN2*B0+TM2*B0)/CST**2
  278. Al,SWPV(UP2~,DO2~,TM2~)=-2.*S*(3.*B21+3.*B1)+3.*(DO2-UP2)*B1-3.*UP2*B0
  279.               -2.*S*(B21+B1)+(TM2-HN2)*B1-HN2*B0
  280. Al,SGZV(UP2~,DO2~,TM2~)=-S*SNT/CST*(2.*(1.-8.*SNT**2/3.)*(2.*B21-B0)
  281.       -(4.*SNT**2/3.-1.)*(2.*B21-B0))
  282.               -S*SNT/CST*(-(4.*SNT**2-1.)*(2.*B21-B0))
  283. Id,CB0=B0
  284. Al,CB1=B1
  285. Al,CB21=B21
  286. Al,HZB0=B0
  287. Al,HZB1=B1
  288. Al,HZB21=B21
  289. Al,CNB0=B0
  290. Al,CNB1=B1
  291. Al,CNB21=B21
  292. Al,CPB0=B0
  293. Al,CPB1=B1
  294. Al,CPB21=B21
  295. Id,CHB0=B0
  296. Al,CHB1=B1
  297. Al,CHB21=B21
  298. Al,W0M2=WCM2/CST**2
  299. Id,CSTM2=1./CST**2
  300. Al,COUPW=GG2/16./PI2
  301. Id,Multi,SNT**2=1.-CST**2
  302. Id,Multi,CST**2=1.-SNT**2
  303. Id,Multi,SNT**2=1.-CST**2
  304. Keep WSG,WSZ,WSP,WSGZ
  305. P output
  306. *next
  307. F  WV,WA,WNV
  308. S  ELM2,UM2
  309. B   DDPI2,GG2,PI2,S
  310. Z  DS2M=-(2.*DW0M*CST/WCM+DM2A)*CST**2/SNT**2
  311. Z  DS2=-0.25*(AA1*DBB-BB1*DAA)/SNT**2
  312. Z  WSGP=WSG
  313. Z  WSZP=WSZ
  314. Z  WSPP=WSP
  315. Z  WSGZP=WSGZ
  316. Z  DEWA=2.*DM2A-2.*DG2AF
  317. Z  DEW=DEWV+DEVX+DEBX+PRCOT
  318. Id,DG2AF=-0.5*DEC-DS2A
  319. Id,DS2A=-(2.*DW0M*CST/WCM+DM2A)*CST**2/SNT**2
  320. Id,DEC=DEWVC+DEVXC+PRCC+W0GC
  321. Id,DEWVC=4.*WV(ELM2)+4.*WV(UM2)
  322. Al,DEVXC=-DDPI2*(SNT**2-5/8/CST**2-0.25)*4.*GG2/16/PI2
  323.      +2.*GG2*0.375*DDPI2*(UM2+ELM2)/16/PI2/WCM2
  324. Al,PRCC=-2.*WSG *SYBS
  325. Al,W0GC=-VT*WSGZ*SABS*CST/SNT/WCM2
  326. Id,DEWV=2.*(WV(UM2)+WA(UM2)+WV(ELM2)+WA(ELM2)+2.*WNV(UM2)+2.*WNV(ELM2))
  327. Al,DEVX=-(1.25+0.125/CST**2)*DDPI2*COFF
  328.         -(UM2+ELM2)*DDPI2/16/WCM2*COFF
  329. Al,DEBX=0.125*SNT**2*DDPI2*CFFF
  330. Al,PRCOT=2.*WSP *SIBS/WCM2
  331. Id,WV(ELM2~)=GG2*((VT**2+1.)*B1/8/CST**2+0.5*B1+0.75*ELM2*B1/WCM2)
  332.       /32./PI2
  333. Al,WA(ELM2~)=GG2*(-VT*B1/4/CST**2+0.5*B1-0.25*ELM2*B1/WCM2)/32/PI2
  334. Al,WNV(ELM2~)=GG2*(0.25*B1/CST**2+0.5*B1+ELM2*B1/4/WCM2)/32/PI2
  335. Id,COFF=-8.*GG2/16/PI2
  336. Al,CFFF=-2.*8.*GG2/16/PI2
  337. Id,S**N~*SIBS=0.
  338. Al,S**N~*SABS=0.
  339. Al,S**N~*SYBS=1.
  340. Id,SIBS=1
  341. Al,SYBS=0
  342. Al,SABS=1
  343. Al,VT=4.*SNT**2-1
  344. Id,DAA=2.*BB1*WEA+RESA*COF+VTNG
  345. Al,DBB=2.*AA1*WEA+RESB*COF
  346. Id,RESA=CST*(SNT**2+0.5+9./16./CST**4 -7./4./CST**2)*ALDEL
  347.       -(12.*SNT**2-2.)*ELM2/32./WCM2/CST*DDPI2
  348. Al,RESB=CST*(-1.5-7./16./CST**4+5./4./CST**2)*ALDEL
  349.       -(-4.*SNT**2-2.)*ELM2/32./WCM2/CST*DDPI2
  350. Id,COF=-GG2*CST/4./PI2
  351. Id,WEA=GG2*(-(4.*SNT**2-1)*B1/4/CST**2+0.5*B1-0.25*ELM2/WCM2*B1)
  352.      /32/PI2
  353. *yep
  354. Id,VTNG=(3.*C24-C24)*16.*WCM2*GG2/16./PI2/S*SNT**2
  355.     + 4.*CST*SNT*(WSGZ+S*WSGZ*CST**2/WCM2)/S
  356. Id,AA1=4.*SNT**2-1.
  357. Al,BB1=-1.
  358. Al,C24=0.25*DDPI2
  359. Id,DM2A=-2.*DWCM/WCM
  360. Id,DWCM=-0.5*WSP*SUBS/WCM
  361. Al,DW0M=-0.5*WSZ*CST*SABS/WCM
  362. Id,S**N~*SUBS=WCM2**N
  363. Al,S**N~*SABS=WCM2**N/CST**N/CST**N
  364. Id,SUBS=1.
  365. Al,SABS=1.
  366. Id,Multi,WCM**-2=1./WCM2
  367. Al,Multi,WCM**2=WCM2
  368. Id,ALDEL=-DDPI2
  369. Id,B0=DDPI2
  370. Al,B1=-DDPI2/2.
  371. Al,B21=DDPI2/3.
  372. Al,CB0=DDPI2
  373. Al,CB1=-DDPI2/2.
  374. Al,CB21=DDPI2/3.
  375. Id,GG2*DDPI2=GG3
  376. Id,GG2=0.
  377. Id,GG3=GG2*DDPI2
  378. Id,Multi,SNT2=SNT**2
  379. Al,Multi,CST2=CST**2
  380. Al,Multi,SNT2**-1=SNT**-2
  381. Al,Multi,CST2**-1=CST**-2
  382. Id,SNT**-2*CST**-2=1./SNT**2+1./CST**2
  383. Id,Multi,SNT**2=1-CST**2
  384. Id,Multi,CST**2=1.-SNT**2
  385. Id,Multi,SNT**2=1-CST**2
  386. Id,SNT**-2*CST**-2=1./SNT**2+1./CST**2
  387. P output
  388. Keep DS2M,DS2,DEW,DEWA
  389. *next
  390. B  DDPI2,GG2,PI2,S
  391. Z  DS22=DS2-DS2M
  392. Id,Multi,SNT**2=1.-CST**2
  393. Id,Multi,CST**2=1.-SNT**2
  394. Id,Multi,SNT**2=1-CST**2
  395. Keep DEW,DEWA
  396. *next
  397. B  DDPI2,GG2,PI2,S
  398. Z  DEWX=DEW-DEWA
  399. *end
  400.  
  401. C Vectors 3. Vector-boson self-energies. Comparison of various expressions.
  402.  
  403. P stat
  404. S  K2,M,M0,ME,MH,MN,MP
  405. F   B21,B1,B0
  406. Z  SG=SNT2*S*(12.*(CB21+0.5*CB1)-4.*CB0-2./3.)
  407.        -S*SNT2*(8.*EB21+4.*EB1-2.*EB0)
  408. Z   SGT = SNT2*( - K2*(12*B21(M,M) - 7*B0(M,M) - 2/3)
  409.       + K2*(8*B21(ME,ME)-4*B0(ME,ME)) )
  410. Z   SGP=SNT2*EA1C
  411.        +2.*SNT2*CA2
  412.        +2.*SNT2*WCM2*CB0
  413.        +4.*SNT2*CB22
  414.         -2.*SNT2*CB22
  415.         -2.*SNT2*CA
  416.       +SNT2*(4.*EA-8.*EB22+2.*S*EB0)
  417. Z  SZ=(12.*CST2-4.+CSTM2)*S*(CB21-0.25*CB0)
  418.        + S*(HZB21+HZB1+0.25*HZB0)/CST2
  419.        + (W0M2-HM2)*(0.5*HZB1+0.25*HZB0)/CST2 + W0M2*HZB0/CST2
  420.        + WCM2*(2./CST2-4.)*CB0 - 2.*S*CST2/3.-4.*S*CB0*CST2
  421.        -S*((4.*SNT2-1.)**2+1.)*(8.*EB21+4.*EB1-2.*EB0)/16./CST2
  422.        - 0.5*EM2*EB0/CST2-0.125*S*(8.*OB21+4.*OB1-2.*OB0)/CST2
  423. Z   SZT = K2*(4-1/CST2 - 12*CST2)*B21(M,M) + 2*K2*CST2/3
  424.       + (K2*(7*CST2-1+0.25/CST2) + WCM2*(2/CST2-4))*B0(M,M)
  425.       - K2/CST2*B21(M0,MH)
  426.       + 0.5*(W0M2-HM2-2*K2)/CST2*B1(M0,MH)
  427.       + 0.25*(5*W0M2-HM2-K2)/CST2*B0(M0,MH)
  428.       + K2/16/CST2*((4*SNT2-1)**2+1)*(8*B21(ME,ME)-4*B0(ME,ME))
  429.       + K2/8/CST2*(8*B21(MN,MN)-4*B0(MN,MN))
  430.       - EM2/2/CST2*B0(ME,ME)
  431. Z   SZP=CST2*EA1C
  432.        +2.*CST2*CA2
  433.        +2.*SNT4*CSTM2*WCM2*CB0
  434.        +CSTM4*WCM2*HNB0
  435.        +CSTM2*HNB22
  436.        +CSTM2*(CST2-SNT2)**2*CB22
  437.         -2.*CST2*CB22
  438.         -0.25*CSTM2*(HA+NA)+2.*(SNT2-0.25*CSTM2)*CA
  439.        +1./16./CST2*(-16.*OB22+4.*S*OB0)
  440.     + 0.25/CST2*(                      -2.*((4.*SNT2-1.)**2+1.)*EB22
  441.        +EM2*((4.*SNT2-1.)**2-1.)*EB0+0.5*((4.*SNT2-1)**2+1.)
  442.         *(2.*EA-(2.*EM2-S)*EB0)    )
  443. Z  SGZ=CST*SNT*((12.-2./CST2)*S*(CB21-0.25*CB0)
  444.         - (4.*S+2.*WCM2/CST2)*CB0 - 2.*S/3.)
  445.        + SNT*CST*(4.*SNT2-1.)*S*(8.*EB21+4.*EB1-2.*EB0) /4./CST2
  446. Z   SGZT = K2*SNT*(2/CST - 12*CST)*B21(M,M)
  447.       + SNT*(7*K2*CST - K2/2/CST - 2*WCM2/CST)*B0(M,M) + 2*K2/3*SNT*CST
  448.       - K2*SNT/CST*(4*SNT2-1)*(2*B21(ME,ME) - B0(ME,ME))
  449. Z  SGZP =CST*SNT*EA1C
  450.         +2.*SNT*CST*CA2
  451.          -2.*SNT3*CSTM1*WCM2*CB0
  452.         +2.*SNT*CSTM1*(CST2-SNT2)*CB22
  453.          -2.*SNT*CST*CB22
  454.         +SNT*CSTM1*(SNT2-CST2)*CA
  455.        +2.*SNT*CST/CST2*(4.*SNT2-1.)*EB22
  456.        - SNT*CST/CST2*(4.*SNT2-1.)*EA
  457.       - 0.5*SNT*CST/CST2*(4.*SNT2-1.)*S*EB0
  458. Z     SWP=(8.*CST2+1.)*(S*(CNB21+CNB1+0.25*CNB0)
  459.         + (W0M2-WCM2)*(0.5*CNB1+0.25*CNB0))
  460.        + 8.*SNT2*(S*(CPB21+CPB1+0.25*CPB0)-WCM2*(0.5*CPB1+0.25*CPB0))
  461.        + S*(CHB21+CHB1+0.25*CHB0)+(WCM2-HM2)*(0.5*CHB1+0.25*CHB0)
  462.        + CNB0*(WCM2*(CSTM2-3.)-4.*S*CST2) - CPB0*SNT2*4.*S
  463.        + WCM2*CHB0-2.*S/3.
  464.        -2.*S*(ENB21+ENB1+0.25*ENB0) + 2.*EM2*(0.5*ENB1+0.25*ENB0)
  465.       -0.5*(EM2-S)*ENB0
  466. Z   SWT = (8*CST2+1)*(-K2*B21(M0,M) + 0.5*(W0M2-WCM2-2*K2)*(B1(M0,M)
  467.       + 0.5*B0(M0,M))
  468.       +0.25*K2*B0(M0,M))  + (WCM2*(1/CST2-3) + 4*K2*CST2)*B0(M0,M)
  469.       + 2*K2/3
  470.       - 8*SNT2*K2*(B21(MP,M) + B1(MP,M) - 0.25*B0(MP,M))
  471.       - 2*SNT2*WCM2*(2*B1(MP,M) + B0(MP,M))
  472.       - K2*B21(M,MH) + 0.5*(WCM2-HM2-2*K2)*B1(M,MH)
  473.       + 0.25*(5*WCM2 - HM2 - K2)*B0(M,MH)
  474.       + 2*K2*(B21(MN,ME) + B1(MN,ME)) + EM2*B1(MN,ME)
  475. Z  SWPW = -CST2*((W0M2+WCM2+4.*S)*CNB0-ZA-CA-10.*CNB22
  476.        -2.*(W0M2+WCM2-S/3.))
  477.              -SNT2*((WCM2+4.*S)*CPB0-CA-10.*CPB22-2.*(WCM2-S/3.))
  478.       -3.*CA-2.*WCM2 + CST2*(-3.*ZA-2.*W0M2)
  479.   +       WCM2*(SNT4*CNB0/CST2+SNT2*CPB0)
  480.         + WCM2*CHB0
  481.        + CHB22
  482.       +CNB22
  483.           -2.*(CST2*CNB22+SNT2*CPB22)
  484.           -0.25*(ZA+HA+2.*CA)
  485.       + 0.25*(-8.*ENB22+2.*EA-2.*(EM2-S)*ENB0)
  486. Id   HNB21=HZB21
  487. Al  HNB22=HZB22
  488. Al   HNB1=HZB1
  489. Al   HNB0=HZB0
  490. Al  NA=ZA
  491. Id   K2 = - S
  492. Id  B21(M,M)=CB21
  493. Al   B1(M,M) = CB1
  494. Al   B0(M,M) = CB0
  495. Id   B21(ME,ME) = EB21
  496. Al   B1(ME,ME) = EB1
  497. Al   B0(ME,ME) = EB0
  498. Id   B21(M0,MH) = HZB21
  499. Al    B1(M0,MH) = HZB1
  500. Al   B0(M0,MH) = HZB0
  501. Id   B21(MN,MN) = OB21
  502. Al   B1(MN,MN) = OB1
  503. Al   B0(MN,MN) = OB0
  504. Id   B21(M0,M) = CNB21
  505. Al   B1(M0,M) = CNB1
  506. Al   B0(M0,M) = CNB0
  507. Id   B21(MP,M) = CPB21
  508. Al   B1(MP,M) = CPB1
  509. Al   B0(MP,M) = CPB0
  510. Id   B21(M,MH) = CHB21
  511. Al   B1(M,MH) = CHB1
  512. Al   B0(M,MH) = CHB0
  513. Id   B21(MN,ME) = ENB21
  514. Al   B1(MN,ME) = ENB1
  515. Al   B0(MN,ME) = ENB0
  516. *yep
  517. Id  ALF2=0.25*HM2/WCM2
  518. Id  EA1C=-2.*((WCM2+2.*S)*CB0-CA-5.*CB22- (-1./3.*S+2.*WCM2))
  519. Al  EB1C=-2.*(-5.*CB21-5.*CB1+CB0+1./3.)
  520. Al  EH2NH=2.*NA-HA+(W0M2-2.*HM2-2.*S)*HNB0
  521. Id  ER1C=CB1+2.*CB0
  522. Al  ER1NH=HNB1+2.*HNB0
  523. Al  ER3NH=HNB0+2.*HNB1
  524. Al  CA2=-3.*CA-2.*WCM2
  525. Al  W0M2=WCM2/CST2
  526. Id  SNT2=1.-CST2
  527. Al  SNT4=(1.-CST2)**2
  528. Al  SNT3=SNT**3
  529. Id  C2S22=(2.*CST2-1.)**2
  530. Al  CSTM1=1./CST
  531. Al  CSTM2=1./CST2
  532. Al  CSTM3=1./CST**3
  533. Al  CSTM4=1./CST2**2
  534. Id  CST2=CST**2
  535. Al,Multi,CST2**-1=CST**-2
  536. Id,Multi,SNT**2=1-CST**2
  537. Id  CB22=(0.5*CA-WCM2*CB0-0.5*S*CB1-0.5*(2.*WCM2-S/3))/3
  538. Al  EB22=(0.5*EA-EM2*EB0-0.5*S*EB1-0.5*(2.*EM2-S/3.))/3.
  539. Al CNB22=(0.5*CA-W0M2*CNB0-0.5*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3
  540. Al  CHB22=(0.5*HA-WCM2*CHB0-0.5*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3
  541. Al  HZB22=(0.5*HA-W0M2*HZB0-0.5*(W0M2-HM2+S)*HZB1-0.5*(W0M2+HM2-S/3))/3
  542. Al  CPB22=(0.5*CA-0.5*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3
  543. Al  ENB22=(0.5*EA-0.5*(-EM2+S)*ENB1-0.5*(EM2-S/3.))/3.
  544. Al  OB22=(-0.5*S*OB1+S/6.)/3.
  545. Id  CB21=(-CA-WCM2*CB0-2.*S*CB1-0.5*(2.*WCM2-S/3.))/3/S
  546. Al  EB21=(-EA-EM2*EB0-2.*S*EB1-0.5*(2.*EM2-S/3.))/3/S
  547. Al  CNB21=(-CA-W0M2*CNB0-2*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3/S
  548. Al  CPB21=(-CA-2.*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3/S
  549. Al  ENB21=(-EA-2.*(-EM2+S)*ENB1-0.5*(EM2-S/3.))/3./S
  550. Al  OB21=(-2.*S*OB1+S/6.)/3./S
  551. Al  CHB21=(-HA-WCM2*CHB0-2.*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3/S
  552. Al  HZB21=(-HA-W0M2*HZB0-2.*(W0M2-HM2+S)*HZB1-0.5*(W0M2+HM2-S/3))/3/S
  553. Id  CB1= - 0.5*CB0
  554. Al  EB1=-0.5*EB0
  555. Al  CNB1=-(0.5*ZA-0.5*CA+0.5*(W0M2-WCM2+S)*CNB0)/S
  556. Al  CHB1=-(0.5*CA-0.5*HA+0.5*(WCM2-HM2+S)*CHB0)/S
  557. Al  HZB1=-(0.5*ZA-0.5*HA+0.5*(W0M2-HM2+S)*HZB0)/S
  558. Al  CPB1=-(-0.5*CA+0.5*(-WCM2+S)*CPB0)/S
  559. Al  ENB1=-(-0.5*EA+0.5*(-EM2+S)*ENB0)/S
  560. Al  OB1=-0.5*OB0
  561. Id  W0M2=WCM2/CST**2
  562. Keep SZ,SZT,SZP,SG,SGT,SGP,SGZ,SGZT,SGZP,SWP,SWT,SWPW
  563. P noutp
  564. *next
  565. P output
  566. Z  SGG=SG-SGP
  567. Z   SZZ=SZ-SZP
  568. Z  SGZZ=SGZ-SGZP
  569. Z  SWPP=SWP-SWPW
  570. Z   VER1=SGT-SGP
  571. Z   VER2=SZT-SZP
  572. Z   VER3=SGZT-SGZP
  573. Z    VER4=SWT-SWPW
  574. *end
  575.  
  576. C Vectors 4. Photon-W0 ward identity.
  577.  
  578. P stats
  579. C  NOTATIONS ARE  N=NEUTRAL,C=CHARGED,P=PHOTON,H=HIGGS,R=MIXING
  580. C      S=-K**2
  581. Z  EANP1=CST*SNT*EA1C
  582. Z  EBNP1=CST*SNT*EB1C
  583. Z  EANP2=2.*SNT*CST*CA2
  584. Z  EANP3=-2.*SNT3*CSTM1*WCM2*CB0
  585. Z  EANP6=2.*SNT*CSTM1*(CST2-SNT2)*CB22
  586. Z  EBNP6=0.5*SNT*CSTM1*(CST2-SNT2)*(CB0+4.*CB1+4.*CB21)
  587. Z  EANP7=-2.*SNT*CST*CB22
  588. Z  EBNP7=-2.*CST*SNT*(CB1+CB21)
  589. Z  EANP8=SNT*CSTM1*(SNT2-CST2)*CA
  590. Z  ERP1=SNT*ER1C
  591. Z  ERP4=-SNT*CB1
  592. Id  ALF2=0.25*HM2/WCM2
  593. Id  EA1C=-2.*((WCM2+2.*S)*CB0-CA-5.*CB22- (-1./3.*S+2.*WCM2))
  594. Id  EB1C=-2.*(-5.*CB21-5.*CB1+CB0+1./3.)
  595. Id  EH2NH=2.*NA-HA+(W0M2-2.*HM2-2.*S)*HNB0
  596. Id  ER1C=CB1+2.*CB0
  597. Id  ER1NH=HNB1+2.*HNB0
  598. Id  ER3NH=HNB0+2.*HNB1
  599. Id  CA2=-3.*CA-2.*WCM2
  600. Id  W0M2=WCM2/CST2
  601. Id  SNT2=1.-CST2
  602. Al  SNT4=(1.-CST2)**2
  603. Id  SNT3=SNT**3
  604. Id  CSTM1=1./CST
  605. Id  CSTM2=1./CST2
  606. Al  CSTM4=1./CST2**2
  607. Id  CSTM3=1./CST**3
  608. Id  CST2=CST**2
  609. Id,Multi,CST2**-1=CST**-2
  610. Id  CB22=(0.5*CA-WCM2*CB0-0.5*S*CB1-0.5*(2.*WCM2-S/3))/3
  611. Al CNB22=(0.5*CA-W0M2*CNB0-0.5*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3
  612. Al  CHB22=(0.5*HA-WCM2*CHB0-0.5*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3
  613. Al  HNB22=(0.5*HA-W0M2*HNB0-0.5*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3
  614. Al  CPB22=(0.5*CA-0.5*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3
  615. Id  CB21=(-CA-WCM2*CB0-2.*S*CB1-0.5*(2.*WCM2-S/3.))/3/S
  616. Al  CNB21=(-CA-W0M2*CNB0-2*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3/S
  617. Al  CPB21=(-CA-2.*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3/S
  618. Al  CHB21=(-HA-WCM2*CHB0-2.*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3/S
  619. Al  HNB21=(-HA-W0M2*HNB0-2.*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3/S
  620. Id  CB1= - 0.5*CB0
  621. Al  CNB1=-(0.5*NA-0.5*CA+0.5*(W0M2-WCM2+S)*CNB0)/S
  622. Al  CHB1=-(0.5*CA-0.5*HA+0.5*(WCM2-HM2+S)*CHB0)/S
  623. Al  HNB1=-(0.5*NA-0.5*HA+0.5*(W0M2-HM2+S)*HNB0)/S
  624. Al  CPB1=-(-0.5*CA+0.5*(-WCM2+S)*CPB0)/S
  625. Id  W0M2=WCM2/CST**2
  626. Keep  EANP1,EBNP1,EANP2,EANP3,EANP6,EBNP6,EANP7,EBNP7,
  627.     EANP8,ERP1,ERP4
  628. *next
  629. Z  REANP=-S*(EANP1+EANP2+EANP3+EANP6+EANP7+EANP8)
  630. Z  REBNP=S**2*(EBNP1+EBNP6+EBNP7)
  631. Z  RERNP=-S*WCM2/CST*(ERP1+ERP4)
  632. Keep  REANP,REBNP,RERNP
  633. *next
  634. Z  RESNP=REANP+REBNP+RERNP
  635. Id  SNT**3=SNT-SNT*CST**2
  636. *end
  637.  
  638. C Vectors 5. Neutral vector boson ward identity.
  639.  
  640. P stats
  641. C  NOTATIONS ARE  N=NEUTRAL,C=CHARGED,P=PHOTON,H=HIGGS,R=MIXING
  642. C      S=-K**2
  643. Z  EAN1=CST2*EA1C
  644. Z  EBN1=CST2*EB1C
  645. Z  EAN2=2.*CST2*CA2
  646. Z  EAN3=2.*SNT4*CSTM2*WCM2*CB0
  647. Z  EAN4=CSTM4*WCM2*HNB0
  648. Z  EAN5=CSTM2*HNB22
  649. Z  EBN5=0.25*CSTM2*(HNB0+4.*HNB1+4.*HNB21)
  650. Z  EAN6=CSTM2*(CST2-SNT2)**2*CB22
  651. Z  EBN6=0.25*CSTM2*(CST2-SNT2)**2*(CB0+4.*CB1+4.*CB21)
  652. Z  EAN7=-2.*CST2*CB22
  653. Z  EBN7=-2.*CST2*(CB1+CB21)
  654. Z  EAN8=-0.25*CSTM2*(HA+NA)+2.*(SNT2-0.25*CSTM2)*CA
  655. Z  EATA=-ALF2*(NA+2.*CA)+CA+0.5*CSTM2*NA-4.*CA
  656.     -2.*CSTM2*NA-2.*WCM2-CSTM2*W0M2-3.*ALF2*HA
  657. Z  EHN2=0.5*(CA-2.*(S+0.5*WCM2)*CB0)
  658. Z  EHN3=0.25*CSTM2*EH2NH
  659. Z  EHN5=4.*ALF2**2*WCM2*HNB0
  660. Z  EHN6=0.5*WCM2*CB0
  661. Z  EHN7=-CSTM2*(NA+0.5*W0M2)-2.*CA-WCM2
  662. Z  EHN8=-0.5*ALF2*HA
  663. Z  EHN9=-ALF2*CA-3./2.*ALF2*NA
  664. Z  ERN1=-SNT2*CSTM1*ER1C
  665. Z  ERN2=-0.5*CSTM3*ER1NH
  666. Z  ERN3=ALF2*CSTM1*ER3NH
  667. Z  ERN4=-CST*CB1
  668. Id  ALF2=0.25*HM2/WCM2
  669. Id  EA1C=-2.*((WCM2+2.*S)*CB0-CA-5.*CB22- (-1./3.*S+2.*WCM2))
  670. Id  EB1C=-2.*(-5.*CB21-5.*CB1+CB0+1./3.)
  671. Id  EH2NH=2.*NA-HA+(W0M2-2.*HM2-2.*S)*HNB0
  672. Id  ER1C=CB1+2.*CB0
  673. Id  ER1NH=HNB1+2.*HNB0
  674. Id  ER3NH=HNB0+2.*HNB1
  675. Id  CA2=-3.*CA-2.*WCM2
  676. Id  W0M2=WCM2/CST2
  677. Id  SNT2=1.-CST2
  678. Al  SNT4=(1.-CST2)**2
  679. Id  SNT3=SNT**3
  680. Id  CSTM1=1./CST
  681. Id  CSTM2=1./CST2
  682. Al  CSTM4=1./CST2**2
  683. Id  CSTM3=1./CST**3
  684. Id  CST2=CST**2
  685. Id,Multi,CST2**-1=CST**-2
  686. Id  CB22=(0.5*CA-WCM2*CB0-0.5*S*CB1-0.5*(2.*WCM2-S/3))/3
  687. Al CNB22=(0.5*CA-W0M2*CNB0-0.5*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3
  688. Al  CHB22=(0.5*HA-WCM2*CHB0-0.5*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3
  689. Al  HNB22=(0.5*HA-W0M2*HNB0-0.5*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3
  690. Al  CPB22=(0.5*CA-0.5*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3
  691. Id  CB21=(-CA-WCM2*CB0-2.*S*CB1-0.5*(2.*WCM2-S/3.))/3/S
  692. Al  CNB21=(-CA-W0M2*CNB0-2*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3/S
  693. Al  CPB21=(-CA-2.*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3/S
  694. Al  CHB21=(-HA-WCM2*CHB0-2.*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3/S
  695. Al  HNB21=(-HA-W0M2*HNB0-2.*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3/S
  696. Id  CB1= - 0.5*CB0
  697. Al  CNB1=-(0.5*NA-0.5*CA+0.5*(W0M2-WCM2+S)*CNB0)/S
  698. Al  CHB1=-(0.5*CA-0.5*HA+0.5*(WCM2-HM2+S)*CHB0)/S
  699. Al  HNB1=-(0.5*NA-0.5*HA+0.5*(W0M2-HM2+S)*HNB0)/S
  700. Al  CPB1=-(-0.5*CA+0.5*(-WCM2+S)*CPB0)/S
  701. Id  W0M2=WCM2/CST**2
  702. Keep  EAN1,EBN1,EAN2,EAN3,EAN4,EAN5,EBN5,EAN6,EBN6,EAN7,
  703.     EBN7,EAN8,EATA,EHN2,EHN3,EHN5,EHN6,EHN7,EHN8,EHN9,ERN1,
  704.    ERN2,ERN3,ERN4
  705. *next
  706. Z  RESAN=-S*(EAN1+EAN2+EAN3+EAN4+EAN5+EAN6+EAN7+EAN8)
  707. Z  RESBN=S**2*(EBN1+EBN5+EBN6+EBN7)
  708. Z  RESHN=W0M2*(EHN2+EHN3+EHN5+EHN6+EHN7+EHN8+EHN9)-0.5*W0M2*EATA
  709. Z     RESRN=-2.*WCM2/CST*S*(ERN1+ERN2+ERN3+ERN4)
  710. Id  W0M2=WCM2/CST**2
  711. Keep  RESAN,RESBN,RESHN,RESRN
  712. *next
  713. Z  RESN=RESAN+RESBN+RESHN+RESRN
  714. *end
  715.  
  716. C Vectors 6. Photon ward identity.
  717.  
  718. P stats
  719. C  NOTATIONS ARE  N=NEUTRAL,C=CHARGED,P=PHOTON,H=HIGGS,R=MIXING
  720. C      S=-K**2
  721. Z  EAP1=SNT2*EA1C
  722. Z  EBP1=SNT2*EB1C
  723. Z  EAP2=2.*SNT2*CA2
  724. Z  EAP3=2.*SNT2*WCM2*CB0
  725. Z  EAP6=4.*SNT2*CB22
  726. Z  EBP6=SNT2*(CB0+4.*CB1+4.*CB21)
  727. Z  EAP7=-2.*SNT2*CB22
  728. Z  EBP7=-2.*SNT2*(CB1+CB21)
  729. Z  EAP8=-2.*SNT2*CA
  730. Id  ALF2=0.25*HM2/WCM2
  731. Id  EA1C=-2.*((WCM2+2.*S)*CB0-CA-5.*CB22- (-1./3.*S+2.*WCM2))
  732. Id  EB1C=-2.*(-5.*CB21-5.*CB1+CB0+1./3.)
  733. Id  EH2NH=2.*NA-HA+(W0M2-2.*HM2-2.*S)*HNB0
  734. Id  ER1C=CB1+2.*CB0
  735. Id  ER1NH=HNB1+2.*HNB0
  736. Id  ER3NH=HNB0+2.*HNB1
  737. Id  CA2=-3.*CA-2.*WCM2
  738. Id  W0M2=WCM2/CST2
  739. Id  SNT2=1.-CST2
  740. Al  SNT4=(1.-CST2)**2
  741. Id  SNT3=SNT**3
  742. Id  CSTM1=1./CST
  743. Id  CSTM2=1./CST2
  744. Al  CSTM4=1./CST2**2
  745. Id  CSTM3=1./CST**3
  746. Id  CST2=CST**2
  747. Id,Multi,CST2**-1=CST**-2
  748. Id  CB22=(0.5*CA-WCM2*CB0-0.5*S*CB1-0.5*(2.*WCM2-S/3))/3
  749. Al CNB22=(0.5*CA-W0M2*CNB0-0.5*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3
  750. Al  CHB22=(0.5*HA-WCM2*CHB0-0.5*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3
  751. Al  HNB22=(0.5*HA-W0M2*HNB0-0.5*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3
  752. Al  CPB22=(0.5*CA-0.5*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3
  753. Id  CB21=(-CA-WCM2*CB0-2.*S*CB1-0.5*(2.*WCM2-S/3.))/3/S
  754. Al  CNB21=(-CA-W0M2*CNB0-2*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3/S
  755. Al  CPB21=(-CA-2.*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3/S
  756. Al  CHB21=(-HA-WCM2*CHB0-2.*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3/S
  757. Al  HNB21=(-HA-W0M2*HNB0-2.*(W0M2-HM2+S)*HNB1-0.5*(W0M2+HM2-S/3))/3/S
  758. Id  CB1= - 0.5*CB0
  759. Al  CNB1=-(0.5*NA-0.5*CA+0.5*(W0M2-WCM2+S)*CNB0)/S
  760. Al  CHB1=-(0.5*CA-0.5*HA+0.5*(WCM2-HM2+S)*CHB0)/S
  761. Al  HNB1=-(0.5*NA-0.5*HA+0.5*(W0M2-HM2+S)*HNB0)/S
  762. Al  CPB1=-(-0.5*CA+0.5*(-WCM2+S)*CPB0)/S
  763. Id  W0M2=WCM2/CST**2
  764. Keep  EAP1,EBP1,EAP2,EAP3,EAP6,EAP7,EBP6,EBP7,EAP8
  765. *next
  766. Z  RESAP=EAP1+EAP2+EAP3+EAP6+EAP7+EAP8
  767. Z  RESBP=-S*(EBP1+EBP6+EBP7)
  768. Keep  RESAP,RESBP
  769. *next
  770. Z  RESP=RESAP+RESBP
  771. *end
  772.  
  773. C Vectors 7. Charged vector boson ward identity.
  774.  
  775. P stats
  776. B  DEL
  777. Z  EA1=
  778.           -CST2*((W0M2+WCM2+4.*S)*CNB0-ZA-CA-10.*CNB22
  779.        -2.*(W0M2+WCM2-S/3.))
  780.              -SNT2*((WCM2+4.*S)*CPB0-CA-10.*CPB22-2.*(WCM2-S/3.))
  781. Z  EB1=
  782.           -CST2*(-10.*CNB21-10.*CNB1+2.*CNB0+2./3.)
  783.              -SNT2*(-10.*CPB21-10.*CPB1+2.*CPB0+2./3.)
  784. Z  EA2 =
  785.       -3.*CA-2.*WCM2 + CST2*(-3.*ZA-2.*W0M2)
  786. Z  EA3 =
  787.           WCM2*(SNT4*CNB0/CST2+SNT2*CPB0)
  788. Z   EA4 = WCM2*CHB0
  789. Z  EA5 = CHB22
  790. Z  EB5 = 0.25*CHB0+CHB1+CHB21
  791. Z  EA6=CNB22
  792. Z  EB6=0.25*CNB0+CNB1+CNB21
  793. Z  EA7 =  -2.*(CST2*CNB22+SNT2*CPB22)
  794. Z  EB7 =  -2.*(CST2*CNB1+SNT2*CPB1+CST2*CNB21+SNT2*CPB21)
  795. Z  EA8 =  -0.25*(ZA+HA+2.*CA)
  796. Z  EATA=-ALF2*(ZA+2.*CA) + CA+0.5*ZA/CST2 -4.*CA-2.*ZA/CST2
  797.     -2.*WCM2-W0M2/CST2
  798.    -3.*ALF2*HA
  799. Z  EH1 =  WCM2*(4.*SNT4*CNB0/CST2+4.*SNT2*CPB0-2.*SNT4/CST2-2.*SNT2)
  800. Z  EH2  = C2S22*0.25*(2.*ZA-CA+(W0M2-2.*WCM2-2.*S)*CNB0)/CST2
  801.         +SNT2*(-CA-2.*(WCM2+S)*CPB0)
  802.        +0.25*(2.*CA-ZA + (WCM2-2.*W0M2-2.*S)*CNB0)
  803. Z  EH3 =  0.25*(2.*CA-HA+(WCM2-2.*HM2-2.*S)*CHB0)
  804. Z  EH5 = 4.*ALF2**2*WCM2*CHB0
  805. Z  EH6=0.5*(CST2-SNT2)*CNB0*WCM2/CST2
  806. Z  EH7 = (SNT2-0.25/CST2)*(4.*ZA+2.*W0M2) -2.*CA - WCM2
  807. Z  EH8 = -0.5*ALF2*HA
  808. Z  EH9 =  -ALF2*(0.5*ZA+2.*CA)
  809. Z  ET1=0.5*SNT2*(CST2-SNT2)*(CNB1+2.*CNB0)/CST2-SNT2*(CPB1+2.*CPB0)
  810. Z  ET2 =   -(CHB0+0.5*CHB1)
  811. Z  ET3 =   ALF2*(CHB0+2.*CHB1)
  812. Z  ET4 =   CNB1+0.5*CNB0-CST2*CNB1-SNT2*CPB1
  813. Z  ET5= - SNT2*(3.*CNB0+6.*CNB1)+SNT2*(3.*CPB0+6.*CPB1)
  814. Id  SNT4=(1-CST2)**2
  815. Al  CST4=CST2**2
  816. Id  SNT2=1-CST2
  817. Id  CSTM4=1./CST2**2
  818. Al  CSTM2=1./CST2
  819. Id  ALF2=0.25*HM2/WCM2
  820. Al  C2S22=(2.*CST2-1.)**2
  821. Id  CB22=(0.5*CA-WCM2*CB0-0.5*S*CB1-0.5*(2.*WCM2-S/3))/3
  822. Al CNB22=(0.5*CA-W0M2*CNB0-0.5*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3
  823. Al  CHB22=(0.5*HA-WCM2*CHB0-0.5*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3
  824. Al  HZB22=(0.5*HA-W0M2*HZB0-0.5*(W0M2-HM2+S)*HZB1-0.5*(W0M2+HM2-S/3))/3
  825. Al  CPB22=(0.5*CA-0.5*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3
  826. Id  CB21=(-CA-WCM2*CB0-2.*S*CB1-0.5*(2.*WCM2-S/3.))/3/S
  827. Al  CNB21=(-CA-W0M2*CNB0-2*(W0M2-WCM2+S)*CNB1-0.5*(W0M2+WCM2-S/3))/3/S
  828. Al  CPB21=(-CA-2.*(-WCM2+S)*CPB1-0.5*(WCM2-S/3))/3/S
  829. Al  CHB21=(-HA-WCM2*CHB0-2.*(WCM2-HM2+S)*CHB1-0.5*(WCM2+HM2-S/3))/3/S
  830. Al  HZB21=(-HA-W0M2*HZB0-2.*(W0M2-HM2+S)*HZB1-0.5*(W0M2+HM2-S/3))/3/S
  831. Id  CB1= - 0.5*CB0
  832. Al  CNB1=-(0.5*ZA-0.5*CA+0.5*(W0M2-WCM2+S)*CNB0)/S
  833. Al  CHB1=-(0.5*CA-0.5*HA+0.5*(WCM2-HM2+S)*CHB0)/S
  834. Al  HZB1=-(0.5*ZA-0.5*HA+0.5*(W0M2-HM2+S)*HZB0)/S
  835. Al  CPB1=-(-0.5*CA+0.5*(-WCM2+S)*CPB0)/S
  836. Id  W0M2=WCM2/CST2
  837. Keep EA1,EB1,EA2,EA3,EA4,EA5,EB5,EA6,EB6,EA7,EB7,EA8,EATA,EH1,
  838.   EH2,EH3,EH5,EH6,EH7,EH8,EH9,ET1,ET2,ET3,ET4,ET5
  839. *next
  840. B  DEL,CA
  841. Z  RESA =- S*(EA1+EA2+EA3+EA4+EA5+EA6+EA7+EA8)
  842. Z  RESB=
  843.    + S**2*(EB1+EB5+EB6+EB7)
  844. Z  RESH=
  845.   + WCM2*(EH1+EH2+EH3+EH5+EH6+EH7+EH8+EH9)
  846.   - 0.5*EATA *WCM2
  847. Z  REST=
  848.   - 2.*S*WCM2*(ET1+ET2+ET3+ET4+ET5)
  849. Keep RESA,RESB,RESH,REST
  850. *next
  851. B  CA,DEL
  852. Z  RESAL=RESA+RESB+RESH+REST
  853. *end
  854.  
  855. C Vectors 8. Vector boson - vector boson scattering. Tree diagrams.
  856.  
  857. P stat
  858. Oldnew,i=I
  859. S     L,S,M,COS
  860. I     IF
  861. I     LA,AL,BE,GA,DE
  862. V     K,P,KP,PP
  863. B     L,PROP1,PROP2,PROP3
  864. Z     DIA1 = AMPL(IA,IB,IC,ID,K,P,PP,KP)*PROP1
  865. Z     DIA2 = AMPL(IA,IB,ID,IC,K,P,KP,PP)*PROP2
  866. Z     DIA3 = AMPL(IC,IB,IA,ID,PP,P,K,KP)*PROP3
  867. Z     DIA4 = ((Epf(IF,ID,IC)*Epf(IF,IB,IA))*
  868.       (2*D(AL,GA)*D(BE,DE)-D(AL,DE)*D(BE,GA)-D(AL,BE)*D(GA,DE))
  869.       + (Epf(IF,ID,IB)*Epf(IF,IC,IA))*
  870.       (2*D(AL,BE)*D(GA,DE) - D(AL,DE)*D(GA,BE) - D(AL,GA)*D(BE,DE)))
  871.       *E(K,AL)*E(KP,DE)*E(P,BE)*E(PP,GA)
  872. Z     HDIA1 = M**2*D(AL,DE)*D(BE,GA)*D(IA,ID)*D(IB,IC)*PR1
  873.       *E(K,AL)*E(KP,DE)*E(P,BE)*E(PP,GA)
  874. Z     HDIA2 = M**2*D(AL,GA)*D(BE,DE)*D(IA,IC)*D(IB,ID)*PR2
  875.       *E(K,AL)*E(KP,DE)*E(P,BE)*E(PP,GA)
  876. Z     HDIA3 = M**2*D(AL,BE)*D(GA,DE)*D(IA,IB)*D(IC,ID)*PR3
  877.       *E(K,AL)*E(KP,DE)*E(P,BE)*E(PP,GA)
  878. Id    AMPL(IA~,IB~,IC~,ID~,K~,P~,PP~,KP~) =
  879.       (Epf(IF,IA,ID)*Epf(IF,IB,IC))*
  880.       (D(LA,GA)*(-2*PP(BE) - P(BE)) + D(BE,GA)*(PP(LA) - P(LA)) +
  881.       D(LA,BE)*(2*P(GA) + PP(GA))) *
  882.       (D(AL,LA)*(2*K(DE) + KP(DE)) + D(DE,LA)*(-2*KP(AL) - K(AL)) +
  883.       D(AL,DE)*(KP(LA) - K(LA)) )
  884.       *E(K,AL)*E(KP,DE)*E(P,BE)*E(PP,GA)
  885. C  ALL MOMENTA INGOING
  886. Id    E(K~,K~) = 0
  887. Id    E(K,AL~) = K(AL)*K0/M/LK - I*M*D(AL,4)/LK
  888. Al    E(P,AL~) = P(AL)*P0/M/LP - I*M*D(AL,4)/LP
  889. Al    E(KP,AL~) = KP(AL)*KP0/M/LKP - I*M*D(AL,4)/LKP
  890. Al    E(PP,AL~) = PP(AL)*PP0/M/LPP - I*M*D(AL,4)/LPP
  891. Id    KDK = - M**2
  892. Al    PDP = - M**2
  893. Al    PPDPP = - M**2
  894. Al    KPDKP = - M**2
  895. *yep
  896. Id    KP(4) = I*KP0
  897. Id    KP(AL~) = - K(AL) - P(AL) - PP(AL)
  898. Id,Dotpr,KP(AL~) = -K(AL) - P(AL) - PP(AL)
  899. Id    KDK = - M**2
  900. Al    PDP = - M**2
  901. Al    PPDPP = - M**2
  902. Al    KPDKP = - M**2
  903. Al    KDPP = M**2 - PDK - PDPP
  904. Id    K(4) = I*K0
  905. Al    P(4) = I*P0
  906. Al    PP(4) = I*PP0
  907. *yep
  908. C   CENTRE OF MASS SYSTEM
  909. Id    K0 = S
  910. Al    LK**-1 = L**-1
  911. Al    P0 = S
  912. Al    LP**-1 = L**-1
  913. Al    PP0 = - S
  914. Al    LPP**-1 = L**-1
  915. Al    KP0 = - S
  916. Al    LKP**-1 = L**-1
  917. Al    PDK = - 2*L**2 - M**2
  918. Al    PDPP = L**2*COS + S**2
  919. Id,Multi,S**2 = L**2 + M**2
  920. *yep
  921. Id    Trick
  922. *yep
  923. B    COS
  924. Id     COS = T**2/L**2/2 - 1
  925. C   PROP1 = (T**2+ M**2)**-1
  926. C   PROP2 = ( - T**2 + 4*L**2 + M**2)**-1
  927. C   PROP3 = ( - 4*L**2 - 3*M**2)**-1
  928. C   PR1 = (T**2 + M**2)**-1
  929. C   PR2 = ( - T**2 + 4*L**2 + MM**2)**-1
  930. C   PR3 = ( - 4*L**2 - 4*M**2 + MM**2)**-1
  931. Id,3,PROP1*T**IA~ = T**IA/T**2 - T**IA/T**2*M**2*PROP1
  932. Al,3,PROP2*T**IA~ = T**IA/T**2*4*L**2*PROP2 + T**IA/T**2*M**2*PROP2
  933.       -T**IA/T**2
  934. Al,3,PROP3*L**IA~ = - 1/4*L**IA/L**2 - 3/4*L**IA/L**2*M**2*PROP3
  935. Id,3,PR1*T**IA~ = T**IA/T**2 - T**IA/T**2*MM**2*PR1
  936. Al,3,PR2*T**IA~ = - T**IA/T**2 + T**IA/T**2*4*L**2*PR2
  937.       + MM**2*T**IA/T**2*PR2
  938. Al,3,PR3*L**IA~ = - 1/4*L**IA/L**2 - L**IA/L**2*M**2*PR3
  939.       + 1/4*MM**2*L**IA/L**2*PR3
  940. Keep,DIA1,DIA2,DIA3,DIA4,HDIA1,HDIA2,HDIA3
  941. *next
  942. B     GG
  943. Z     DIAW = - GG**2*(DIA1 + DIA2 + DIA3 + DIA4)
  944. Z     DIAH = GG**2*(HDIA1 + HDIA2 + HDIA3)
  945. Keep,DIAW,DIAH
  946. *next
  947. B     GG
  948. Z     DIA = DIAW + DIAH
  949. *end
  950.  
  951. C Vectors 9. Vector boson box diagram.
  952.  
  953. P stats
  954. B  QDP1,QDP2,QDP3,QDP4,QDQ
  955. V     Q,P1,P2,P3,P4
  956. Z      BOX=(D(MU,LA)*(P1(KA)-Q(KA)) + D(KA,LA)*(2*Q(MU)+P1(MU))
  957.         + D(MU,KA)*(-Q(LA)-2*P1(LA)))
  958.        *(D(NU,KA)*(P2(JD)-P1(JD)-Q(JD))
  959.         + D(JD,KA)*(2*Q(NU)+2*P1(NU)+P2(NU))
  960.         + D(NU,JD)*(-Q(KA)-P1(KA)-2*P2(KA)))
  961.       *(D(JA,JD)*(2*P3(JE)+P4(JE)-Q(JE))
  962.         + D(JE,JD)*(2*Q(JA)-P3(JA)-2*P4(JA))
  963.         + D(JA,JE)*(-Q(JD)+P4(JD)-P3(JD)))
  964.       *(D(JB,JE)*(2*P4(LA)-Q(LA))
  965.         + D(LA,JE)*(2*Q(JB)-P4(JB))
  966.         + D(JB,LA)*(-Q(JE)-P4(JE)))
  967. Al,Multi,P2DP2=-M2
  968. Id,Multi,P1DP1=-M2
  969. Al,Multi,P3DP3=-M2
  970. Al,Multi,P4DP4=-M2
  971. *end
  972.  
  973. C Vectors 10. Example of a gauge field theory. One loop poles.
  974.  
  975. P stats
  976. Oldnew i=I
  977. S    GG,AA,M,SM
  978. S     GM,TP,TW1,TW2,LAM,KAP,DIV
  979. I     A=3,B=3,C=3,E=3,AP=3,BP=3,CP=3,AL,BE,GA,EP
  980. I     MU,NU,MU1,NU1,MU2,NU2,A1=3,A2=3,A3=3,A1P=3,A2P=3,A3P=3
  981. I     AL1,AL2,AL3,AL1P,AL2P,AL3P
  982. I     APP=3,BEP,GAP,ALP,ALQ,ALPP
  983. V     K,P,Q,KP,KK,QP
  984. F     NOM,BET,GAM
  985. F     OUT1,OUT2,IN23,IN24,IN1,DUO2,SIN2,SIN1
  986. F     QX,QY,X,F,OUT3,IN33,IN34A,IN34B,IN34C
  987. F     DUO,TRIO
  988. F     VER3,PROP,VER4
  989. X     DVV(N)=DT(N+4)*DIV**N*DIV**5
  990. X     NUM(M1,M2,M3,M4)=1-0.5*DK(M1,M4)*DK(M2,M3)
  991. X     FOUR(M1,M2,M3,M4) = DT(Integ(- 1 +
  992.       DK(M1,M2)*DK(M3,M4) + DK(M1,M3)*DK(M2,M4) + DK(M1,M4)*DK(M2,M3)) )
  993. T     CHF(N)="W,"P,"Z,"P,"W
  994. T     CHL(N)="W,"P,"Z,"W,"P
  995. X     WW(A,AL,K,B,BE,P) = D(A,B)*D(AL,BE)*NOM(K,M)
  996.         + D(A,B)*K(AL)*K(BE)*BET(K)
  997. X     ZZ(A,AL,K,B,BE,P) = NOM(K,SM)
  998. X     PP(A,AL,K,B,BE,P) = D(A,B)*GAM(K)
  999. X     PW(A,AL,K,B,BE,P) = - I*M*TP*K(BE)*NOM(K,GM)*NOM(K,GM)*D(A,B)
  1000. X     XY(A,AL,K,B,BE,P) = D(A,B)*NOM(K,GM)/KAP
  1001. X     PPP=0
  1002. X     PWW=0
  1003. X     PZZ=0
  1004. X     WZZ=0
  1005. X     WWW(A,AL,K,B,BE,P,C,GA,Q) = - I*GG*EP3(A,B,C)*
  1006.        ( D(AL,GA)*(K(BE)-Q(BE)) + D(BE,GA)*(Q(AL)-P(AL))
  1007.         + D(AL,BE)*(P(GA) - K(GA)) )
  1008. X     WWWW(A,AL,B,BE,C,GA,E,EP) = - (D(E,B)*D(C,A) - D(E,A)*D(C,B))
  1009.         *GG**2*(2*D(AL,GA)*D(BE,EP) - D(AL,EP)*D(BE,GA) - D(AL,BE)
  1010.         *D(GA,EP)) - (D(E,C)*D(B,A) - D(E,A)*D(B,C))*GG**2
  1011.         *(2*D(AL,BE)*D(GA,EP) - D(AL,EP)*D(GA,BE) - D(AL,GA)*D(BE,EP))
  1012. X     PPW(B,BE,P,C,GA,Q,A,AL,K) = 0.5*I*GG*EP3(A,B,C)*(P(AL)-Q(AL))
  1013. X     PWZ(B,BE,P,A,AL,K,C,GA,Q) = 0.5*I*GG*D(A,B)*(P(AL)-Q(AL))
  1014. X     WWZ(A,AL,K,B,BE) = - GG*M*D(A,B)*D(AL,BE)
  1015. X     PPZ(A,AL,K,B) = - 2*AA*M*GG*D(A,B)
  1016. X     ZZZ = -6*AA*M*GG
  1017. X     WXY(A,AL,K,B,BE,P,C,GA,Q) = I*GG*EP3(A,B,C)*P(AL)*KAP
  1018. X     XYZ(A,AL,K,B) = - 0.5*M*GG*D(A,B)*LAM
  1019. X     PXY(A,AL,K,B,BE,P,C) = 0.5*M*GG*EP3(A,B,C)*LAM
  1020. X     PPWW(C,GA,E,EP,A,AL,B,BE) = - 0.5*GG**2*D(A,B)*D(C,E)*D(AL,BE)
  1021. X     WWZZ(A,AL,B,BE) = - 0.5*GG**2*D(A,B)*D(AL,BE)
  1022. X     PPPP(A,AL,B,BE,C,GA,E,EP) = -AA*GG**2*(D(A,B)*D(C,E)
  1023.         + D(A,C)*D(B,E) + D(A,E)*D(B,C))
  1024. X     PPZZ(A,AL,B,BE) = - AA*GG**2*D(A,B)
  1025. X     ZZZZ = - 3*AA*GG**2
  1026. X     EP3EP(A,B,C,AP,BP,CP) = D(A,AP)*(D(B,BP)*D(C,CP) - D(B,CP)
  1027.         *D(C,BP)) - D(A,BP)*(D(B,AP)*D(C,CP) - D(B,CP)*D(C,AP))
  1028.         - D(A,CP)*(D(B,BP)*D(C,AP) - D(B,AP)*D(C,BP))
  1029. *fix
  1030. BLOCK Subs{}
  1031. P input
  1032. B     A123
  1033. Id     INTER =
  1034.        TRIO(5) + DUO(IN34A,5) + DUO(IN34B,5) + DUO(IN34C,5)
  1035.         - IN33("X,"Y,"X,"Y,"X,"Y)
  1036.         - IN33("Y,"X,"Y,"X,"Y,"X)
  1037. Al    INTE2 = DUO2(5) + SIN2(4) - IN23("X,"Y,"X,"Y)
  1038. Id    TRIO(N~) = DS(J1,1,N,(DS(J2,1,N,(DS(J3,1,N,(
  1039.         IN33(CHF(J1),CHL(J1),CHF(J2),CHL(J2),CHF(J3),CHL(J3) )
  1040.           )   )   )   )   )   )
  1041. Al     DUO(IN34A~,N~) = DS(J1,1,N,(DS(J2,J1,N,(
  1042.         IN34A(CHF(J1),CHL(J1),CHL(J2),CHF(J2)  )
  1043.           )   )   )   )
  1044. Al     DUO2(N~) = DS(J1,1,N,(DS(J2,J1,N,(
  1045.         IN23(CHF(J1),CHL(J1),CHL(J2),CHF(J2)  )
  1046.         )   )   )   )
  1047. Al   SIN2(N~) = DS(J1,1,N,(
  1048.           IN24(CHF(J1),CHL(J1) )
  1049.         )   )
  1050. Al   SIN1(N~) = DS(J1,1,N,(IN1(CHF(J1),CHL(J1) ) )  )
  1051. Id    OUT3(N1~,N2~,N3~)*IN33(M11~,M12~,M22~,M23~,M33~,M31~) =
  1052.        VER3(N1,M11,M31,*,A,AL,K,*,A1,AL1,Q,*,A3,AL3,P)*
  1053.        VER3(N2,M12,M22,*,AP,ALP,KP,*,A1P,AL1P,-Q,*,A2,AL2,-QP)*
  1054.        VER3(N3,M23,M33,*,APP,ALPP,KK,*,A2P,AL2P,QP,*,A3P,AL3P,-P)*
  1055.        PROP(M11,M12,*,A1,AL1,Q,*,A1P,AL1P,-Q)*
  1056.        PROP(M22,M23,*,A2,AL2,-QP,*,A2P,AL2P,QP)*
  1057.        PROP(M31,M33,*,A3,AL3,P,*,A3P,AL3P,-P)
  1058. Al     OUT3(N1~,N2~,N3~)*IN34A(M1~,M2~,M3~,M4~) =
  1059.        VER3(N1,M1,M4,*,A,AL,K,*,A1,AL1,Q,*,A2,AL2,P)*
  1060.        VER4(N2,N3,M2,M3,*,AP,ALP,*,APP,ALPP,*,A1P,AL1P,*,A2P,AL2P)*
  1061.        PROP(M1,M2,*,A1,AL1,Q,*,A1P,AL1P,-Q)*
  1062.        PROP(M4,M3,*,A2,AL2,P,*,A2P,AL2P,-P)*FOUR(N2,N3,M2,M3)*
  1063.          NUM(M1,M2,M3,M4)
  1064. Al    OUT3(N1~,N2~,N3~)*IN34B(M1~,M2~,M3~,M4~) =
  1065.        VER3(N2,M1,M4,*,AP,ALP,KP,*,A1,AL1,-Q,*,A2,AL2,-QP)*
  1066.        VER4(N1,N3,M2,M3,*,A,AL,*,APP,ALPP,*,A1P,AL1P,*,A2P,AL2P)*
  1067.        PROP(M1,M2,*,A1,AL1,-Q,*,A1P,AL1P,Q)*
  1068.        PROP(M4,M3,*,A2,AL2,-QP,*,A2P,AL2P,QP)*
  1069.         FOUR(N1,N3,M2,M3)*NUM(M1,M2,M3,M4)
  1070. Al     OUT3(N1~,N2~,N3~)*IN34C(M1~,M2~,M3~,M4~) =
  1071.         VER3(N3,M1,M4,*,APP,ALPP,KK,*,A1,AL1,QP,*,A2,AL2,-P)*
  1072.        VER4(N1,N2,M2,M3,*,A,AL,*,AP,ALP,*,A1P,AL1P,*,A2P,AL2P)*
  1073.        PROP(M1,M2,*,A1,AL1,QP,*,A1P,AL1P,-QP)*
  1074.        PROP(M4,M3,*,A2,AL2,-P,*,A2P,AL2P,P)*
  1075.          FOUR(N1,N2,M2,M3)*NUM(M1,M2,M3,M4)
  1076. Al     OUT2(N1~,N2~)*IN23(M1~,M2~,M3~,M4~) =
  1077.           VER3(N1,M1,M4,*,A,AL,K,*,C,GA,Q,*,B,BE,P)*
  1078.           PROP(M4,M3,*,B,BE,P,*,BP,BEP,-P)*
  1079.           PROP(M1,M2,*,C,GA,Q,*,CP,GAP,-Q)
  1080.         *VER3(N2,M2,M3,*,AP,ALP,-K,*,CP,GAP,-Q,*,BP,BEP,-P)
  1081.           *NUM(M1,M2,M3,M4)
  1082. Al    OUT2(N1~,N2~)*IN24(M1~,M2~) =
  1083.         VER4(N1,N2,M1,M2,*,A,AL,*,AP,ALP,*,C,GA,*,CP,GAP)
  1084.         *PROP(M1,M2,*,C,GA,P,*,CP,GAP,-P)
  1085.         *NUM(M1,M2,M1,M2)*FOUR(N1,N2,M1,M2)
  1086. Al     OUT1(N1~)*IN1(N2~,N3~) =
  1087.       VER3(N1,N2,N3,*,A,AL,K,*,B,BE,P,*,C,GA,-P)*
  1088.         PROP(N2,N3,*,B,BE,P,*,C,GA,-P)*NUM(N2,N3,N2,N3)
  1089. Id    Compo,<X>,VER3,VER4,PROP
  1090. Id     VER3(WWW~,A~,AL~,K~,B~,BE~,P~,C~,GA~,Q~) =
  1091.        WWW(A,AL,K,B,BE,P,C,GA,Q)
  1092. Al     VER4(WWWW~,A~,AL~,B~,BE~,C~,GA~,E~,EP~) =
  1093.         WWWW(A,AL,B,BE,C,GA,E,EP)
  1094. Al     PROP(WW~,A~,AL~,K~,B~,BE~,P~) = WW(A,AL,K,B,BE,P)
  1095. Id    Count,DVV,P,1,Q,1,QP,1,NOM,-2,BET,-4,GAM,-2
  1096. Id,2   NOM(-P,M~) = NOM(P,M)
  1097. Al,2   NOM(-Q,M~) = NOM(Q,M)
  1098. Al,2   NOM(-QP,M~) = NOM(QP,M)
  1099. Al,2   BET(-P) = BET(P)
  1100. Al,2   BET(-Q) = BET(Q)
  1101. Al,2   BET(-QP) = BET(QP)
  1102. Al,2   GAM(-P)=GAM(P)
  1103. Al,2    GAM(-Q) = GAM(Q)
  1104. Al,2    GAM(-QP)=GAM(QP)
  1105. Id   EP3(A,A1,A3)*EP3(AP,A1,A2)*EP3(APP,A2,A3) = -A123
  1106. Id,Adiso,EP3(A~,B~,C~)*EP3(AP~,BP~,CP~) = EP3EP(A,B,C,AP,BP,CP)
  1107. Id   Asymm,EP3,1,2,3
  1108. Id   EP3(APP,AP,A) = - A123
  1109. *yep
  1110. Id    DIV**2*QDQ**2 = PDP**2*DIV**2 + 4*PDP*PDK*DIV
  1111. Al   DIV**3*QDQ**2 = PDP**2*DIV**3 + 4*PDP*PDK*DIV**2
  1112.           + 2*PDP*KDK*DIV + 4*PDK**2*DIV
  1113. Al    DIV*QDQ**2 = PDP**2*DIV
  1114. Al    DIV**2*QDQ = PDP*DIV**2 + 2*PDK*DIV
  1115. Al    DIV**3*QDQ = PDP*DIV**3 + 2*PDK*DIV**2 + KDK*DIV
  1116. Al     DIV*QDQ = PDP*DIV
  1117. Id,Dotpr,Q(MU~) = QX(MU)
  1118. Id    Q(MU~) = QX(MU)
  1119. Id,4   DIV**2*QX(MU~) = - DIV*K(MU) - DIV**2*P(MU)
  1120. Al,4   DIV**3*QX(MU~) = - DIV**2*K(MU) - DIV**3*P(MU)
  1121. Al,4   DIV*QX(MU~) = - P(MU)*DIV
  1122. Id    DIV**2*QPDQP**2 = PDP**2*DIV**2 - 4*PDP*PDKK*DIV
  1123. Al     DIV*QPDQP**2 = PDP**2*DIV
  1124. Al     DIV**2*QPDQP = PDP*DIV**2 - 2*PDKK*DIV
  1125. Al    DIV*QPDQP = DIV*PDP
  1126. Id,Dotpr,QP(MU~) = QY(MU)
  1127. Al    QP(MU~) = QY(MU)
  1128. Id,4  DIV**2*QY(MU~) = - DIV*KK(MU) + DIV**2*P(MU)
  1129. Al,4   DIV*QY(MU~) = DIV*P(MU)
  1130. Id,2   DIV**N~*BET(K~) = DIV**N*TW1*NOM(K,M)*NOM(K,GM)
  1131.        + DT(N-3)*DIV**N/DIV**2*TW2*M**2/PDP**3
  1132. Id,3   DIV**N~*GAM(K~) = DIV**N*NOM(K,GM)
  1133.        + DT(N-3)*DIV**N/DIV**2*M**2*TP/PDP**2
  1134. Id,2   DIV**3*NOM(Q,M~) = DIV**3/PDP - 2*PDK*PDP**-2*DIV**2
  1135.        - DIV*(KDK + M**2)/PDP**2 + 4*DIV*PDK**2/PDP**3
  1136. Al,2   DIV**2*NOM(Q,M~) = DIV**2/PDP - 2*PDK*PDP**-2*DIV
  1137. Id,2   DIV**2*NOM(QP,M~) = DIV**2/PDP + 2*PDKK*PDP**-2*DIV
  1138. Id,4   DIV**3*NOM(P,M~) = DIV**3/PDP - DIV*M**2/PDP**2
  1139. Al,4   DIV**2*NOM(P,M~) = DIV**2/PDP
  1140. Al,6   DIV*NOM(Q~,M~) = DIV/PDP
  1141. Id   DIV**N~ = DK(N,1)*DIV
  1142. Al   Numer,PDP,1
  1143. *yep
  1144. Id,Dotpr,P(MU~) = X(MU)
  1145. Al   P(MU~) = X(MU)
  1146. Id    X(MU~)*X(M1~) = F(2,M1,MU)
  1147. Id,Adiso,F(2,M1~,M2~)*X(MU~) = F(3,M1,M2,MU)
  1148. Id,Adiso,F(3,M1~,M2~,M3~)*X(MU~) = F(4,M1,M2,M3,MU)
  1149. Id    X(MU~) = 0
  1150. Al    F(3,M1~,M2~,M3~) = 0
  1151. C   IN UNITS  I*PI**2/(N-4)
  1152. Id    DIV**N~*F(2,M1~,M2~) = -DK(N,1)*0.5*D(M1,M2)
  1153. Al    DIV**N~*F(4,M1~,M2~,M3~,M4~) = - 1/12*DK(N,1)*
  1154.        (D(M1,M2)*D(M3,M4) + D(M1,M3)*D(M2,M4) + D(M1,M4)*D(M2,M3) )
  1155. Al    DIV**N~ = - 2*DK(N,1)
  1156. *yep
  1157. B   I,GG
  1158. Id   SM**2=4*AA*M**2
  1159. Id   KP(MU~) = - K(MU) - KK(MU)
  1160. Al,Dotpr,KP(MU~) = - K(MU) - KK(MU)
  1161. Id   TW1 = 1/KAP**2 - 1
  1162. Al    TW2 = (1+LAM**2 - LAM/KAP - LAM*KAP)/KAP**2
  1163. Al    TP = 1/KAP**2 - LAM/KAP
  1164. Al,Multi,GM**2 = LAM*M**2/KAP
  1165. Id   EP3(A~,B~,C~)*EP3(AP~,BP~,CP~) = EP3EP(A,B,C,AP,BP,CP)
  1166. Id    A123=EP3(A,AP,APP)
  1167. Id   Asymm,EP3,1,2,3
  1168. ENDBLOCK
  1169. P input
  1170. Z   WSELF = OUT2("W,"W)*INTE2
  1171. Subs{}
  1172. *begin
  1173. Z  GHOST = OUT2("Y,"X)*(
  1174.       IN23("X,"Y,"Z,"Z) + IN23("X,"Y,"W,"W)
  1175.       + IN23("X,"Y,"P,"P) + IN23("X,"Y,"P,"W) + IN23("X,"Y,"W,"P) )
  1176. Z  TADP = OUT1("Z)*(SIN1(4) - IN1("X,"Y))
  1177. Z  PSELF = OUT2("P,"P)*INTE2
  1178. Z   PSWTR = OUT2("P,"W)*INTE2
  1179. Z  ZSELF = OUT2("Z,"Z)*INTE2
  1180. Subs{}
  1181. *begin
  1182. Z   WWWV = OUT3("W,"W,"W)*(
  1183.     TRIO(5) + DUO(IN34A,5) + DUO(IN34B,5) + DUO(IN34C,5)
  1184.    - IN33("X,"Y,"X,"Y,"X,"Y)
  1185.      - IN33("Y,"X,"Y,"X,"Y,"X) )
  1186. Subs{}
  1187. *end
  1188.