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Text File  |  1991-06-14  |  42KB  |  1,618 lines
  1. C Varia 1. F-G series.
  2. C Varia 2. Two-point function, coefficients of F(N).
  3. C Varia 3. Table test.
  4. C Varia 4. Test of Tables, character-number facility.
  5. C Varia 5. Calculation of two-component Riemann tensor from metric.
  6. C Varia 6. Calculation of Riemann tensors from metric.
  7. C Varia 7. Lagrangian for SU(5) once broken to SU(3)*SU(2)*U(1).
  8. C Varia 8. Lagrangian for SU(5) twice broken to SU(3)*U(1).
  9. *end
  10.  
  11. C Varia 1. F-G series.
  12.  
  13.   P. Sconzo, A. Le Schack and R. Tobey, The Astronomical Journal 70(1965)269.
  14.  
  15. C Calculate up to and including F(25), G(25).
  16.  
  17. C Running time:
  18. C        CRDS         32 secs, without cache 50 sec.
  19. C        HP PC        257 secs. (run from floppy)
  20. C        Torch        47 secs.
  21. C        Atari ST     41 secs. (run from ram disk)
  22. C        Sun 3/60    15 secs.
  23. C        Amiga 2000    52 secs. (run from ram disk)
  24. C        Amiga 3000    11 secs.
  25. C        Mac II         12 secs.
  26. C        NeXT         3 secs.
  27.  
  28. BLOCK Subs{}
  29. Id,mu**n~*Diff=Diff*mu**n + n*mup*mu**(n-1)
  30. Id,si**n~*Diff=Diff*si**n + n*sip*si**(n-1)
  31. Id,ep**n~*Diff=Diff*ep**n + n*epp*ep**(n-1)
  32. Id,Diff=0
  33. Id,mup=-3*mu*si
  34. Al,epp=-si*(mu+2*ep)
  35. Al,sip=ep-2*si**2
  36. ENDBLOCK
  37.  
  38. F Diff
  39. S mu,ep,si,mup,epp,sip
  40. I K,N
  41. Z FF(0)=1
  42. Z FG(0)=0
  43. Keep FF,FG
  44. *next
  45. DO L1=1,25
  46. Z FF('L1')=FF('L1'-1)*Diff - mu*FG('L1'-1)
  47. Z FG('L1')=FF('L1'-1) + FG('L1'-1)*Diff
  48. Subs{}
  49. Keep FF('L1'),FG('L1')
  50. *next
  51. ENDDO
  52. *end
  53.  
  54. C Varia 2. Two-point function, coefficients of F(N).
  55.  
  56. P stat
  57. C  COEFFICIENTS OF  F(N) FOR USE WITH THE TWO-POINT FUNCTION.
  58. N  13,R0
  59. X  C(N)=1./N
  60. X  EX(N,Y)=DS(J,1,16,(N**J*Y**J),(J**-1)) + 1
  61. Z  F1=DS(J,1,16,(X**J*C(1+J)))
  62. Z  F2=DS(J,1,16,(X**J*C(2+J)))
  63. Z  F3=DS(J,1,16,(X**J*C(3+J)))
  64. Z  F4=DS(J,1,16,(X**J*C(4+J)))
  65. Z  F5=DS(J,1,16,(X**J*C(5+J)))
  66. Z  F6=DS(J,1,16,(X**J*C(6+J)))
  67. Z  F7=DS(J,1,16,(X**J*C(7+J)))
  68. Z  F8=DS(J,1,16,(X**J*C(8+J)))
  69. Id  X**N~=1-DS(J,1,N,(DB(N,J)*Z**J),(-1))
  70. *yep
  71. Id  Z**N~ = EX(N,Y)
  72. *end
  73.  
  74. C Varia 3. Table test.
  75.  
  76. T A(K1)=(A1_A2**2),A3,"F,"Z
  77. T B(K1)=0,1,-1,2,-2
  78.  
  79. Z XX=0.1*F2(A(1),A(2))
  80.     +0.2*F3(A(3),A(4))
  81.     +C1*DC(1,2,3) + 2*C2*DC(1,2,-3)
  82.     +3*C3*DC(B(2),B(2),B(5)) + 4*C4*DC(B(2),B(2),B(4))
  83.     +5*C5*DC(B(1),B(2),B(3),B(1)) + 6*C6*DC(B(2),B(3),B(2),B(3))
  84.     +7*C7*DC(B(2),B(3),B(2),B(1))
  85. Id,F2(X~,Y~)=B1*X+B2*Y
  86. *begin
  87. B D1,D2,D3,D4
  88. S A1=c,A2=c,A3=c,A4=c
  89. T A(K)=Conjg(A1+A2),-Conjg(A3+A4),Integ(5+7),-Integ(5+7)
  90.  
  91. Z X=F1(A(1),A(2),-A(1),-A(2),A(3),A(4),-A(3),-A(4))
  92.  
  93. Id,F1(B1~,B2~,B3~,B4~,B5~,B6~,B7~,B8~)=
  94.    F2(B5,B6,B7,B8)+11*D1*B1+12*D2*B2+13*D3*B3+14*D4*B4
  95. *next
  96. T T0(K1)=A7,-4
  97. T T1(K1)=4,2,T0,5
  98. T T2(K1)=A1,A2,A3,A4,-A5
  99. Z xx=F1(B1,-T2(T1(-T1(3,2))),B2)
  100. Id,F1(C1~,C2~,C3~)=11*C1*D1+12*C2*D2+13*C3*D3
  101. *begin
  102. S A1=c,A2=c,A3=c,A4=c,B1,B2,B3,B4,B5,B6,FA1,FA2,FA3
  103. B BR,BR1,BR2,BR3,BR4
  104. D TIC(K)=C1,C2,C3,C4,C5,C6,C7,C8
  105. T TE(K1)=A1,A2
  106. T TC(K1,B1,B2,B3,B4,TE)=A1,A2,(BR3*(B1-B2)+BR4*(B3-B4))
  107. T TB(K1,K2,B1,B2,B3,B4,TE)=A1,TC
  108. T TA(K1,K2,K3,B1,B2,B3,B4,TE)=((B1+B2)*BR1),((B1-B2)*BR2)
  109.   ,((B3+B4)*BR3),((B3-B4)*BR4),TE
  110.  
  111. Z XX=DS(J1,4,8,(F1(A1,A2,A3,A4,-J1,3)*BR**J1*TIC(J1)))
  112.  
  113. Id,F1(B1~,B2~,B3~,B4~,B5~,B6~)=
  114.    F3(Conjg(B1+B2),-Conjg(B1+B2),
  115.        TA(-Integ(B5+B6),2,3,Conjg(B3+B4),-Conjg(B3+B4),
  116.               Integ(B5-B6),-Integ(B5-B6),TB))
  117. Id,F3(B1~,B2~,B3~)=FA1*B1+FA2*B2+FA3*B3
  118. *end
  119.  
  120. C Varia 4. Test of Tables, character-number facility.
  121.  
  122. P brackets
  123. T TT(n)=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
  124.     21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
  125.     38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56
  126. T ALF(N)="A,"B,"C,"D,"E,"F,"G,"H,"I,"J,"K,"L,"M,"N,"O,"P,"Q,
  127.     "R,"S,"T,"U,"V,"W,"X,"Y,"Z,
  128.     "a,"b,"c,"d,"e,"f,"g,"h,"i,"j,"k,"l,"m,"n,"o,"p,"q,
  129.     "r,"s,"t,"u,"v,"w,"x,"y,"z
  130.  
  131. Z xx=DS{J1,1,52,(f1(ALF(J1)))}
  132.  
  133. Id,f1(a1~)=f2(TT(a1))*f0(a1)
  134. Id,f2(n1~)=a2**n1
  135. *end
  136.  
  137. C Varia 5. Calculation of two-component Riemann tensor from metric.
  138.  
  139. C Calculation of components of Rieman tensor from
  140. C a given form for the metric tensor g(mu,nu).
  141. C That form was:
  142. C
  143. C            a k l 0
  144. C            k b m 0
  145. C    g(mu,nu) =    l m c 0
  146. C            0 0 0 e
  147.  
  148.  
  149. P lists
  150. P stats
  151.  
  152. S Det,a,b,c,e,k,l,m
  153.  
  154. V ap,bp,cp,ep,kp,lp,mp
  155.  
  156. X zero(n,j) = 1 - DK(n,j)
  157.  
  158. BLOCK GGX{x,n,y}
  159. D gg'x'('n') = a'y',k'y',l'y',0,
  160.     k'y',b'y',m'y',0,
  161.     l'y',m'y',c'y',0,
  162.     0,0,0,e'y'
  163. ENDBLOCK
  164.  
  165. C***** The metric tensor g(mu,nu) :
  166.  
  167. GGX{,n}
  168.  
  169. C***** The first derivative of g(mu,nu), i.e. d/dx(n) g(mu,nu) :
  170.  
  171. GGX{d,{n1,n},p(n)}
  172.  
  173. C***** The second derivative d^2/dx(n)/dx(j) g(mu,nu) :
  174.  
  175. GGX{dd,{n1,n,j},{pp(n,j)}}
  176.  
  177. D ggi(n) =    (b*c - m**2),(l*m - k*c),(k*m - l*b),0,
  178.         (l*m - k*c),(a*c - l^2),(k*l - a*m),0,
  179.         (k*m - l*b),(k*l - a*m),(a*b - k^2),0,
  180.         0,0,0,(2*k*l*m + a*b*c - a*m^2 - c*k^2 - b*l^2)/e
  181.  
  182. X tg(j,n) = gg(j*4+n+1)
  183.  
  184. X tgi(j,n)=ggi(j*4+n+1)*e
  185.  
  186. X tgd(n,j,j1) = ggd(n*4+j+1,j1)
  187.  
  188. X tgdd(n,j,j1,j2) = DT(j2-j1)*ggdd(n*4+j+1,j1,j2) +
  189.     DT(j1-j2-1)*ggdd(n*4+j+1,j2,j1)
  190.  
  191. C***** The Christoffel symbol:
  192.  
  193. X chr(n1,n2,n3) = 0.5*tgd(n3,n1,n2) + 0.5*tgd(n3,n2,n1)
  194.     - 0.5*tgd(n1,n2,n3)
  195.  
  196. C***** The derivative of the Christoffel symbol:
  197.  
  198. X chd(n1,n2,n3,n4) = 0.5*tgdd(n3,n1,n2,n4) + 0.5*tgdd(n3,n2,n1,n4)
  199.     - 0.5*tgdd(n1,n2,n3,n4)
  200.  
  201. C***** Gamma in terms of the Christoffel symbol:
  202.  
  203. X ga(n1,n2,n3) = DS{n4,0,3,{tgi(n3,n4)*chr(n1,n2,n4) } }
  204.  
  205. C***** The Riemann tensor:
  206.  
  207. X Rt4(n1,n2,n3,n4) = Det*chd(n2,n4,n1,n3) - Det*chd(n2,n3,n1,n4)
  208.     + DS{n5,0,3,{    chr(n2,n3,n5)*ga(n1,n4,n5) -
  209.             chr(n2,n4,n5)*ga(n1,n3,n5) } }
  210.  
  211. C***** This the the two-index Riemann tensor:
  212.  
  213. X Rt2(n1,n2) = DS{n3,0,3,{zero(n3,n1)*
  214.     DS{n4,0,3,{zero(n4,n2)*tgi(n3,n4)*Rt4(n3,n1,n4,n2)} } } }
  215.  
  216. *fix
  217.  
  218. B e,Det,a
  219.  
  220. C***** Now calculate some component, here Rt2(0,0) :
  221.  
  222. Z R00 = Rt2(0,0)
  223.  
  224. *begin
  225.  
  226. B e,Det,a
  227.  
  228. Z R01 = Rt2(0,1)
  229.  
  230. *end
  231.  
  232. C Varia 6. Calculation of Riemann tensors from metric.
  233. C Calculation of components of Rieman tensors from
  234. C a given form for the metric tensor g(mu,nu).
  235. C That form was:
  236. C
  237. C            a k l 0
  238. C            k b m 0
  239. C    g(mu,nu) =    l m c 0
  240. C            0 0 0 e
  241.  
  242.  
  243. P lists
  244. P stats
  245.  
  246. S Det,a,b,c,e,k,l,m
  247.  
  248. V ap,bp,cp,ep,kp,lp,mp
  249.  
  250. X zero(n,j) = 1 - DK(n,j)
  251.  
  252. C The metric tensor is given further down. The inverse was calculated
  253. C by hand and follows here as a one dimensional array:
  254.  
  255. D ggi(n) =    (b*c - m**2),(l*m - k*c),(k*m - l*b),0,
  256.         (l*m - k*c),(a*c - l^2),(k*l - a*m),0,
  257.         (k*m - l*b),(k*l - a*m),(a*b - k^2),0,
  258.         0,0,0,(2*k*l*m + a*b*c - a*m^2 - c*k^2 - b*l^2)/e
  259.  
  260. C This is the two-dimensional form of ggi:
  261.  
  262. X tgi(j,n)=ggi(j*4+n+1)*e
  263.  
  264. X R5(n1,n2,n3,n4) = zero(n1,n2)*zero(n3,n4)*
  265.     { DT(n4-n3)*R6(n1,n2,n3,n4) - DT(n3-n4)*R6(n1,n2,n4,n3) }
  266.  
  267. X R4(n1,n2,n3,n4) = DT(n4-n2)*R5(n1,n2,n3,n4)
  268.     - DT(n2-n4-1)*{ R5(n1,n4,n2,n3) + R5(n1,n3,n4,n2) }
  269.  
  270. X R3(n1,n2,n3,n4) = DT(n3-n1)*R4(n1,n2,n3,n4)
  271.     + DT(n1-n3-1)*R4(n3,n4,n1,n2)
  272.  
  273. X R2(n1,n2,n3,n4) = DT(n4-n3)*R3(n1,n2,n3,n4)
  274.     - DT(n3-n4)*R3(n1,n2,n4,n3)
  275.  
  276. X R1(n1,n2,n3,n4) = zero(n1,n2)*zero(n3,n4)*
  277.     { DT(n2-n1)*R2(n1,n2,n3,n4) - DT(n1-n2)*R2(n2,n1,n3,n4) }
  278.  
  279. *fix
  280.  
  281. BLOCK GGX{x,n,y}
  282. D gg'x'('n') = a'y',k'y',l'y',0,
  283.     k'y',b'y',m'y',0,
  284.     l'y',m'y',c'y',0,
  285.     0,0,0,e'y'
  286. ENDBLOCK
  287.  
  288. C***** The metric tensor g(mu,nu) :
  289.  
  290. GGX{,n}
  291.  
  292. C***** The first derivative of g(mu,nu), i.e. d/dx(n) g(mu,nu) :
  293.  
  294. GGX{d,{n1,n},p(n)}
  295.  
  296. C***** The second derivative d^2/dx(n)/dx(j) g(mu,nu) :
  297.  
  298. GGX{dd,{n1,n,j},{pp(n,j)}}
  299.  
  300. C***** Two component forms:
  301.  
  302. X tg(j,n) = gg(j*4+n+1)
  303.  
  304. X tgd(n,j,j1) = ggd(n*4+j+1,j1)
  305.  
  306. X tgdd(n,j,j1,j2) = DT(j2-j1)*ggdd(n*4+j+1,j1,j2) +
  307.     DT(j1-j2-1)*ggdd(n*4+j+1,j2,j1)
  308.  
  309. C***** The Christoffel symbol:
  310.  
  311. X chr(n1,n2,n3) = 0.5*tgd(n3,n1,n2) + 0.5*tgd(n3,n2,n1)
  312.     - 0.5*tgd(n1,n2,n3)
  313.  
  314. C***** The derivative of the Christoffel symbol:
  315.  
  316. X chd(n1,n2,n3,n4) = 0.5*tgdd(n3,n1,n2,n4) + 0.5*tgdd(n3,n2,n1,n4)
  317.     - 0.5*tgdd(n1,n2,n3,n4)
  318.  
  319. C***** Gamma in terms of the Christoffel symbol:
  320.  
  321. X ga(n1,n2,n3) = DS{n4,0,3,{tgi(n3,n4)*chr(n1,n2,n4) } }
  322.  
  323. C***** The Riemann tensor:
  324.  
  325. X Rt4(n1,n2,n3,n4) = Det*chd(n2,n4,n1,n3) - Det*chd(n2,n3,n1,n4)
  326.     + DS{n5,0,3,{    chr(n2,n3,n5)*ga(n1,n4,n5) -
  327.             chr(n2,n4,n5)*ga(n1,n3,n5) } }
  328.  
  329. C***** Now compute the components of the Riemann tensor:
  330.  
  331. BLOCK R{n,n1,n2,n3,n4}
  332. Z Rt('n') = Rt4('n1','n2','n3','n4')
  333. ENDBLOCK
  334. R{18,0,1,0,1}
  335. R{19,0,1,0,2}
  336. R{23,0,1,1,2}
  337. R{35,0,2,0,2}
  338. R{39,0,2,1,2}
  339. R{20,0,1,0,3}
  340. R{24,0,1,1,3}
  341. R{28,0,1,2,3}
  342. R{36,0,2,0,3}
  343. R{40,0,2,1,3}
  344. R{44,0,2,2,3}
  345. R{52,0,3,0,3}
  346. R{56,0,3,1,3}
  347. R{60,0,3,2,3}
  348. R{103,1,2,1,2}
  349. R{104,1,2,1,3}
  350. R{108,1,2,2,3}
  351. R{120,1,3,1,3}
  352. R{124,1,3,2,3}
  353. R{198,2,3,2,3}
  354. Keep Rt
  355. P noutput
  356. *next
  357.  
  358. B e,Det,a
  359.  
  360. C***** This the the two-index Riemann tensor:
  361.  
  362. X Rt2(n1,n2) = DS{n3,0,3,{zero(n3,n1)*
  363.     DS{n4,0,3,{zero(n4,n2)*tgi(n3,n4)*R1(n3,n1,n4,n2)} } } }
  364.  
  365. C***** Now calculate some component, here Rt2(0,0) :
  366.  
  367. Z R00 = Rt2(0,0)
  368.  
  369. *yep
  370.  
  371. C***** Use the components of the four-index tensor as computed before:
  372.  
  373. Id,R6(n1~,n2~,n3~,n4~) = Rt(64*n1+16*n2+4*n3+n4+1)
  374.  
  375. *end
  376.  
  377. C Varia 7. Lagrangian for SU(5) once broken to SU(3)*SU(2)*U(1).
  378.  
  379. P error
  380. C PROGRAM WRITTEN BY MARTIN GREEN, AUGUST 1981.
  381. P stat
  382. Oldnew i=I
  383. Common A,DIF,DIFH,CDIFH,DIFHH,F1,F2,DIFZ,DIFZB,Zb,GAUGE,H,HH,F1B,F0,MZ
  384.    ,HSH,HHHH,HH2,LH1,LH2,LH3,LH4,LH5,LH6,LH7,LH8,LH9
  385. F TA
  386. *fix
  387. C RT12=SQRT(1/2) ETC
  388. C GG = GAUGE COUPLING CONSTANT
  389. C UNIT = 3 BY 3 UNIT MATRIX
  390. C UNI=2*2 UNIT MATRIX
  391. C          SUMMATION CONVENTIONS
  392. C LG(MU)=LAMBDA(A)*GL(A,MU)
  393. C TB(MU)=TAU(A)*B(A,MU)
  394. C LDIFF(GL)=LAMBDA(A)*DIFF(GL(A))
  395. C LDIFF(B)=TAU(A)*DIFF(B(A))
  396. B GG
  397. S GG,UNIT,RT12,RT13,RT15,UNI
  398. I MU1,MU2,MU3,MU4,I1=3,I2=3,I3=3,I4=3
  399. V B,B0,GL,XM,XP
  400. F DIFF,LDIFF,LG,MX=c,TB
  401. Oldnew MXC=PX
  402. C DIFFERENTIAL OF A(MU)
  403. Z DIF(MU1,MU2,I1,I2)=-I*RT12*(
  404.    +DIFF(MU1,XM,MU2)*D(I1,1)*D(I2,2)
  405.    +DIFF(MU1,XP,MU2)*D(I1,2)*D(I2,1)
  406.    +(RT12*LDIFF(MU1,GL,MU2)+UNIT*2*RT12*RT13*RT15*DIFF(MU1,B0,MU2))
  407.    *D(I1,1)*D(I2,1)
  408.    +(RT12*LDIFF(MU1,B,MU2)-UNI*3*RT12*RT13*RT15*DIFF(MU1,B0,MU2))
  409.    *D(I1,2)*D(I2,2))
  410. Id RT12**2=1/2
  411.  
  412. *next
  413. C                                      A(MU)
  414. Z A(MU1,I1,I2)=DIF(MU2,MU1,I1,I2)
  415. Id DIFF(MU1~,XM,MU2~)=MX(MU2)
  416. Al DIFF(MU1~,XP,MU2~)=PX(MU2)
  417. Al LDIFF(MU1~,GL,MU2~)=LG(MU2)
  418. Al LDIFF(MU1~,B,MU2~)=TB(MU2)
  419. Id DIFF(MU1~,B0~,MU2~)=B0(MU2)
  420. *next
  421. C SUMMED COLOUR IN XX IS XP.XM ETC
  422. B GG,I
  423. S FF,MMX,HA,HB,HB0,PHI=c,HXM=c,XX,HXX,XHX,HXHX
  424. Oldnew HXMC=HXP,PHIC=PHIG
  425. F HT,TA,EHBB,HL,HMX=c,LA,FHAGL
  426. Oldnew HMXC=HPX
  427. C          SUMMATION CONVENTIONS
  428. C HM*HP*XMDXP=XM(MU1,I1)*HP(I1)*XP(MU1,I2)*HM(I2)    I.E.  P.M  ETC
  429. S HM=c
  430. Oldnew HMC=HP
  431. X HH1(I1,I2)=HMX*D(I1,1)*D(I2,2)
  432. C                 HIGGS 24
  433. Z HH(I1,I2)=-I*HH1(I1,I2)+I*Conjg(HH1(I2,I1))
  434.    +(HL*RT12+UNIT*(2*HB0*RT12*RT13*RT15+4*RT12*FF/GG/5))*D(I1,1)*D(I2,1)
  435.    +(HT*RT12-UNI*(3*HB0*RT12*RT13*RT15+6*RT12*FF/GG/5))*D(I1,2)*D(I2,2)
  436. C                     HIGGS 5
  437. Z H(I1)=I*HM*D(I1,1)+I*PHI*D(I1,2)
  438. *next
  439. X DIFFH(I1)=I*DIFF(MU1,HM)*D(I1,1)+I*DIFF(MU1,PHI)*D(I1,2)
  440. Z DIFH(I1)=DIFFH(I1)+GG*A(MU1,I1,I2)*H(I2)
  441. Z DIFHH(I1,I2)=GG*A(MU1,I1,I3)*HH(I3,I2)-HH(I1,I3)*A(MU1,I3,I2)*GG
  442.  -I*DIFF(MU1,HXM)*D(I1,1)*D(I2,2)+DIFF(MU1,HXP)*D(I1,2)*D(I2,1)*I
  443.    +(DIFF(MU1,HL)*RT12+UNIT*UNIT* DIFF(MU1,HB0)*2*RT12*RT13*RT15)
  444.             *D(I1,1)*D(I2,1)
  445.    +(DIFF(MU1,HT)*RT12-UNI*UNI*3*DIFF(MU1,HB0)*RT12*RT13*RT15)
  446.    *D(I1,2)*D(I2,2)
  447. Id UNIT**N~=UNIT**N/UNIT
  448. Al UNI**N~=UNI**N/UNI
  449. Al,Multi,RT12**2=1/2
  450. Al RT13**2=1/3
  451. Al RT15**2=1/5
  452. Id HL*LG(MU1)=LG(MU1)*HL+2*I*FHAGL*LA
  453. Al HT*TB(MU1)=TB(MU1)*HT+2*I*EHBB*TA
  454. Id HL=HA*LA
  455. Al HT=HB*TA
  456. Al LG(MU1)=GL(MU1)*LA
  457. Al TB(MU1)=B(MU1)*TA
  458. Al DIFF(MU1,HL)=DIFF(MU1,HA)*LA
  459. Al DIFF(MU1,HT)=DIFF(MU1,HB)*TA
  460. *next
  461. B GG
  462. Z CDIFH(I1)=Conjg(DIFH(I1))
  463. *next
  464. B GG,I,FF
  465. Z Z=-CDIFH(I1)*DIFH(I1)
  466.    -DIFHH(I1,I2)*DIFHH(I2,I1)/2
  467.    -FF      *(DIFF(XP,HXM)+DIFF(XM,HXP))
  468. C PART OF GAUGE FIXING TERM
  469. Id UNIT**2=3
  470. Al UNI**2=2
  471. Al RT13**2=1/3
  472. Al RT15**2=1/5
  473. Al,Multi,RT12**2=1/2
  474. Id UNIT=1
  475. Al UNI=1
  476. Al,Ainbe,LA*LA=2
  477. Al,Ainbe,TA*TA=2
  478. Id LA=0
  479. Al TA=0
  480. *yep
  481. Id MX(MU1)*HPX*MX(MU1)*HPX=HXX**2
  482. Al MX(MU1)*HPX*HMX*PX(MU1)=HXHX*XX
  483. Al PX(MU1)*HMX*PX(MU1)*HMX=XHX**2
  484. Al PX(MU1)*HMX*HPX*MX(MU1)=XHX*HXX
  485. Al HMX*PX(MU1)*MX(MU1)*HPX=XX*HXHX
  486. Al HMX*PX(MU1)*HMX*PX(MU1)=XHX**2
  487. Al HPX*MX(MU1)*PX(MU1)*HMX=HXX*XHX
  488. Al HPX*MX(MU1)*HPX*MX(MU1)=HXX**2
  489. *yep
  490. Id MX(MU1~)=XM(MU1)
  491. Al PX(MU1~)=XP(MU1)
  492. Al HMX=HXM
  493. Al HPX=HXP
  494. Id,Commu,DIFF
  495. Print STAT
  496. P output
  497. C HIGGS KINETIC TERM
  498. *next
  499. F ZXM=c,ZXP=c,ZA=c,ZB=c,ZB0=c
  500. Oldnew ZXMC=ZXMG,ZXPC=ZXPG,ZAC=ZAG,ZBC=ZBG,ZB0C=ZB0G
  501. C     DIFFERENTIAL OF F.P. GHOST MULTIPLET
  502. Z DIFZ(I1,I2)=
  503.        D(I1,1)*D(I2,2)*DIFF(MU1,ZXM)
  504.    +D(I1,2)*D(I2,1)*DIFF(MU1,ZXP)
  505.    +D(I1,1)*D(I2,1)*(RT12*LA*DIFF(MU1,ZA)+UNIT*2*RT12*RT13*RT15*DIFF(MU1
  506.    ,ZB0))
  507.    +D(I1,2)*D(I2,2)*(RT12*TA*DIFF(MU1,ZB)-UNI*3*RT12*RT13*RT15*DIFF(MU1,
  508.    ZB0))
  509. *next
  510. Z DIFZB(I1,I2)=Conjg(DIFZ(I2,I1))
  511. Z HH(I1,I2)=HH(I1,I2)
  512. Id HMX=HXM
  513. Al HPX=HXP
  514. *next
  515. C          GHOST MULTIPLET
  516. Z GAUGE(I1,I2)=DIFZ(I1,I2)
  517. Z Zb(I1,I2)=DIFZB(I1,I2)
  518. Id DIFF(MU1,ZB0~)=ZB0
  519. *next
  520. B GG,I
  521. F FZAHA,FZAGL,EZBHB,EZBB
  522. C          SUMMATION CONVENTIONS
  523. C FZAHA=F(A,B,C)*ZA(B)*HA(C)
  524. C EZBB=Epf(A,B,C)*ZB(B)*B(C)
  525. C   ETC
  526. Z F0(I1,I2)=GAUGE(I1,I3)*A(MU1,I3,I2)-A(MU1,I1,I3)*GAUGE(I3,I2)
  527. Z F2(I1,I2)=-I*GG*RT12*(GAUGE(I1,I3)*HH(I3,I2)-HH(I1,I3)*GAUGE(I3,I2))
  528. Id LA*ZA*HL=HL*LA*ZA+2*I*FZAHA*LA
  529. Al TA*ZB*HT=HT*TA*ZB+2*I*EZBHB*TA
  530. Al LA*ZA*LG(MU1)=LG(MU1)*LA*ZA+2*I*LA*FZAGL(MU1)
  531. Al TA*ZB*TB(MU1)=TB(MU1)*TA*ZB+2*I*TA*EZBB(MU1)
  532. Al,Multi,RT12**2=1/2
  533. Al UNIT=1
  534. Al UNI=1
  535. Id HL=HA*LA
  536. Al HT=HB*TA
  537. Al LG(MU1)=LA*GL(MU1)
  538. Al TB(MU1)=TA*B(MU1)
  539. *next
  540. B GG,I,FF
  541. Z MZ(I1,I2)=I*FF* (F2(1,2)*D(I1,1)*D(I2,2)-F2(2,1)*D(I1,2)*D(I2,1))
  542. *next
  543. B GG,I,FF
  544. Z LFP1=-DIFZB(I1,I2)*DIFZ(I2,I1)
  545. Z LFP2=DIFZB(I1,I2)*F0(I2,I1)*GG
  546. Z LFP3=Zb(I1,I2)*MZ(I2,I1)
  547. *yep
  548. B GG,I,FF
  549. Id,Ainbe,LA*LA=2
  550. Al,Ainbe,TA*TA=2
  551. Al,UNIT**2=3
  552. Al UNI**2=2
  553. Al MX(MU1)=XM(MU1)
  554. Al PX(MU1)=XP(MU1)
  555. Id LA=0
  556. Al TA=0
  557. Al UNIT=1
  558. Al UNI=1
  559. Al RT13**2=1/3
  560. Al RT15**2=1/5
  561. Al,Multi,RT12**2=1/2
  562. P output
  563. C FADEEV POPOV GHOST LAGRANGIAN
  564. *next
  565. B GG,I,FF
  566. Z HSH=Conjg(H(I1))*H(I1)
  567. Z HHHH=HH(I1,I2)*HH(I2,I1)
  568. Id UNIT**2=3
  569. Al UNI**2=2
  570. Al RT13**2=1/3
  571. Al RT15**2=1/5
  572. Al,Multi,RT12**2=1/2
  573. Al HL*HL=2*HA*HA
  574. Al HT*HT=2*HB*HB
  575. Id UNIT=1
  576. Al UNI=1
  577. Al HL=0
  578. Al HT=0
  579. *next
  580. B GG,I,FF
  581. Z HH2(I1,I2)=HH(I1,I3)*HH(I3,I2)
  582. Id UNIT**N~=UNIT**N/UNIT
  583. Al UNI**N~=UNI**N/UNI
  584. Al,RT13**2=1/3
  585. Al RT15**2=1/5
  586. Al,Multi,RT12**2=1/2
  587. *next
  588. S MM1,MM2
  589. B MM1,MM2,GG,I,FF
  590. Z LH1=-MM1**2*HSH
  591. Z LH2=-MM2**2/2*HHHH
  592. Id GG**-2=0
  593. *next
  594. S MM3,MM4
  595. B MM3,GG,I,FF
  596. C LH3 COLOUR IS HP.LA*HA.HM
  597. C LH3 COLOUR IS PHIG.TA*HB.PHI
  598. Z LH3=-GG*MM3*Conjg(H(I1))*HH(I1,I2)*H(I2)
  599. Id UNIT=1
  600. Al UNI=1
  601. Al HL=LA*HA
  602. Al HT=TA*HB
  603. Al,Multi,RT12**2=1/2
  604. Al GG**-2=0
  605. *next
  606. B MM4,GG,I,FF
  607. Z LH4=-GG*MM4*HH(I1,I2)*HH(I2,I3)*HH(I3,I1)
  608. Id UNIT**3=3
  609. Al UNI**3=2
  610. Al HL*HL*HL=0
  611. Al HT*HT*HT=0
  612. Id UNIT=1
  613. Al UNI=1
  614. Al GG**-2=0
  615. Al HL*HL=2*HA*HA
  616. Al HT*HT=2*HB*HB
  617. Al,Multi,RT12**2=1/2
  618. Al,Multi,RT13**2=1/3
  619. Al,Multi,RT15**2=1/5
  620. Id HL=0
  621. Al HT=0
  622. *next
  623. S LL5,LL6,LL7,LL8,LL9
  624. B LL5,LL6,LL7,GG,I,FF
  625. C LH5 COLOUR IS POWERS OF HP.HM AND PHIG.PHI
  626. C LH6 COLOUR IS HP.HM AND PHIG.PHI AND HXP.HXM
  627. C LH7 COLOUR IS POWERS OF HXP.HXM
  628. Z LH5=-LL5*GG*GG*HSH*HSH
  629. Z LH6=-LL6*GG*GG*HSH*HHHH
  630. Z LH7=-LL7*GG*GG*HHHH*HHHH
  631. Id GG**-2=0
  632. Al RT12**2=1/2
  633. Al RT13**2=1/3
  634. Al RT15**2=1/5
  635. *next
  636. B LL8,GG,I,FF
  637. C LH8 QUARTIC COLOUR IS HP.LA.LA.HM OR HP.HXM.HXP.HM OR HP.LA.HXM.PHI
  638. C  OR HP.HXM.TA.PHI OR PHIG.TA.TA.PHI OR PHIG.HXP.HXM.PHI OR
  639. C    PHIG.HXP.LA.HM OR PHIG.TA.HXP.HM
  640. C LH8 CUBIC COLOUR IS HP.LA.HM OR HP.HXM.PHI OR PHIG.TA.PHI OR PHIG.HXP.
  641. Z LH8=-LL8*Conjg(H(I1))*HH2(I1,I2)*H(I2)*GG*GG
  642. Id UNIT=1
  643. Al UNI=1
  644. Al HL=LA*HA
  645. Al HT=TA*HB
  646. Id,Multi,RT12**2=1/2
  647. Al GG**-2=0
  648. Al,Commu,LA
  649. Al,Commu,TA
  650. *next
  651. B LL9,GG,I,FF
  652. F HL4,HT4
  653. C LH9 COLOUR IS TR(HXP.HXM.HXP.HXM) = HXP(A,J)*HYM(A,I)*HXP(B,I)*HXM(B,J
  654. Z LH9=-LL9*GG*GG*HH2(I1,I2)*HH2(I2,I1)
  655. Id UNIT**2=3
  656. Al UNI**2=2
  657. Al GG**-2=0
  658. Al HL*HL*HL*HL=HL4
  659. Al HT*HT*HT*HT=HT4
  660. Al RT13**2=1/3
  661. Al RT15**2=1/5
  662. Al,Multi,RT12**2=1/2
  663. Id UNIT=1
  664. Al UNI=1
  665. Al HL*HL*HL=0
  666. Al HT*HT*HT=0
  667. Id,Ainbe,HL*HL=2*HA*HA
  668. Al,Ainbe,HT*HT=2*HB*HB
  669. Id HL=0
  670. Al HT=0
  671. *next
  672. S LL10,LL11,LL12,LL21,LL23
  673. B GG,I,HP,HM,PHIG,PHI,HA,HB0,HB,HXP,HXM,MMX
  674. Z LHA=LH1+LH2+LH3+LH4+LH5+LH6+LH7+LH8+LH9
  675.    -MMX**2*HXP*HXM
  676. C PART OF GAUGE FIXING TERM
  677. Id MM2**2=6*RT12/5*FF*MM4-48/5*FF**2*LL7-56/25*FF**2*LL9
  678. Id MM4=-FF*LL11*RT12/15+4*FF*LL12*RT12/15
  679. Al LL7=-LL11/32-LL12/48+5*LL10/96
  680. Al LL9=LL12/8+LL11/8
  681. Al MM1**2=6*FF*MM3*RT12/5-12*FF**2*LL6/5-18*FF**2*LL8/25+FF**2*LL21
  682. Id MM3=2*FF*LL8*RT12/5+RT12*FF*LL23-RT12*FF*LL21
  683. Id,Multi,RT12**2=1/2
  684. P output
  685. C HIGGS POTENTIAL
  686. *begin
  687. Common A,E,DIF
  688. C RT12=SQRT(1/2) ETC
  689. C GG = GAUGE COUPLING CONSTANT
  690. C          SUMMATION CONVENTIONS
  691. C UNIT = 3 BY 3 UNIT MATRIX
  692. C UNI= 2 BY 2 MATRIX
  693. C LG(MU)=LAMBDA(A)*GL(A,MU)
  694. C TB(MU)=TAU(A)*B(A,MU)
  695. C LDIFF(GL)=LAMBDA(A)*DIFF(GL(A))
  696. C TDIFF(B)=TAU(A)*DIFF(B(MU))
  697. C FGGDG(MU,NU,RO,SI)=F(A,B,C)*GL(A,MU)*GL(B,NU)*D(RO)*GL(C,SI)
  698. C EBBDB(MU,NU,RO,SI)=Epf(A,B,C)*B(A,MU)*B(B,NU)*D(RO)*B(C,SI)
  699. C FGGL(MU,NU)=F(A,B,C)*GL(A,MU)*GL(B,NU)*LAMBDA(C)
  700. C EBBT(MU,NU)=Epf(A,B,C)*B(A,MU)*B(B,NU)*TAU(C)
  701. C F2G4(MU,NU,RO,SI)=F(A,B,E)*F(C,D,E)*GL(A,MU)*GL(B,NU)*GL(C,RO)*GL(D,SI
  702. C E2B4(MU,NU,RO,SI)=Epf(A,B,E)*Epf(C,D,E)*B(A,MU)*B(B,NU)*B(C,RO)*B(D,SI
  703. C E2B4(MU,NU,MU,NU)=B(I,MU)*B(I,MU)*B(J,NU)*B(J,NU)-B(I,MU)*B(I,NU)*B(J,
  704. C    B(J,NU)
  705. C XXXX=XP(A,I,MU)*XM(A,J,NU)*XP(B,J,NU)*XM(B,I,MU)
  706. C XP.XP*XM.XM=XP(A,I,MU)*XM(A,J,NU)*XP(B,J,MU)*XM(B,I,NU)
  707. C (XP.XM)**2=XP(A,I,MU)*XM(A,J,MU)*XP(B,J,NU)*XM(B,I,NU)
  708. B GG
  709. S GG,UNIT,RT12,RT13,RT15,UNI
  710. I MU1,MU2,MU3,MU4,I1=3,I2=3,I3=3,I4=3
  711. V GL,B,B0,XM,XP
  712. F XXXX,DIFF,LDIFF,TDIFF,LG,TB,FGGDG,EBBDB,FGGL,EBBT,F2G4,E2B4,MX=c
  713. Oldnew MXC=PX
  714. Z DIF(MU1,MU2,I1,I2)=-I*RT12*(
  715.    +DIFF(MU1,XM,MU2)*D(I1,1)*D(I2,2)
  716.    +DIFF(MU1,XP,MU2)*D(I1,2)*D(I2,1)
  717.    +(RT12*LDIFF(MU1,GL,MU2)+UNIT*2*RT12*RT13*RT15*DIFF(MU1,B0,MU2))
  718.    *D(I1,1)*D(I2,1)
  719.    +(RT12*TDIFF(MU1,B,MU2)-UNI*3*RT12*RT13*RT15*DIFF(MU1,B0,MU2))
  720.    *D(I1,2)*D(I2,2))
  721. Id RT12**2=1/2
  722. *next
  723. Z A(MU1,I1,I2)=DIF(MU2,MU1,I1,I2)
  724. Id DIFF(MU1~,XM,MU2~)=MX(MU2)
  725. Al DIFF(MU1~,XP,MU2~)=PX(MU2)
  726. Al LDIFF(MU1~,GL,MU2~)=LG(MU2)
  727. Al TDIFF(MU1~,B,MU2~)=TB(MU2)
  728. Id DIFF(MU1~,B0~,MU2~)=B0(MU2)
  729. *next
  730. B GG
  731. Z E(I1,I3)=GG*(A(MU1,I1,I2)*A(MU2,I2,I3)-A(MU2,I1,I2)*A(MU1,I2,I3))
  732. *yep
  733. Id,Multi,RT12**2=1/2
  734. Al LG(MU1)*LG(MU2)=LG(MU2)*LG(MU1)+2*I*FGGL(MU1,MU2)
  735. Al TB(MU1)*TB(MU2)=TB(MU2)*TB(MU1)+2*I*EBBT(MU1,MU2)
  736. Al UNIT**N~=UNIT**N/UNIT
  737. Al UNI**N~=UNI**N/UNI
  738. *next
  739. B GG
  740. Z ZG0=DIF(MU1,MU2,I1,I2)*DIF(MU1,MU2,I2,I1)
  741. Z ZG00=-DIF(MU1,MU1,I1,I2)*DIF(MU2,MU2,I2,I1)
  742. C ZG00=0 WHEN THE GAUGE FIXING TERM IS ADDED
  743. Z ZG1=2*E(I1,I2)*DIF(MU1,MU2,I2,I1)
  744. Z ZG2=E(I1,I2)*E(I2,I1)/2
  745. *yep
  746. Id UNIT**N~=UNIT**N/UNIT
  747. Al UNI**N~=UNI**N/UNI
  748. Al RT12**2=1/2
  749. Al RT13**2=1/3
  750. Al RT15**2=1/5
  751. Sum MU1,MU2
  752. Id,Ainbe,LG(MU1~)*LG(MU2~)=2*GL(MU1)*GL(MU2)
  753. Al,Ainbe,TB(MU1~)*TB(MU2~)=2*B(MU1)*B(MU2)
  754. Al LDIFF(MU1~,GL,MU2~)*LDIFF(MU3~,GL,MU4~)=2*DIFF(MU1,GL,MU2)*DIFF(MU3,
  755.    GL,MU4)
  756. Al TDIFF(MU1~,B,MU2~)*TDIFF(MU3~,B,MU4~)=2*DIFF(MU1,B,MU2)*DIFF(MU3,B,
  757.    MU4)
  758. Al FGGL(MU1~,MU2~)*LDIFF(MU3~,GL,MU4~)=2*FGGDG(MU1,MU2,MU3,MU4)
  759. Al EBBT(MU1~,MU2~)*TDIFF(MU3~,B,MU4~)=2*EBBDB(MU1,MU2,MU3,MU4)
  760. Al FGGL(MU1~,MU2~)*FGGL(MU3~,MU4~)=2*F2G4(MU1,MU2,MU3,MU4)
  761. Al EBBT(MU1~,MU2~)*EBBT(MU3~,MU4~)=2*E2B4(MU1,MU2,MU3,MU4)
  762. Id FGGL(MU1~,MU2~)=0
  763. Al EBBT(MU1~,MU2~)=0
  764. Al LG(MU1~)=0
  765. Al TB(MU1~)=0
  766. Al LDIFF(MU1~,GL,MU2~)=0
  767. Al TDIFF(MU1~,B,MU2~)=0
  768. Al UNIT=3
  769. Al UNI=2
  770. *yep
  771. B GG,B0DB0,BDB,GLDGL,XPDXM,XMDXM,XPDXP
  772. Id PX(MU1~)*MX(MU2~)*PX(MU2~)*MX(MU1~)=XXXX
  773. Id MX(MU1~)=XM(MU1)
  774. Al PX(MU1~)=XP(MU1)
  775. Id,Commu,DIFF
  776. C -1/4*F(MU,NU,A)*F(MU,NU,A)
  777. C ZG0+ZG1+ZG2=-1/4*F(MU,NU)**2   + PART OF GAUGE FIXING
  778. *begin
  779. B I,GG,RT12,RT13,RT15
  780. C THERE IS IMPLICIT LA IN G(1,GL) AND TA IN G(1,B)
  781. S GG,RT12,RT13,RT15,T
  782. I I1=5,I2=5,I3=5
  783. V GL,B,B0,XM,XP,K
  784. F CH
  785. F C=c,Cc=c,L=c,UPB=c,DNB=c,ELB=c,UDB=c,ENB=c
  786. Oldnew CC=CG,Cc=CC,CcC=CCG
  787. Oldnew LC=R,UPBC=UP,DNBC=DN,ELBC=EL,UDBC=UD,ENBC=EN
  788. X ASLSH(I1,I2)=-I*RT12*(G(1,XM)*(D(I1,1)+D(I1,2))*(D(I2,4)+D(I2,5))
  789.    +G(1,XP)*(D(I1,4)+D(I1,5))*(D(I2,1)+D(I2,2)))
  790.    -I/2*((G(1,GL)+2*RT13*RT15*G(1,B0))*D(I1,1)*D(I2,1)
  791.    +(-2*G(1,GL)+2*RT13*RT15*G(1,B0))*D(I1,2)*D(I2,2)
  792.    +(G(1,B)-3*RT13*RT15*G(1,B0))*D(I1,4)*D(I2,4)
  793.    +(-2*G(1,B)-3*RT13*RT15*G(1,B0))*D(I1,5)*D(I2,5))
  794. X DSLSH(T,I1,I2)=I*G(1,K)*D(I1,I2)+T*GG*ASLSH(I1,I2)
  795. X MM(I1,I2,L,CC,C)=RT12*(
  796.    C(L,UP  )*(D(I1,1)*D(I2,2)-D(I1,2)*D(I2,1))*Epf(1,2,3)
  797.    +CC(L,UD)*(D(I1,1)*D(I2,4)-D(I1,4)*D(I2,1))
  798.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4))*Epf(1,2))
  799. X M(I1,I2)=MM(I1,I2,L,CC,C)
  800. X MB(I1,I2)=Conjg(MM(I2,I1,L,CC,C))
  801. X P(I1)=CC(R,DN)*D(I1,1)+C(R,EN)*D(I1,4)
  802. X PB(I1)=Conjg(P(I1))
  803. Z LGRN1=
  804.    -PB(I1)*DSLSH(1,I1,I2)*P(I2)
  805. Z LGRN2=
  806.    -MB(I1,I2)*DSLSH(2,I2,I3)*M(I3,I1)
  807. *yep
  808. Id,Multi,RT12**2=1/2
  809. Al Epf(1,2,3)*Epf(1,2,3)=-1
  810. Al Epf(1,2)*Epf(1,2)=-1
  811. Al CG(R~,DN~)*G(1,K )*C(L~,EL~)= Conjg(EL)*L*G(1,K)*R*Conjg(DN)
  812. Id CG(R~,DN~)*G(1,K~)*C(L~,EL~)=-Conjg(EL)*L*G(1,K)*R*Conjg(DN)
  813. Id CC(L~,EL~)=L*EL
  814. Al CCG(R~,ELB~)=ELB*R
  815. Al C(L~,EL~)=L*CH*EL
  816. Al CG(R~,ELB~)=ELB*CH*R
  817. *yep
  818. Id,Adiso,L*G(1,K)*R=G(1,K)
  819. Id L*G(1,B~)*R=G(1,B)*R
  820. Al R*G(1,B~)*L=G(1,B)*L
  821. P output
  822. C FERMION KINETIC TERMS
  823. C   AND FERMION INTERACTIONS WITH GAUGE FIELD
  824. *yep
  825. Id L=G6(1)/2
  826. Al R=G7(1)/2
  827. *begin
  828. S HM=c,PHI=c
  829. Oldnew HMC=HP,PHIC=PHIG
  830. I I1=5,I2=5
  831. Z H(I1)=I*HM*D(I1,1)+I*PHI*(D(I1,4)+D(I1,5))
  832. *next
  833. C EN*Epf(1,2)*PHIG=Epf(I1,I2)*EN(I1)*PHIG(I2)
  834. C ENB*Epf(1,2)*PHI=Epf(I1,I2)*PHI(I1)*ENB(I2)
  835. S RT12,L2
  836. B L2,I,RT12,HM,HP,PHI,PHIG
  837. F CH
  838. F C=c,Cc=c,L=c,UPB=c,DNB=c,ELB=c,UDB=c,ENB=c
  839. Oldnew CC=CG,Cc=CC,CcC=CCG
  840. Oldnew LC=R,UPBC=UP,DNBC=DN,ELBC=EL,UDBC=UD,ENBC=EN
  841. X MM(I1,I2,L,CC,C)=RT12*(
  842.    -C(L,UP)*(D(I1,1)*D(I2,3)-D(I1,3)*D(I2,1))*Epf(3,2,1)
  843.    +CC(L,UD)*(D(I1,1)*D(I2,4)-D(I1,4)*D(I2,1))
  844.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4))*Epf(1,2))
  845. X P(I1)=CC(R,DN)*(D(I1,1)+D(I1,3))+C(R,EN)*D(I1,4)
  846. X PB(I1)=Conjg(P(I1))
  847. X M(I1,I2)=MM(I1,I2,L,CC,C)
  848. X MB(I1,I2)=Conjg(MM(I2,I1,L,CC,C))
  849. Z Z=-L2*(H(I1)*MB(I1,I2)*P(I2)+PB(I1)*M(I1,I2)*Conjg(H(I2)))
  850. *yep
  851. Al CG(R~,UP~)*C(L~,EL~)=Conjg(EL)*L*R*Conjg(UP)
  852. Id CC(L~,EL~)=L*EL
  853. Al CCG(R~,ELB~)=ELB*R
  854. Al C(L~,EL~)=L*CH*EL
  855. Al CG(R~,ELB~)=ELB*CH*R
  856. Id R*R=R
  857. Al L*L=L
  858. P output
  859. C FERMION HIGGS COUPLING 2
  860. *yep
  861. Id L=G6(1)/2
  862. Al R=G7(1)/2
  863. *begin
  864. S HM=c,PHI=c
  865. Oldnew HMC=HP,PHIC=PHIG
  866. I I1=5,I2=5,I3=5,I4=5,I5=5
  867. Z H(I1)=I*HM*D(I1,1)+I*PHI*D(I1,4)
  868. *next
  869. S RT12,L1
  870. B L1,I,RT12,HM,HP,PHI,PHIG
  871. F CH
  872. F C=c,Cc=c,L=c,UPB=c,UDB=c,ELB=c
  873. Oldnew CC=CG,Cc=CC,CcC=CCG
  874. Oldnew LC=R,UPBC=UP,UDBC=UD,ELBC=EL
  875. X MM(I1,I2,L,CC,C)=RT12*(
  876.    C(L,UP  )*(D(I1,1)*D(I2,2)-D(I1,2)*D(I2,1))
  877.   +C(L,UP  )*(D(I1,2)*D(I2,3)-D(I1,3)*D(I2,2))
  878.   +CC(L,UD  )*(D(I1,2)*D(I2,4)-D(I1,4)*D(I2,2))*Epf(3,2,1)*Epf(2,1)
  879.  /2
  880.   +CC(L,UD  )*(D(I1,3)*D(I2,5)-D(I1,5)*D(I2,3))
  881.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4)))
  882. X M(I1,I2)=MM(I1,I2,L,CC,C)
  883. X MC(I1,I2)=MM(I1,I2,R,C,CC)
  884. X MB(I1,I2)=Conjg(MM(I2,I1,L,CC,C))
  885. X MCB(I1,I2)=Conjg(MM(I2,I1,R,C,CC))
  886. Z Z=-L1*Epf(I1,I2,I3,I4,I5)*
  887.    (MCB(I1,I2)*M(I3,I4)*H(I5)+MB(I1,I2)*MC(I3,I4)*Conjg(H(I5)))
  888. *yep
  889. Id Epf(1,2,3,4,5)=1
  890. Al CG(R~,UP~)*C(L~,EL~)=Conjg(EL)*L*R*Conjg(UP)
  891. Al CCG(R~,UP~)*C(L~,EL)=ELB*L*R*CH*Conjg(UP)
  892. Al CG(R~,ELB)*CC(L~,UP~)=Conjg(UP)*CH*L*R*EL
  893. Id CC(L~,EL~)=L*EL
  894. Al CCG(R~,ELB~)=ELB*R
  895. Al C(L~,EL~)=L*CH*EL
  896. Al CG(R~,ELB~)=ELB*CH*R
  897. Id,Multi,RT12**2=1/2
  898. Id Epf(1,2,3)*Epf(1,2)=Epf(1,2)*Epf(1,2,3)
  899. Id R*R=R
  900. Al L*L=L
  901. P output
  902. C FERMION HIGGS COUPLING 1
  903. *yep
  904. Id L=G6(1)/2
  905. Al R=G7(1)/2
  906. *end
  907.  
  908. C Varia 8. Lagrangian for SU(5) twice broken to SU(3)*U(1).
  909.  
  910. C PROGRAM WRITTEN BY MARTIN GREEN, AUGUST 1981.
  911. P stat
  912. Common A,DIF,DIFH,CDIFH,DIFHH,F1,F2,DIFZ,DIFZB,ZB,GAUGE
  913.    ,H,HH,F1B,F0,MZ,HSH,HHHH,HH2
  914.    ,LH1,LH2,LH3,LH4,LH5,LH6,LH7,LH8,LH9
  915. C RT12=SQRT(1/2) ETC
  916. C GG = GAUGE COUPLING CONSTANT
  917. C UNIT = 3 BY 3 UNIT MATRIX
  918. C          SUMMATION CONVENTIONS
  919. C LG(MU)=LAMBDA(A)*GL(A,MU)
  920. C LDIFF(GL)=LAMBDA(A)*DIFF(GL(A))
  921. P noutp
  922. Oldnew i=I
  923. B GG
  924. S GG,UNIT,RT12,RT13,RT15
  925. I MU1,MU2,MU3,MU4,I1=3,I2=3,I3=3,I4=3
  926. V Z,PH,GL,WP,WM,XM,XP,YM,YP
  927. F DIFF,LDIFF,LG,MX=c,MY=c
  928. Oldnew MXC=PX,MYC=PY
  929. C   DIFFERENTIAL OF A(MU)
  930. Z DIF(MU1,MU2,I1,I2)=-I*RT12*(
  931.    DIFF(MU1,WP,MU2)*D(I1,2)*D(I2,3)+DIFF(MU1,WM,MU2)*D(I1,3)*D(I2,2)
  932.    +DIFF(MU1,XM,MU2)*D(I1,1)*D(I2,2)+DIFF(MU1,YM,MU2)*D(I1,1)*D(I2,3)
  933.    +DIFF(MU1,XP,MU2)*D(I1,2)*D(I2,1)+DIFF(MU1,YP,MU2)*D(I1,3)*D(I2,1)
  934.  +(RT12*LDIFF(MU1,GL,MU2)+UNIT*DIFF(MU1,Z,MU2)*RT15/2-UNIT*DIFF(MU1,PH,
  935.    MU2)*RT13/2)*D(I1,1)*D(I2,1)+(DIFF(MU1,Z,MU2)*RT15/2+3*DIFF(MU1,PH,MU
  936.    2)*RT13/2)*D(I1,2)*D(I2,2)-2*DIFF(MU1,Z,MU2)*RT15*D(I1,3)*D(I2,3))
  937. Id RT12**2=1/2
  938. *next
  939. C                     A(MU)
  940. Z A(MU1,I1,I2)=DIF(MU2,MU1,I1,I2)
  941. Id DIFF(MU1~,XM,MU2~)=MX(MU2)
  942. Al DIFF(MU1~,XP,MU2~)=PX(MU2)
  943. Al DIFF(MU1~,YM,MU2~)=MY(MU2)
  944. Al DIFF(MU1~,YP,MU2~)=PY(MU2)
  945. Al LDIFF(MU1~,GL,MU2~)=LG(MU2)
  946. Id DIFF(MU1~,Z~,MU2~)=Z(MU2)
  947. *next
  948. C          SUMMATION CONVENTIONS
  949. C SUMMED COLOUR IS OF THE FORM PX.MY OR PY.MX ETC
  950. C SUMMED COLOUR IN XX IS XP.XM ETC
  951. B GG,I
  952. S MMW,MMY,MMX
  953. S C1,S1,C2,S2
  954. F HM1=c
  955. Oldnew HM1C=HP1
  956. S HB0,HB3
  957. S XX,YY,HXX,HYY,XHX,YHY,HXHX,HYHY
  958. S H1Y,H1H1,YH1,H1HY,HYH1
  959. S HA,HZ,HPH,HWP=c,FF
  960. S HXM=c,HYM=c
  961. Oldnew HXMC=HXP,HYMC=HYP
  962. F HL,HMX=c,HMY=c,LA,FHAGL
  963. Oldnew HWPC=HWM,HMXC=HPX,HMYC=HPY
  964. C          SUMMATION CONVENTIONS
  965. C HM*HP*YMDYP=YM(MU1,I1)*HP(I1)*YP(MU1,I2)*HM(I2)    I.E.  P.M  ETC
  966. S HM=c,PHIP=c,F,H0,PHI0
  967. Oldnew HMC=HP,PHIPC=PHIM
  968. X HH1(I1,I2)=HMX*D(I1,1)*D(I2,2)+(C1*HMY+S1*HM1)*D(I1,1)*D(I2,3)
  969.    +(C2*HWP-S2*PHIP)*D(I1,2)*D(I2,3)
  970. C                       HIGGS 24
  971. Z HH(I1,I2)=-I*HH1(I1,I2)+I*Conjg(HH1(I2,I1))
  972.    +(HL*RT12+UNIT*(2*HB0*RT12*RT13*RT15+4*RT12*FF/GG/5))*D(I1,1)*D(I2,1)
  973.    +(HB3*RT12-3*HB0*RT12*RT13*RT15-6*RT12*FF/GG/5)*D(I1,2)*D(I2,2)
  974.    -(HB3*RT12+3*HB0*RT12*RT13*RT15+6*RT12*FF/GG/5)*D(I1,3)*D(I2,3)
  975.    +EPS/GG*(D(I1,2)*D(I2,2)-D(I1,3)*D(I2,3))*2*RT12
  976. C                         HIGGS 5
  977. Z H(I1)=I*(C1*HM-S1*HYM)*D(I1,1)+I*(C2*PHIP+S2*HWP)*D(I1,2)
  978.    +(H0+2*F/GG-I*PHI0)*RT12*D(I1,3)
  979. *next
  980. X DIFFH(I1)=I*(C1*DIFF(MU1,HM)-S1*DIFF(MU1,HYM))*D(I1,1)
  981.    +I*(C2*DIFF(MU1,PHIP)+S2*DIFF(MU1,HWP))*D(I1,2)
  982.    +(DIFF(MU1,H0)*RT12-I*DIFF(MU1,PHI0)*RT12)*D(I1,3)
  983. Z DIFH(I1)=DIFFH(I1)+GG*A(MU1,I1,I2)*H(I2)
  984. Z DIFHH(I1,I2)=GG*A(MU1,I1,I3)*HH(I3,I2)-HH(I1,I3)*A(MU1,I3,I2)*GG
  985.  -I*DIFF(MU1,HXM)*D(I1,1)*D(I2,2)+DIFF(MU1,HXP)*D(I1,2)*D(I2,1)*I
  986.    -I*(C1*DIFF(MU1,HYM)+S1*DIFF(MU1,HM))*D(I1,1)*D(I2,3)
  987.    +I*(C1*DIFF(MU1,HYP)+S1*DIFF(MU1,HP))*D(I1,3)*D(I2,1)
  988.    -I*(C2*DIFF(MU1,HWP)-S2*DIFF(MU1,PHIP))*D(I1,2)*D(I2,3)
  989.    +I*(C2*DIFF(MU1,HWM)-S2*DIFF(MU1,PHIM))*D(I1,3)*D(I2,2)
  990.    +(DIFF(MU1,HL)*RT12+UNIT*UNIT* DIFF(MU1,HB0)*2*RT12*RT13*RT15)
  991.             *D(I1,1)*D(I2,1)
  992.    +(DIFF(MU1,HB3)*RT12-3*DIFF(MU1,HB0)*RT12*RT13*RT15)*D(I1,2)*D(I2,2)
  993.    -(DIFF(MU1,HB3)*RT12+3*DIFF(MU1,HB0)*RT12*RT13*RT15)*D(I1,3)*D(I2,3)
  994. Id UNIT**N~=UNIT**N/UNIT
  995. Al,Multi,RT12**2=1/2
  996. Al RT13**2=1/3
  997. Al RT15**2=1/5
  998. Id HL*LG(MU1)=LG(MU1)*HL+2*I*FHAGL*LA
  999. Id HL=HA*LA
  1000. Al LG(MU1)=GL(MU1)*LA
  1001. Al DIFF(MU1,HL)=DIFF(MU1,HA)*LA
  1002. *next
  1003. B GG
  1004. Z CDIFH(I1)=Conjg(DIFH(I1))
  1005. Id WP(MU1)=GL(MU1)
  1006. Id WM(MU1)=WP(MU1)
  1007. Id GL(MU1)=WM(MU1)
  1008. *next
  1009. B GG,I,F,EPS,FFEPS,MMW,MMY
  1010. Z Z=-CDIFH(I1)*DIFH(I1)
  1011.    -DIFHH(I1,I2)*DIFHH(I2,I1)/2
  1012.    -4*F*RT12*RT15*DIFF(Z,PHI0)
  1013.    -(FF-EPS)*(DIFF(XP,HXM)+DIFF(XM,HXP))
  1014.    -MMY*(DIFF(YP,HYM)+DIFF(YM,HYP))
  1015.    -MMW*(DIFF(WM,PHIP)+DIFF(WP,PHIM))
  1016. C PART OF GAUGE FIXING TERM
  1017. Id UNIT**2=3
  1018. Al RT13**2=1/3
  1019. Al RT15**2=1/5
  1020. Al,Multi,RT12**2=1/2
  1021. Id UNIT=1
  1022. Al,Ainbe,LA*LA=2
  1023. Id LA=0
  1024. Al S1**2=1-C1*C1
  1025. Al S2**2=1-C2*C2
  1026. Al S2*F=-2*EPS*C2
  1027. Al S1*FF=-EPS*S1-F*C1
  1028. Al S1*F=(FF+EPS)*C1-MMY
  1029. Al S2*EPS=F*C2/2-MMW/2
  1030. *yep
  1031. C          SUMMATION CONVENTIONS
  1032. Id MX(MU1)*HPX*MX(MU1)*HPX=HXX**2
  1033. Al MX(MU1)*HPX*HMX*PX(MU1)=HXHX*XX
  1034. Al PX(MU1)*HMX*PX(MU1)*HMX=XHX**2
  1035. Al PX(MU1)*HMX*HPX*MX(MU1)=XHX*HXX
  1036. Al HMX*PX(MU1)*MX(MU1)*HPX=XX*HXHX
  1037. Al HMX*PX(MU1)*HMX*PX(MU1)=XHX**2
  1038. Al HPX*MX(MU1)*PX(MU1)*HMX=HXX*XHX
  1039. Al HPX*MX(MU1)*HPX*MX(MU1)=HXX**2
  1040. Al MY(MU1)*HPY*MY(MU1)*HPY=HYY**2
  1041. Al MY(MU1)*HP1*MY(MU1)*HP1=H1Y**2
  1042. Al MY(MU1)*HP1*MY(MU1)*HPY=HYY*H1Y
  1043. Al MY(MU1)*HPY*MY(MU1)*HP1=HYY*H1Y
  1044. Al MY(MU1)*HPY*HMY*PY(MU1)=HYHY*YY
  1045. Al MY(MU1)*HPY*HM1*PY(MU1)=HYH1*YY
  1046. Al MY(MU1)*HP1*HMY*PY(MU1)=H1HY*YY
  1047. Al MY(MU1)*HP1*HM1*PY(MU1)=H1H1*YY
  1048. Al PY(MU1)*HMY*PY(MU1)*HMY=YHY**2
  1049. Al PY(MU1)*HM1*PY(MU1)*HMY=YHY*YH1
  1050. Al PY(MU1)*HMY*PY(MU1)*HM1=YHY*YH1
  1051. Al PY(MU1)*HM1*PY(MU1)*HM1=YH1**2
  1052. Al PY(MU1)*HMY*HPY*MY(MU1)=YHY*HYY
  1053. Al PY(MU1)*HM1*HPY*MY(MU1)=YH1*HYY
  1054. Al PY(MU1)*HMY*HP1*MY(MU1)=YHY*H1Y
  1055. Al PY(MU1)*HM1*HP1*MY(MU1)=YH1*H1Y
  1056. Al HMY*PY(MU1)*MY(MU1)*HPY=YY*HYHY
  1057. Al HM1*PY(MU1)*MY(MU1)*HP1=YY*H1H1
  1058. Al HM1*PY(MU1)*MY(MU1)*HPY=YY*HYH1
  1059. Al HMY*PY(MU1)*MY(MU1)*HP1=YY*H1HY
  1060. Al HMY*PY(MU1)*HMY*PY(MU1)=YHY**2
  1061. Al HM1*PY(MU1)*HMY*PY(MU1)=YHY*YH1
  1062. Al HMY*PY(MU1)*HM1*PY(MU1)=YHY*YH1
  1063. Al HM1*PY(MU1)*HM1*PY(MU1)=YH1**2
  1064. Al HPY*MY(MU1)*PY(MU1)*HMY=HYY*YHY
  1065. Al HPY*MY(MU1)*PY(MU1)*HM1=HYY*YH1
  1066. Al HP1*MY(MU1)*PY(MU1)*HM1=H1Y*YH1
  1067. Al HP1*MY(MU1)*PY(MU1)*HMY=H1Y*YHY
  1068. Al HPY*MY(MU1)*HPY*MY(MU1)=HYY**2
  1069. Al HP1*MY(MU1)*HPY*MY(MU1)=HYY*H1Y
  1070. Al HPY*MY(MU1)*HP1*MY(MU1)=HYY*H1Y
  1071. Al HP1*MY(MU1)*HP1*MY(MU1)=H1Y**2
  1072. *yep
  1073. Id MX(MU1~)=XM(MU1)
  1074. Al PX(MU1~)=XP(MU1)
  1075. Al HMX=HXM
  1076. Al HPX=HXP
  1077. Al MY(MU1~)=YM(MU1)
  1078. Al PY(MU1~)=YP(MU1)
  1079. Al HMY=HYM
  1080. Al HPY=HYP
  1081. Al HM1=HM
  1082. Al HP1=HP
  1083. Al S1=-F/MMY
  1084. Al S2=-2*EPS/MMW
  1085. Al C1=(FF+EPS)/MMY
  1086. Al C2=F/MMW
  1087. Id,Commu,DIFF
  1088. Id FF=FFEPS-EPS
  1089. *yep
  1090. B GG,I,F,FF
  1091. C    THROWING AWAY VERY NEGLIGABLE TERMS
  1092. Id,Count,0,F,-1,EPS,-2,MMW,-1,H0,1,PHI0,1,PHIP,1,PHIM,1
  1093.    ,WM,1,WP,1,Z,1
  1094. Id FFEPS=FF
  1095. Al MMY**N~=FF**N
  1096. Al MMW**N~=F**N
  1097. Al GG**1=GG*GG1
  1098. Id,Count,-2,GG,-1,GG1,-1,F,-1,EPS,-2
  1099. Id GG1=1
  1100. C HIGGS KINETIC TERM
  1101. *next
  1102. P noutput
  1103. F ZXM=c,ZXP=c,ZYM=c,ZYP=c,ZWM=c,ZWP=c,ZA=c,ZPH=c,ZZ=c
  1104. Oldnew ZXMC=ZXMG,ZYMC=ZYMG,ZYPC=ZYPG,ZWMC=ZWMG,ZWPC=ZWPG,ZAC=ZAG,ZPHC=ZPHG
  1105. Oldnew ZZC=ZZG,ZXPC=ZXPG
  1106. C   DIFFERENTIAL OF F.P. GHOST MULTIPLET
  1107. Z DIFZ(I1,I2)=
  1108.        D(I1,1)*D(I2,2)*DIFF(MU1,ZXM)+D(I1,1)*D(I2,3)*DIFF(MU1,ZYM)
  1109.    +D(I1,2)*D(I2,1)*DIFF(MU1,ZXP)+D(I1,3)*D(I2,1)*DIFF(MU1,ZYP)
  1110.    +D(I1,2)*D(I2,3)*DIFF(MU1,ZWP)+D(I1,3)*D(I2,2)*DIFF(MU1,ZWM)
  1111.    +D(I1,1)*D(I2,1)*(RT12*LA*DIFF(MU1,ZA)+UNIT*(-DIFF(MU1,ZPH)*RT13+DIFF
  1112.    (MU1,ZZ)*RT15)/2)
  1113.    +D(I1,2)*D(I2,2)*(3*DIFF(MU1,ZPH)*RT13+DIFF(MU1,ZZ)*RT15)/2
  1114.    -D(I1,3)*D(I2,3)*2*RT15*DIFF(MU1,ZZ)
  1115. *next
  1116. Z DIFZB(I1,I2)=Conjg(DIFZ(I2,I1))
  1117. Z HH(I1,I2)=HH(I1,I2)
  1118. Id HMX=HXM
  1119. Al HPX=HXP
  1120. Al HMY=HYM
  1121. Al HPY=HYP
  1122. Al HM1=HM
  1123. Al HP1=HP
  1124. *next
  1125. C      GHOST MULTIPLET
  1126. Z GAUGE(I1,I2)=DIFZ(I1,I2)
  1127. Z ZB(I1,I2)=DIFZB(I1,I2)
  1128. Id DIFF(MU1,ZZ~)=ZZ
  1129. *next
  1130. B GG,I
  1131. F FZAHA,FZAGL
  1132. C          SUMMATION CONVENTIONS
  1133. C FZAHA=F(A,B,C)*ZA(B)*HA(C)      ETC
  1134. C   INFINITESIMAL GAUGE TRANSFORMATIONS OF FIELDS
  1135. Z F0(I1,I2)=GAUGE(I1,I3)*A(MU1,I3,I2)-A(MU1,I1,I3)*GAUGE(I3,I2)
  1136. Z F1(I1)=-I*GG*RT12*H(I2)*GAUGE(I1,I2)
  1137. Z F1B(I1)=I*GG*RT12*Conjg(H(I2))*GAUGE(I2,I1)
  1138. Z F2(I1,I2)=-I*GG*RT12*(GAUGE(I1,I3)*HH(I3,I2)-HH(I1,I3)*GAUGE(I3,I2))
  1139. Id LA*ZA*HL=HL*LA*ZA+2*I*FZAHA*LA
  1140. Al LA*ZA*LG(MU1)=LG(MU1)*LA*ZA+2*I*LA*FZAGL(MU1)
  1141. Al,Multi,RT12**2=1/2
  1142. Al UNIT=1
  1143. Id HL=HA*LA
  1144. Al LG(MU1)=LA*GL(MU1)
  1145. *next
  1146. B GG,I,F,FF,EPS
  1147. C   INFINITESIMAL GAUGE TRANSFORMATIONS OF GAUGE FIXING TERM
  1148. Z MZ(I1,I2)=I*GG*RT12*(4*RT12*EPS/GG
  1149.         *(F2(2,3)*D(I1,2)*D(I2,3)-F2(3,2)*D(I1,3)*D(I2,2))
  1150.    +2*RT12*(FF-EPS)/GG
  1151.                 *(F2(1,2)*D(I1,1)*D(I2,2)-F2(2,1)*D(I1,2)*D(I2,1))
  1152.    +2*RT12*(FF+EPS)/GG
  1153.                 *(F2(1,3)*D(I1,1)*D(I2,3)-F2(3,1)*D(I1,3)*D(I2,1))
  1154.    +2*RT12*F/GG
  1155.      *(-F1(1)*D(I1,1)*D(I2,3)+F1B(1)*D(I1,3)*D(I2,1)
  1156.    -F1(2)*D(I1,2)*D(I2,3)+F1B(2)*D(I1,3)*D(I2,2)
  1157.    +(F1(3)-F1B(3))/5*(UNIT*D(I1,1)*D(I2,1)+D(I1,2)*D(I2,2)-4*D(I1,3)*D(I
  1158.    2,3))))
  1159. *next
  1160. B GG,I,F,FF
  1161. Z LFP1=-DIFZB(I1,I2)*DIFZ(I2,I1)
  1162. Z LFP2=DIFZB(I1,I2)*F0(I2,I1)*GG
  1163. Z LFP3=ZB(I1,I2)*MZ(I2,I1)
  1164. *yep
  1165. B MMW,MMY,GG,I,F,FFEPS,EPS
  1166. Id,Ainbe,LA*LA=2
  1167. Al,UNIT**2=3
  1168. Al MX(MU1)=XM(MU1)
  1169. Al PX(MU1)=XP(MU1)
  1170. Al MY(MU1)=YM(MU1)
  1171. Al PY(MU1)=YP(MU1)
  1172. Id LA=0
  1173. Al UNIT=1
  1174. Al RT13**2=1/3
  1175. Al RT15**2=1/5
  1176. Al,Multi,RT12**2=1/2
  1177. Al S1=-F/MMY
  1178. Al S2=-2*EPS/MMW
  1179. Al C1=(FF+EPS)/MMY
  1180. Al C2=F/MMW
  1181. Id FF=FFEPS-EPS
  1182. *yep
  1183. B GG,I,F,FF
  1184. C    THROWING AWAY VERY NEGLIGABLE TERMS
  1185. Id,Count,0,F,-1,EPS,-2,MMW,-1,H0,1,PHI0,1,PHIP,1,PHIM,1
  1186.    ,ZWMG,1,ZWM,1,ZZG,1,ZZ,1,ZWPG,1,ZWP,1
  1187. Id FFEPS=FF
  1188. Al MMY**N~=FF**N
  1189. Al MMW**N~=F**N
  1190. Al GG**1=GG*GG1
  1191. Id,Count,-2,GG,-1,GG1,-1,F,-1,EPS,-2
  1192. Id GG1=1
  1193. C FADEEV POPOV GHOST LAGRANGIAN
  1194. *next
  1195. P noutp
  1196. B GG,I,F,FF,EPS
  1197. Z HSH=Conjg(H(I1))*H(I1)
  1198. Z HHHH=HH(I1,I2)*HH(I2,I1)
  1199. Id UNIT**2=3
  1200. Al RT13**2=1/3
  1201. Al RT15**2=1/5
  1202. Al,Multi,RT12**2=1/2
  1203. Al HL*HL=2*HA*HA
  1204. Id UNIT=1
  1205. Al HL=0
  1206. *next
  1207. B GG,I,FF,EPS
  1208. Z HH2(I1,I2)=HH(I1,I3)*HH(I3,I2)
  1209. Id UNIT**N~=UNIT**N/UNIT
  1210. Al,RT13**2=1/3
  1211. Al RT15**2=1/5
  1212. Al,Multi,RT12**2=1/2
  1213. *next
  1214. S MM1,MM2
  1215. B MM1,MM2,GG,I,F,FF,EPS
  1216. Z LH1=-MM1**2*HSH
  1217. Z LH2=-MM2**2/2*HHHH
  1218. Id GG**-2=0
  1219. *next
  1220. S MM3,MM4
  1221. B MM3,GG,I,F,FF,EPS
  1222. C LH3 COLOUR IS HP.LA*HA.HM
  1223. Z LH3=-GG*MM3*Conjg(H(I1))*HH(I1,I2)*H(I2)
  1224. Id UNIT=1
  1225. Al HL=LA*HA
  1226. Al,Multi,RT12**2=1/2
  1227. Al GG**-2=0
  1228. *next
  1229. B MM4,GG,I,F,FF,EPS
  1230. Z LH4=-GG*MM4*HH(I1,I2)*HH(I2,I3)*HH(I3,I1)
  1231. Id UNIT**3=3
  1232. Al HL*HL*HL=0
  1233. Id UNIT=1
  1234. Al GG**-2=0
  1235. Al HL*HL=2*HA*HA
  1236. Al,Multi,RT12**2=1/2
  1237. Al,Multi,RT13**2=1/3
  1238. Al,Multi,RT15**2=1/5
  1239. Id HL=0
  1240. *next
  1241. S LL5,LL6,LL7,LL8,LL9
  1242. B LL5,LL6,LL7,GG,I,F,FF,EPS
  1243. C LH5 COLOUR IS POWERS OF HP.HM
  1244. C LH6 COLOUR IS HP.HM AND X.X OR Y.Y
  1245. C LH7 COLOUR IS POWERS OF X.X AND Y.Y
  1246. Z LH5=-LL5*GG*GG*HSH*HSH
  1247. Z LH6=-LL6*GG*GG*HSH*HHHH
  1248. Z LH7=-LL7*GG*GG*HHHH*HHHH
  1249. Id GG**-2=0
  1250. Al RT12**2=1/2
  1251. Al RT13**2=1/3
  1252. Al RT15**2=1/5
  1253. *next
  1254. B LL8,GG,I,F,FF,EPS
  1255. C SUMMED COLOUR IS HP.HXM , HXP.HM AND SAME FOR Y
  1256. C ALSO COLOUR HP.LA.LA.HM AND HP.LA.HM
  1257. Z LH8=-LL8*Conjg(H(I1))*HH2(I1,I2)*H(I2)*GG*GG
  1258. Id UNIT=1
  1259. Al HL=LA*HA
  1260. Id,Multi,RT12**2=1/2
  1261. Al GG**-2=0
  1262. Al,Commu,LA
  1263. *next
  1264. B LL9,GG,I,FF,EPS
  1265. F HL4
  1266. C SUMMED COLOUR IS OF THE FORM HXP,HYM OR HYP.HXM OR (HXP.HXM)**2 OR SAM
  1267. Z LH9=-LL9*GG*GG*HH2(I1,I2)*HH2(I2,I1)
  1268. Id UNIT**2=3
  1269. Al GG**-2=0
  1270. Al HL*HL*HL*HL=HL4
  1271. Al RT13**2=1/3
  1272. Al RT15**2=1/5
  1273. Al,Multi,RT12**2=1/2
  1274. Id UNIT=1
  1275. Al HL*HL*HL=0
  1276. Id,Ainbe,HL*HL=2*HA*HA
  1277. Id HL=0
  1278. *next
  1279. S FFEPS
  1280. B GG,I,HP,HM,PHIP,PHIM,H0,PHI0,HA,HB0,HB3,HYP,HYM,HXP,HXM,HWP,HWM,MMW
  1281.    ,MMX,MMY
  1282.    ,FF,F
  1283. Z LHA=LH1+LH2+LH3+LH4+LH5+LH6+LH7+LH8+LH9
  1284.    -4*F*F/5*PHI0**2-MMW**2*PHIP*PHIM-MMY**2*HYP*HYM-MMX**2*HXP*HXM
  1285. C PART OF GAUGE FIXING TERM
  1286. C    REPLACING HIGGS PARAMETERS IN TERMS OF V.E.V.,S
  1287. Id MM1**2=6*RT12/5*FF*MM3-12/5*LL6*FF**2-18/25*FF**2*LL8-4*LL5*F*F
  1288.       -4*LL6*EPS**2-2*LL8*EPS**2-12/5*EPS*FF*LL8+2*RT12*MM3*EPS
  1289. Al MM2**2=6*RT12/5*FF*MM4-48/5*FF**2*LL7-56/25*FF**2*LL9-4*F*F*LL6
  1290.    -6*EPS*MM4*RT12+32/5*LL9*EPS*(EPS+FF)+6/5*F*F*LL8
  1291.    -6/5*LL8*F*F
  1292.    -72/5*EPS**2*LL9
  1293.    -16*LL7*EPS**2
  1294. Id MM3=-6*MM4*EPS*(FF+EPS)/F/F+LL8*(12/5*FF+4*EPS)*RT12
  1295.    +64/5*LL9*EPS*FF*(FF+EPS)*RT12/F/F
  1296. Id,Multi,RT12**2=1/2
  1297. Id S1=-F/MMY
  1298. Al S2=-2*EPS/MMW
  1299. Al C1=(FF+EPS)/MMY
  1300. Al C2=F/MMW
  1301. *yep
  1302. C    THROWING AWAY VERY NEGLIGABLE TERMS
  1303. Id,Count,0,F,-1,EPS,-2,MMW,-1
  1304.    ,H0,1,PHI0,1,PHIP,1,PHIM,1
  1305. *yep
  1306. S LL,LL10,LL11,LL12,LL13,LL14,LL15
  1307. C REPLACING HIGGS PARAMETERS BY MASSES OF PHYSICAL HIGGS FIELDS
  1308. Id MM4=-RT12*FF*LL11/15+4*RT12*LL12*FF/15
  1309. Al LL7=-LL11/32-LL12/48+5*LL10/96
  1310. Al LL9=LL12/8+LL11/8
  1311. Al LL8=LL13/2-FF*EPS/F/F*LL11
  1312. Al LL6=LL11*EPS*FF/F/F/4+LL14*RT13*RT15*5/16*LL10
  1313. Id MMW**N~=F**N
  1314. Al RT12**2=1/2
  1315. Al RT13**2=1/3
  1316. Al RT15**2=1/5
  1317. Al MMX=FF
  1318. Al MMY**N~=FF**N
  1319. *yep
  1320. S F10,F11,F12,F13,F14,F15
  1321. C     DIAGONALISING NEUTRAL HIGGS FIELDS
  1322. Id HB3=HB3+2*EPS*H0/F
  1323. Al HB0=HB0-F*LL14*H0/FF/2
  1324. Al LL5=LL15/8+FF**2*EPS**2/F**4*LL11/2+LL14*LL10/32*LL14
  1325. *yep
  1326. Id GG**1=GG*GG1
  1327. C    THROWING AWAY VERY NEGLIGABLE TERMS
  1328. Id Count,-2,GG,-1,GG1,-1,F,-1,EPS,-2
  1329. Id GG1=1
  1330. Id EPS=LL*F*F/FF
  1331. P outp
  1332. C HIGGS POTENTIAL
  1333. *begin
  1334. Common A,E,DIF
  1335. C RT12=SQRT(1/2) ETC
  1336. C GG = GAUGE COUPLING CONSTANT
  1337. C UNIT = 3 BY 3 UNIT MATRIX
  1338. C          SUMMATION CONVENTIONS
  1339. C LG(MU)=LAMBDA(A)*GL(A,MU)
  1340. C LDIFF(GL)=LAMBDA(A)*DIFF(GL(A))
  1341. C FGGDG(MU,NU,RO,SI)=F(A,B,C)*GL(A,MU)*GL(B,NU)*D(RO)*GL(C,SI)
  1342. C FGGL(MU,NU)=F(A,B,C)*GL(A,MU)*GL(B,NU)*LAMBDA(C)
  1343. C F2G4(MU,NU,RO,SI)=F(A,B,E)*F(C,D,E)*GL(A,MU)*GL(B,NU)*GL(C,RO)*GL(D,SI
  1344. C XYYX=XP(A,MU)*YM(A,NU)*YP(B,NU)*XM(B,MU)   ETC
  1345. C P.PM.M=P(A,MU)*P(B,MU)*M(A,NU)*M(B,NU)
  1346. C (P.M)**2=(P(A,MU)*M(A,MU))**2
  1347. P noutp
  1348. B GG
  1349. S GG,UNIT,RT12,RT13,RT15
  1350. I MU1,MU2,MU3,MU4,I1=3,I2=3,I3=3,I4=3
  1351. V Z,PH,GL,WP,WM,XM,XP,YM,YP
  1352. F XXXX,XYYX,YYYY,DIFF,LDIFF,LG,FGGDG,FGGL,F2G4,MX=c,MY=c
  1353. Oldnew MXC=PX,MYC=PY
  1354. Z DIF(MU1,MU2,I1,I2)=-I*RT12*(
  1355.    DIFF(MU1,WP,MU2)*D(I1,2)*D(I2,3)+DIFF(MU1,WM,MU2)*D(I1,3)*D(I2,2)
  1356.    +DIFF(MU1,XM,MU2)*D(I1,1)*D(I2,2)+DIFF(MU1,YM,MU2)*D(I1,1)*D(I2,3)
  1357.    +DIFF(MU1,XP,MU2)*D(I1,2)*D(I2,1)+DIFF(MU1,YP,MU2)*D(I1,3)*D(I2,1)
  1358.  +(RT12*LDIFF(MU1,GL,MU2)+UNIT*DIFF(MU1,Z,MU2)*RT15/2-UNIT*DIFF(MU1,PH,
  1359.    MU2)*RT13/2)*D(I1,1)*D(I2,1)+(DIFF(MU1,Z,MU2)*RT15/2+3*DIFF(MU1,PH,MU
  1360.    2)*RT13/2)*D(I1,2)*D(I2,2)-2*DIFF(MU1,Z,MU2)*RT15*D(I1,3)*D(I2,3))
  1361. Id RT12**2=1/2
  1362. *next
  1363. P noutp
  1364. Z A(MU1,I1,I2)=DIF(MU2,MU1,I1,I2)
  1365. Id DIFF(MU1~,XM,MU2~)=MX(MU2)
  1366. Al DIFF(MU1~,XP,MU2~)=PX(MU2)
  1367. Al DIFF(MU1~,YM,MU2~)=MY(MU2)
  1368. Al DIFF(MU1~,YP,MU2~)=PY(MU2)
  1369. Al LDIFF(MU1~,GL,MU2~)=LG(MU2)
  1370. Id DIFF(MU1~,Z~,MU2~)=Z(MU2)
  1371. *next
  1372. P noutp
  1373. B GG
  1374. Z E(I1,I3)=GG*(A(MU1,I1,I2)*A(MU2,I2,I3)-A(MU2,I1,I2)*A(MU1,I2,I3))
  1375. *yep
  1376. Id,Multi,RT12**2=1/2
  1377. Al LG(MU1)*LG(MU2)=LG(MU2)*LG(MU1)+2*I*FGGL(MU1,MU2)
  1378. Al UNIT**N~=UNIT**N/UNIT
  1379. *next
  1380. B GG
  1381. Z ZG0=DIF(MU1,MU2,I1,I2)*DIF(MU1,MU2,I2,I1)
  1382. Z ZG00=-DIF(MU1,MU1,I1,I2)*DIF(MU2,MU2,I2,I1)
  1383. C ZG00=0 WHEN THE GAUGE FIXING TERM IS ADDED
  1384. Z ZG1=2*E(I1,I2)*DIF(MU1,MU2,I2,I1)
  1385. Z ZG2=E(I1,I2)*E(I2,I1)/2
  1386. *yep
  1387. Id UNIT**N~=UNIT**N/UNIT
  1388. Al RT12**2=1/2
  1389. Al RT13**2=1/3
  1390. Al RT15**2=1/5
  1391. Sum MU1,MU2
  1392. Id,Ainbe,LG(MU1~)*LG(MU2~)=2*GL(MU1)*GL(MU2)
  1393. Al LDIFF(MU1~,GL,MU2~)*LDIFF(MU3~,GL,MU4~)=2*DIFF(MU1,GL,MU2)*DIFF(MU3,
  1394.    GL,MU4)
  1395. Al FGGL(MU1~,MU2~)*LDIFF(MU3~,GL,MU4~)=2*FGGDG(MU1,MU2,MU3,MU4)
  1396. Al FGGL(MU1~,MU2~)*FGGL(MU3~,MU4~)=2*F2G4(MU1,MU2,MU3,MU4)
  1397. Id FGGL(MU1~,MU2~)=0
  1398. Al LG(MU1~)=0
  1399. Al LDIFF(MU1~,GL,MU2~)=0
  1400. Al UNIT=3
  1401. *yep
  1402. B GG,PHDPH,ZDZ,GLDGL,WPDWM,XPDXM,YPDYM,XMDXM,YMDYM,XMDYM,XPDXP,YPDYP
  1403.    ,XPDYP,XPDYM,YPDXM
  1404. Id PX(MU1~)*MX(MU2~)*PX(MU2~)*MX(MU1~)=XXXX
  1405. Al PX(MU1~)*MY(MU2~)*PY(MU2~)*MX(MU1~)=XYYX
  1406. Al PY(MU1~)*MY(MU2~)*PY(MU2~)*MY(MU1~)=YYYY
  1407. Al PY(MU1~)*MX(MU2~)*PX(MU2~)*MY(MU1~)=XYYX
  1408. Id MX(MU1~)=XM(MU1)
  1409. Al PX(MU1~)=XP(MU1)
  1410. Al MY(MU1~)=YM(MU1)
  1411. Al PY(MU1~)=YP(MU1)
  1412. Id,Commu,DIFF
  1413. C -1/4*F(MU,NU,A)*F(MU,NU,A)
  1414. C ZG0+ZG1+ZG2=-1/4*F(MU,NU)**2+PART OF GAUGE FIXING
  1415. *begin
  1416. B I,GG,RT12,RT13,RT15
  1417. C THERE IS IMPLICIT LA IN G(1,GL)
  1418. S GG,RT12,RT13,RT15,T
  1419. I I1=5,I2=5,I3=5
  1420. V WP,WM,XM,XP,YM,YP,GL,PH,Z,K
  1421. F UQB=c
  1422. Oldnew UQBC=UQ
  1423. F CH=c,TR
  1424. F C=c,Cc=c,L=c,UPB=c,DNB=c,ELB=c,NUB=c
  1425. Oldnew CC=CG,Cc=CC,CcC=CCG,CHC=CHG
  1426. Oldnew LC=R,UPBC=UP,DNBC=DN,ELBC=EL,NUBC=NU
  1427. X ASLSH(I1,I2)=-I*RT12*(G(1,WP)*D(I1,4)*D(I2,5)+G(1,WM)*D(I1,5)*D(I2,4)
  1428.   +(RT12*G(1,GL)+RT15/2*G(1,Z)-RT13/2*G(1,PH))*D(I1,1)*D(I2,1)
  1429.    +(-2*
  1430.     RT12*G(1,GL)+RT15/2*G(1,Z)-RT13/2*G(1,PH))*D(I1,2)*D(I2,2)
  1431.    +(RT15/2*G(1,Z)+3*RT13/2*G(1,PH))*D(I1,4)*D(I2,4)
  1432.    -2*RT15*G(1,Z)*D(I1,5)*D(I2,5)
  1433.    +G(1,XM)*(D(I1,1)+D(I1,2))*D(I2,4)+G(1,XP)*D(I1,4)*(D(I2,1)+D(I2,2))
  1434.    +G(1,YM)*(D(I1,1)+D(I1,2))*D(I2,5)+G(1,YP)*D(I1,5)*(D(I2,1)+D(I2,2)))
  1435. X DSLSH(T,I1,I2)=I*G(1,K)*D(I1,I2)+T*GG*ASLSH(I1,I2)
  1436. X MM(I1,I2,L,CC,C)=RT12*(
  1437.    C(L,UQ  )*(D(I1,1)*D(I2,2)-D(I1,2)*D(I2,1))*Epf(1,2,3)
  1438.    +CC(L,UP)*(D(I1,1)*D(I2,4)-D(I1,4)*D(I2,1))
  1439.    +CC(L,DN)*(D(I1,1)*D(I2,5)-D(I1,5)*D(I2,1))
  1440.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4)))
  1441. X M(I1,I2)=MM(I1,I2,L,CC,C)
  1442. X MB(I1,I2)=Conjg(MM(I2,I1,L,CC,C))
  1443. X P(I1)=CC(R,DN)*D(I1,1)+C(R,EL)*D(I1,4)-C(R,NU)*D(I1,5)
  1444. X PB(I1)=Conjg(P(I1))
  1445. Z LAGRN=
  1446.    -PB(I1)*DSLSH(1,I1,I2)*P(I2)
  1447.    -MB(I1,I2)*DSLSH(2,I2,I3)*M(I3,I1)
  1448. *yep
  1449. Id,Multi,RT12**2=1/2
  1450. Al Epf(1,2,3)*Epf(1,2,3)=-1
  1451. Al CG(R~,NU~)*G(1,K )*C(L~,EL~)= Conjg(EL)*L*G(1,K)*R*Conjg(NU)
  1452. Id CG(R~,NU~)*G(1,K~)*C(L~,EL~)=-Conjg(EL)*L*G(1,K)*R*Conjg(NU)
  1453. Id CC(L~,EL~)=L*EL
  1454. Al CCG(R~,ELB~)=ELB*R
  1455. Al C(L~,EL~)=L*CH*TR*Conjg(EL)
  1456. Al CG(R~,ELB~)=Conjg(ELB)*TR*CHG*R
  1457. P outp
  1458. *yep
  1459. F UU=c,UUT=c,U7=c
  1460. Oldnew UUTC=UUS,UUC=UUG,U7C=U7G
  1461. C T=TRANSPOSE , S=STAR , G=DAGGER=INVERSE
  1462. Id UP=UUG*UP
  1463. Al UPB=UPB*UU
  1464. Al UQ*TR*CHG*R=UP*TR*CHG*U7*UU*R
  1465. Al L*CH*TR*UQB=L*UUG*U7G*CH*TR*UPB
  1466. Al R*UQ=R*UUT*U7*UP
  1467. Al UQB*L=UPB*U7G*UUS*L
  1468. Id,Ainbe,UU*UUG=1
  1469. Al,Ainbe,UUS*UUT=1
  1470. Al,Adiso,U7*U7G=1
  1471. *yep
  1472. Id L*G(1,Z~)*R=L*G(1,Z)
  1473. Al R*G(1,Z~)*L=R*G(1,Z)
  1474. Id R*G(1,K)=(1-L)*G(1,K)
  1475. Al R*G(1,PH)=(1-L)*G(1,PH)
  1476. Al R*G(1,GL)=(1-L)*G(1,GL)
  1477. Id NUB*L=0
  1478. Al L*G(1,Z)=G(1,Z)*(1+G5(1))/2
  1479. Al R*G(1,Z)=G(1,Z)*(1-G5(1))/2
  1480. Al ELB*CH*R*G(1,XP)=ELB*CH*(1-L)*G(1,XP)
  1481. Al R*G(1,XM)*CH*EL=(1-L)*G(1,XM)*CH*EL
  1482. P stat
  1483. C FERMION KINETIC TERMS
  1484. C   AND FERMION INTERACTIONS WITH GAUGE FIELD
  1485. *begin
  1486. S HM=c,PHIP=c,F,H0,PHI0,RT12
  1487. Oldnew HMC=HP,PHIPC=PHIM
  1488. I I1=5,I2=5
  1489. Z H(I1)=I*HM*D(I1,1)+I*PHIP*D(I1,4)+RT12*(H0+2*F/GG-I*PHI0)*D(I1,5)
  1490. P noutp
  1491. *next
  1492. C UPB*CH*DN*HM*Epf(1,2,3)=Epf(I1,I2,I3)*UPB(I1)*CH*DN(I2)*HM(I3)   ETC
  1493. S L2,M2,GGM2M
  1494. B L2,M2,F,HM,HP,PHIP,PHIM,H0,PHI0,GGM2M
  1495. F UQB=c
  1496. Oldnew UQBC=UQ
  1497. F CH=c,TR
  1498. F C=c,Cc=c,L=c,UPB=c,DNB=c,ELB=c,NUB=c
  1499. Oldnew CC=CG,Cc=CC,CcC=CCG,CHC=CHG
  1500. Oldnew LC=R,UPBC=UP,DNBC=DN,ELBC=EL,NUBC=NU
  1501. X MM(I1,I2,L,CC,C)=RT12*(
  1502.    -C(L,UQ)*(D(I1,1)*D(I2,3)-D(I1,3)*D(I2,1))*Epf(3,2,1)
  1503.    +CC(L,UP)*(D(I1,1)*D(I2,4)-D(I1,4)*D(I2,1))
  1504.    +CC(L,DN)*(D(I1,1)*D(I2,5)-D(I1,5)*D(I2,1))
  1505.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4)))
  1506. X P(I1)=CC(R,DN)*(D(I1,1)+D(I1,3))+C(R,EL)*D(I1,4)-C(R,NU)*D(I1,5)
  1507. X PB(I1)=Conjg(P(I1))
  1508. X M(I1,I2)=MM(I1,I2,L,CC,C)
  1509. X MB(I1,I2)=Conjg(MM(I2,I1,L,CC,C))
  1510. Z Z=-L2*(H(I1)*MB(I1,I2)*P(I2)+PB(I1)*M(I1,I2)*Conjg(H(I2)))
  1511. Id L2=GG*M2/F
  1512. Al CG(R~,UP~)*C(L~,EL~)=Conjg(EL)*L*R*Conjg(UP)
  1513. Id CC(L~,EL~)=L*EL
  1514. Al CCG(R~,ELB~)=ELB*R
  1515. Al C(L~,EL~)=L*CH*TR*Conjg(EL)
  1516. Al CG(R~,ELB~)=Conjg(ELB)*TR*CHG*R
  1517. Al M2*F**-1=GGM2M/GG
  1518. Id,Multi,RT12**2=1/2
  1519. P outp
  1520. *yep
  1521. F UU=c,UUT=c,U7=c
  1522. Oldnew UUTC=UUS,UUC=UUG,U7C=U7G
  1523. C T=TRANSPOSE , S=STAR , G=DAGGER=INVERSE
  1524. Id UP=UUG*UP
  1525. Al UPB=UPB*UU
  1526. Al UQ*TR*CHG*R=UP*TR*CHG*U7*UU*R
  1527. Al L*CH*TR*UQB=L*UUG*U7G*CH*TR*UPB
  1528. Id R*R=R
  1529. Al L*L=L
  1530. Id L*M2=G6(1)/2*M2
  1531. Al R*M2=G7(1)/2*M2
  1532. Al L*H0=G6(1)/2*H0
  1533. Al R*H0=G7(1)/2*H0
  1534. Al L*PHI0=G6(1)/2*PHI0
  1535. Al R*PHI0=G7(1)/2*PHI0
  1536. Id Trick,1
  1537. Id Gi(1)=1
  1538. P outp
  1539. C FERMION HIGGS COUPLING 2
  1540. *yep
  1541. S FFEPS,EPS,MMW,MMY,HYM,HYP,HWP,HWM
  1542. B FFEPS,EPS,F,MMW,MMY,M2,GGM2M
  1543. Id HM=FFEPS/MMY*HM+F*HYM/MMY
  1544. Al HP=FFEPS/MMY*HP+F*HYP/MMY
  1545. Al PHIP=F*PHIP/MMW-2*EPS/MMW*HWP
  1546. Al PHIM=F*PHIM/MMW-2*EPS/MMW*HWM
  1547. P noutp
  1548. *begin
  1549. Common Z
  1550. S HM=c,PHIP=c,F,H0,PHI0,RT12
  1551. Oldnew HMC=HP,PHIPC=PHIM
  1552. I I1=5,I2=5,I3=5,I4=5,I5=5
  1553. Z H(I1)=I*HM*D(I1,1)+I*PHIP*D(I1,4)+RT12*(H0+2*F/GG-I*PHI0)*D(I1,5)
  1554. P noutp
  1555. *next
  1556. F L1,M1
  1557. B F,HM,HP,PHIP,PHIM,H0,PHI0,GG
  1558. F UQB=c
  1559. Oldnew UQBC=UQ
  1560. F CH=c,TR
  1561. F C=c,Cc=c,L=c,UPB=c,DNB=c,ELB=c
  1562. Oldnew CC=CG,Cc=CC,CcC=CCG,CHC=CHG
  1563. Oldnew LC=R,UPBC=UP,DNBC=DN,ELBC=EL
  1564. X MM(I1,I2,L,CC,C)=RT12*(
  1565.    C(L,UQ  )*(D(I1,1)*D(I2,2)-D(I1,2)*D(I2,1))
  1566.   +C(L,UQ  )*(D(I1,2)*D(I2,3)-D(I1,3)*D(I2,2))
  1567.   +CC(L,UP  )*(D(I1,2)*D(I2,4)-D(I1,4)*D(I2,2))*Epf(3,2,1)
  1568.   +CC(L,UP  )*(D(I1,3)*D(I2,4)-D(I1,4)*D(I2,3))
  1569.   +CC(L,DN  )*(D(I1,3)*D(I2,5)-D(I1,5)*D(I2,3))
  1570.   +C(L,EL  )*(D(I1,4)*D(I2,5)-D(I1,5)*D(I2,4)))
  1571. X M(I1,I2)=MM(I1,I2,L,CC,C)
  1572. X MCT(I1,I2)=Conjg(MM(I2,I1,R,C,CC))
  1573. Z Z=-Epf(I1,I2,I3,I4,I5)*MCT(I1,I2)*L1*M(I3,I4)*H(I5)
  1574. *yep
  1575. Id Epf(1,2,3,4,5)=1
  1576. Id CG(R~,UP~)*L1~*C(L~,EL~)=Conjg(EL)*L*L1*R*Conjg(UP)
  1577. Al CG(R~,DNB)*L1~*CC(L~,UP~)*Epf(1,2,3)=-UP*TR*CHG*L*L1*R*DN*Epf(1,2,3)
  1578. Id CC(L~,EL~)=L*EL
  1579. Al CCG(R~,ELB~)=ELB*R
  1580. Al C(L~,EL~)=L*CH*TR*Conjg(EL)
  1581. Al CG(R~,ELB~)=Conjg(ELB)*TR*CHG*R
  1582. Id,Multi,RT12**2=1/2
  1583. P outp
  1584. *yep
  1585. F UU=c,UUT=c,U7=c
  1586. Oldnew UUTC=UUS,UUC=UUG,U7C=U7G
  1587. C T=TRANSPOSE , S=STAR , G=DAGGER=INVERSE
  1588. Id L1=UUT*L1*U7*UU
  1589. Al UQB*L=UPB*L*U7G*UUS
  1590. Al UP*TR*CHG*L=UP*TR*CHG*L*UUS
  1591. Al L*CH*TR*UQB=UUG*U7G*L*CH*TR*UPB
  1592. Al L*UP=UUG*L*UP
  1593. Id,Ainbe,L*L=L
  1594. Id UU*UUG=1
  1595. Al UUS*UUT=1
  1596. Id U7*U7G=1
  1597. Id U7G*L1*U7=L1
  1598. P noutp
  1599. *next
  1600. P outp
  1601. B F,HM,HP,PHIP,PHIM,H0,PHI0,GGM1M
  1602. Z Z=Z+Conjg(Z)
  1603. Id UPB*L1*L=UPB*(1-G5(1))/2*L1
  1604. Al R*L1*UP=(1+G5(1))/2*L1*UP
  1605. Id L1=-GG*M1*RT12/4/F
  1606. Id RT12**2=1/2
  1607. P outp
  1608. C FERMION HIGGS COUPLING 1
  1609. *yep
  1610. S FFEPS,EPS,MMW,MMY,HYM,HYP,HWP,HWM
  1611. B FFEPS,EPS,F,MMW,MMY,GGM1M
  1612. C    INCLUDING EXCEEDINGLY SMALL TERMS
  1613. Id HM=FFEPS/MMY*HM+F*HYM/MMY
  1614. Al HP=FFEPS/MMY*HP+F*HYP/MMY
  1615. Al PHIP=F*PHIP/MMW-2*EPS/MMW*HWP
  1616. Al PHIM=F*PHIM/MMW-2*EPS/MMW*HWM
  1617. *end
  1618.