C C Two-loop large Higgs mass correction to the ro-parameter. C J.van der Bij and M. Veltman, Nucl. Phys. B231 (1984) 205. C C RO-parameter 1. Divergencies of one-loop diagrams, two external lines. C RO-parameter 2. Divergencies of one-loop diagrams, three external lines. C RO-parameter 3. Divergencies of one-loop diagrams, four external lines. C RO-parameter 4. Divergencies of one-loop diagrams, ghost external lines. C RO-parameter 5. Two-loop self-energy diagrams. C RO-parameter 6. One-loop subtractions. RO-parameter result. C RO-parameter 7. Two-loop self-energy diagrams. A-A wave-function. C RO-parameter 8. Two-loop self-energy diagrams. A-W wave-function. C RO-parameter 9. Subtractions for A-A and A-W wave-functions. C RO-parameter 10. Tadpoles in A-A wave-function. C RO-parameter 11. Diagrams with tadpole insertions. C RO-parameter 12. Counter-term Lagrangian for the standard model. C RO-parameter 13. Counter terms for the Ghost Lagrangian, standard model. C RO-parameter 14. Rationalization. C RO-parameter 15. Epsilon expansion and projection operators. C RO-parameter 16. Differentiating F111. C RO-parameter 17. Differentiating F211. C RO-parameter 18. Expansion of F211(SM,M1,M2) for large SM. C RO-parameter 19. Higher orders of F211(M,M0,SM) expansion for large SM. C RO-parameter 20. Expansion of F211(SM,SM,M) for large SM. *end C RO-parameter 1. Divergencies of one-loop diagrams, two external lines. C ONE-LOOP DIAGRAMS WITH TWO EXTERNAL LINES. C CALCULATION OF ONE-LOOP DIVERGENCIES. C CHECKING OF COUNTERTERMS ALSO DONE. C Running time (CPU only) on Lansing CDC: 27 sec. C The new character sum techniques give about a factor 2 improvement. Oldnew i=I P ninp Read Roblocks.e C P input VERT{,,,,} X NUM(K1,K2)=1.-2.*DT(K1-9)*DT(K2-9) *fix P ninput BLOCK WORK{TADP} P ninput Id,SELF(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2;TAP,1,(DIB(I1,J1,-J1,J2,-J2,I2) *DC("F,TFE,-1,J1,J2) )) + DS(I1;J3;-J3;I2;Sym;J3,-J3;TAP,2,(DIC(I1,J3,-J3,I2) )) +CONTR(I1,I2)*DLP/EP Id,Anti,TAP Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)= VE3(I1,K1,K3,*,MU,Q,*,L1,-K,*,L3,P)* VE3(K2,I2,K4,*,L2,K,*,NU,-Q,*,L4,-P)* PROP(K1,K2,*,L1,K,*,L2,K)* PROP(K3,K4,*,L3,P,*,L4,P) Id,DIC(I1~,K1~,K2~,I2~)= VE4(I1,K1,K2,I2,*,MU,*,L1,*,L2,*,NU)* PROP(K1,K2,*,L1,P,*,L2,P) B EP,I,PI2,DEL,TIPI2 Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,NOM(P,M~)*NOM(K,M0~)=F2(M,M0) Al,NOM(P,M~)=F1(M) Id,P(MU~)*F1(M~)=0. *yep Id,2,K(MU~)=P(MU)+Q(MU) Al,PDQ*F2(M~,M0~)=QDQ*B1(M,M0) Al,PDK*F2(M~,M0~)=PDP*F2(M,M0)+QDQ*B1(M,M0) Al,QDK*F2(M~,M0~)=QDQ*F2(M,M0)+QDQ*B1(M,M0) Id,PDP*F2(M~,M0~)=F1(M0)-M**2*F2(M,M0) Al,KDK*F2(M~,M0~)=F1(M)-M0**2*F2(M,M0) Id,P(MU~)*P(NU~)*F2(M~,M0~)=D(MU,NU)*B22(M,M0) +Q(MU)*Q(NU)*B21(M,M0) Id,P(MU~)*F2(M~,M0~)=Q(MU)*B1(M,M0) *yep Id,B22(M~,M0~)=(-0.5*F1(M0)+M**2*F2(M,M0) -0.5*(QDQ+M0**2-M**2)*B1(M,M0))/OMN Id,B21(M~,M0~)=-((0.5*N-1)*F1(M0) -0.5*N*(QDQ+M0**2-M**2)*B1(M,M0) +M**2*F2(M,M0) )/QDQ/OMN Id,B1(M~,M0~)=(0.5*F1(M)-0.5*F1(M0) -0.5*(QDQ+M0**2-M**2)*F2(M,M0) )/QDQ Id,F1(PM)=0. Al,PM=0. Al,Multi,M0**2=M**2/C**2 Al,C2MS2=2*C**2-1 Id,Multi,S**2=1.-C**2 *yep Id,F1(M~)=TIPI2*M**2/EP-0.5*TIPI2*M**2*(1.-LG(M)) +0.5*EP*TIPI2*M**2*(PI2/24+0.5-0.5*LG(M)+0.25*LG(M)*LG(M)) Al,N*OMN**-1=-4/3+EP/9-EP**2/27 Al,N=4.+EP Al,OMN**-1=-1/3+EP/9-EP**2/27 Al,Symme,F2,1,2 Id,ZTAG*F2(SM,SM)=-0.5*TIPI2*(PI/W3-2)*(QDQ+SM**2)/SM**2 -TIPI2/EP - 0.5*TIPI2*(LG(SM)-2+PI/W3) Al,ZTAG*F2(M~,M~)=0.5*TIPI2*(LG(SM)-LG(M)-2)*(QDQ+SM**2)/SM**2 -TIPI2/EP-0.5*TIPI2*(LG(SM)-2) Id,F2(M~,M~)=-TIPI2/EP-0.5*TIPI2*LG(M)+QDQ*BB0(M,M)/M**2 -0.5*TIPI2*EP*(PI2/24+0.25*LG(M)*LG(M)) +EP*QDQ*BB0E(M,M)/M**2 Al,F2(M~,SM)=-TIPI2/EP+0.5*TIPI2*(1.-LG(SM) +M**2*LG(M,SM)/SM**2-0.5*QDQ/SM**2) +TIPI2*EP*(-0.25-PI2/48+0.25*LG(SM)-LG(SM)*LG(SM)/8 +1/SM**2*(3*QDQ/16-QDQ*LG(SM)/8-M**2/4*LG(M,SM) +M**2/8*LG(M)*LG(M)-M**2/8*LG(SM)*LG(SM))) Al,F2(M~,M0~)=-TIPI2/EP+0.5*TIPI2-0.5*TIPI2*LG(M0) -0.5*TIPI2*M**2*DIF(M,M0)*LG(M,M0)+QDQ*BB0(M,M0)/M0**2 +EP*BB0E(M,M0) Id,Multi,EP**2=0 Al,PM=0 Al,Multi,M0**2=M**2/C**2 Al,ZTAG=1 Id,EP**-1=ATEL9**10*DEL/TIPI2 Al,F1F(SM)=F1F(SM)*ATEL9**2 Id,Count,1,ATEL9,1,SM,1,CONTR,4,ET,2 Id,ATEL9=1. Id,LG(M,S~)=LG(M)-LG(S) Al,LG(M0,S~)=LG(M0)-LG(S) Al,LG(SM,S~)=LG(SM)-LG(S) Id,DIF(PM,M~)=-1./M**2 Al,DIF(M,M0)=-C**2/M**2/S**2 Id,Multi,C**2=1.-S**2 Id,Multi,S**2=1.-C**2 *yep SVERT{,~,~} Id,CONTR(I1~,I2~)=CONT(I1,I2,"N,*,MU,Q,*,NU,-Q,*,AL,P0) Id,Compo,,CONT Id,CONT(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P) E1EZF{,,,,} Id,EP**-1=DEL/TIPI2 Al,C2MS2=2*C**2-1 Id,Multi,S**2=1-C**2 Id,EP*DEL=TIPI2 Al,EP**2*DEL=TIPI2*EP P output *yep Id,DLP=-1 *next P input ENDBLOCK Z TADP=DS(J1,1,16,(0.5*NUM(J1,J1)* DIB("Z,CHG(J1),CHH(J1) ) )) -M*SM**2*ET*DLP/EP Id,DIB(K1~,K2~,K3~)= VE3(K1,K2,K3,*,L1,P0,*,L2,-P,*,L3,P)* PROP(K2,K3,*,L2,P,*,L3,P) *ATEL9**10 WORK{TADP} Z IAA=SELF("A,"A) WORK{IAA} Z IAF=SELF("A,"F) WORK{IAF} Z IAW=SELF("A,"W) WORK{IAW} Z IAZ=SELF("A,"Z) WORK{IAZ} Z IFF=SELF("F,"F) WORK{IFF} Z IFW=SELF("F,"W) WORK{IFW} Z IFZ=SELF("F,"Z) WORK{IFZ} Z IGH=SELF("G,"G_) WORK{IGH} Z IGV=SELF("G,"U_) WORK{IGV} Z IHU=SELF("G_,"U) WORK{IHU} Z IUV=SELF("U,"U_) WORK{IUV} Z IWW=SELF("W,"W) WORK{IWW} Z IWZ=SELF("W,"Z) WORK{IWZ} Z IZZ=SELF("Z,"Z)*ZTAG C SET QDQ=-SM**2 TO FIND THAT MASS RENORMALIZATION OK. C NO COUNTER-TERMS PROPORTIONAL TO EP HAVE BEEN INTRODUCED. C SUCH TERMS HAVE ALSO BEEN NEGLECTED IN THE CALCULATION. WORK{IZZ} Z IOP=SELF("P_,"P) WORK{IOP} Z IQR=SELF("R_,"R) WORK{IQR} Z IQT=SELF("R_,"T) WORK{IQT} Z IRS=SELF("R,"T_) WORK{IRS} Z IST=SELF("T_,"T) WORK{IST} Z IXY=SELF("Y_,"Y) WORK{IXY} *end C RO-parameter 2. Divergencies of one-loop diagrams, three external lines. C ONE-LOOP DIAGRAMS WITH THREE EXTERNAL LINES. C CALCULATION OF ONE-LOOP DIVERGENCIES. C COUNTER-TERMS ARE CHECKED. C CDC CPU time: 35.2 sec. Oldnew i=I P ninput Read Roblocks.e C P input VERT{,,,,} V R,T,U,V X HUM(K1,K2)=1.-0.5*DK(K1,K2) *fix P ninput BLOCK WORK{TADP} P ninput Id,VERT(K1~,K2~,K3~)= DS(K1;J1;-J2;TAP,(DS(K2;-J1;J3;TAP,( DIB(K1,K2,K3,J1,-J1,J3,-J3,J2,-J2)*DC("F,TFE,-1,J1,J2) )))) +DS(K1;K2;J4;-J5;Sym;J4;-J5;TAP,(VIR1(K1,K2,K3,J4,-J4,-J5,J5) )) +DS(K2;K3;J6;-J7;Sym;J6;-J7;TAP,(VIR2(K1,K2,K3,J6,-J6,-J7,J7) )) +DS(K1;K3;J8;-J9;Sym;J8;-J9;TAP,(VIR3(K1,K2,K3,J8,-J8,-J9,J9) )) +CONTR(K1,K2,K3) Id,Anti,TAP Id,DIB(K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~)= VE3(K1,K4,K9,*,MU,Q,*,L4,P,*,L9,-R)* VE3(K2,K5,K6,*,NU,T,*,L5,-P,*,L6,V)* VE3(K3,K7,K8,*,AL,K,*,L7,-V,*,L8,R)* PROP(K4,K5,*,L4,P,*,L5,P)* PROP(K6,K7,*,L6,V,*,L7,V)* PROP(K8,K9,*,L8,R,*,L9,R) Al,VIR1(K1~,K2~,K3~,K4~,K5~,K6~,K7~)= VE4(K1,K2,K4,K6,*,MU,*,NU,*,L4,*,L6)* VE3(K3,K5,K7,*,AL,K,*,L5,P,*,L7,-U)* PROP(K6,K7,*,L6,U,*,L7,U)*PROP(K4,K5,*,L4,P,*,L5,P) Al,VIR2(K1~,K2~,K3~,K4~,K5~,K6~,K7~)= VE4(K2,K3,K4,K6,*,NU,*,AL,*,L4,*,L6)* VE3(K1,K5,K7,*,MU,Q,*,L5,P,*,L7,-R)* PROP(K6,K7,*,L6,R,*,L7,R)*PROP(K4,K5,*,L4,P,*,L5,P) Al,VIR3(K1~,K2~,K3~,K4~,K5~,K6~,K7~)= VE4(K1,K3,K4,K6,*,MU,*,AL,*,L5,*,L7)* VE3(K2,K5,K7,*,NU,T,*,L4,-P,*,L6,V)* PROP(K4,K5,*,L4,P,*,L5,P)*PROP(K6,K7,*,L6,V,*,L7,V) B EP,I,TIPI2 Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,P0(MU~)=0. Al,Dotpr,P0(MU~)=0. Id,Commu,NOM Id,NOM(P,M~)*NOM(R,M0~)*NOM(V,SM~)=1. Al,NOM(P,M~)*NOM(Q~,M0~)=F2(Q) Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 *yep Id,R(MU~)=P(MU)+Q(MU) Id,V(MU~)=P(MU)+Q(MU)+K(MU) Id,U(MU~)=P(MU)+K(MU) Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 Id,RDR=PDP+2.*PDQ Al,VDV=PDP-2.*PDT Al,PDR=PDP+PDQ Al,PDV=PDP-PDT Al,VDR=PDP+2.*PDQ+PDK-QDT Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 Id,VDK=PDK Al,VDT=PDT Al,VDQ=PDQ Al,RDK=PDK Al,RDT=PDT Al,RDQ=PDQ Al,N=4 Al,C2MS2=2.*C**2-1 *yep Id,P(MU~)*P(NU~)*P(AL~)=D3(MU,NU,AL,Q)*DEL*TIPI2/EP/6. +D3(MU,NU,AL,K)*DEL*TIPI2/EP/12. Id,P(MU~)*PDP=Q(MU)*DEL*TIPI2/EP+K(MU)*DEL*TIPI2/EP/2. Al,PDP=-DEL*TIPI2/EP Id,P(MU~)*P(NU~)=-0.25*D(MU,NU)*DEL*TIPI2/EP Id,P(MU~)*PDK=-0.25*K(MU)*DEL*TIPI2/EP Id,P(MU~)*PDQ=-0.25*Q(MU)*DEL*TIPI2/EP Id,P(MU~)*PDT=-0.25*DEL*TIPI2/EP*T(MU) Id,P(MU~)*F2(R)=0.5*DEL*TIPI2/EP*Q(MU) Id,P(MU~)*F2(U)=0.5*DEL*TIPI2/EP*K(MU) Id,P(MU~)*F2(V)=0.5*DEL*TIPI2/EP*(Q(MU)+K(MU)) Id,F2(Q~)=-DEL*TIPI2/EP *yep Id,T(MU~)=-K(MU)-Q(MU) Al,TDT=QDQ+KDK+2.*QDK Id,Dotpr,T(MU~)=-K(MU)-Q(MU) Id,D3(MU~,NU~,AL~,Q~)=D(MU,NU)*Q(AL)+D(MU,AL)*Q(NU)+D(NU,AL)*Q(MU) Id,Multi,S**2=1.-C**2 Keep 'TADP' Nprint 'TADP' *next SVERT{~,,~} Z 'TADP'='TADP'(AL,P,BE,Q,GA,K) Id,CONTR(K1~,K2~,K3~)=CONT(K1,K2,K3,/,"K)* VE3(K1,K2,K3,*,AL,P,*,BE,Q,*,GA,K)/EP Id,Compo,,CONT,,VE3 Id,CONT(S~)=S Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P) *yep CVERT{,~,~} SCVERT{,~,~} Id,C2MS2=2*C**2-1 *yep E1EZF{,,~,~,~} Id,Count,1,EP,-2,E1F,-2,EZF,-2 B EP,I,TIPI2 Id,Multi,S**2=1-C**2 Al,Q(MU~)=-P(MU)-K(MU) P output *yep Id,DEL=-1. *next P input ENDBLOCK P input Z IUVW(MU,Q,NU,T,AL,K)=VERT("U,"U_,"W) WORK{IUVW} Z IAUV(MU,Q,NU,T,AL,K)=VERT("A,"U,"U_) WORK{IAUV} Z IUVZ(MU,Q,NU,T,AL,K)=VERT("U,"U_,"Z) WORK{IUVZ} Z IFHU(MU,Q,NU,T,AL,K)=VERT("F,"G_,"U) WORK{IFHU} Z IAHU(MU,Q,NU,T,AL,K)=VERT("A,"G_,"U) WORK{IAHU} Z IFFZ(MU,Q,NU,T,AL,K)=VERT("F,"F,"Z) WORK{IFFZ} Z IZZZ(MU,Q,NU,T,AL,K)=VERT("Z,"Z,"Z) WORK{IZZZ} Z IAGH(MU,Q,NU,T,AL,K)=VERT("A,"G,"G_) WORK{IAGH} Z IAGV(MU,Q,NU,T,AL,K)=VERT("A,"G,"U_) WORK{IAGV} Z IFGV(MU,Q,NU,T,AL,K)=VERT("F,"G,"U_) WORK{IFGV} Z IFWZ(MU,Q,NU,T,AL,K)=VERT("F,"W,"Z) WORK{IFWZ} Z IGHZ(MU,Q,NU,T,AL,K)=VERT("G,"G_,"Z) WORK{IGHZ} Z IGHW(MU,Q,NU,T,AL,K)=VERT("G,"G_,"W) WORK{IGHW} Z IGVW(MU,Q,NU,T,AL,K)=VERT("G,"U_,"W) WORK{IGVW} Z IGVZ(MU,Q,NU,T,AL,K)=VERT("G,"U_,"Z) WORK{IGVZ} Z IHUW(MU,Q,NU,T,AL,K)=VERT("G_,"U,"W) WORK{IHUW} Z IHUZ(MU,Q,NU,T,AL,K)=VERT("G_,"U,"Z) WORK{IHUZ} Z IWWZ(MU,Q,NU,T,AL,K)=VERT("W,"W,"Z) WORK{IWWZ} Z IAFZ(MU,Q,NU,T,AL,K)=VERT("A,"F,"Z) WORK{IAFZ} Z IAWZ(MU,Q,NU,T,AL,K)=VERT("A,"W,"Z) WORK{IAWZ} *end C RO-parameter 3. Divergencies of one-loop diagrams, four external lines. C ONE-LOOP DIAGRAMS WITH FOUR EXTERNAL LINES. C CALCULATION OF ONE-LOOP DIVERGENCIES. C COMPARISON WITH COUTERTERMS INCLUDED. C CDC CPU time: 178.37 sec. Oldnew i=I P ninput Read Roblocks.e VERT{,~,,,~} I LA=N,LB=N X HUM(K1,K2)=1.-0.5*DK(K1,K2) *fix P ninput BLOCK WORK{TADP} P ninput Id,VIERP(K1~,K2~,K3~,K4~)= VIER(K1,K2,K3,K4,L1,L2,L3,L4) + VIER(K1,K3,K2,K4,L1,L3,L2,L4) + VIER(K1,K2,K4,K3,L1,L2,L4,L3) +CONTR(K1,K2,K3,K4) Id,VIER(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~)= DS(K1;J1;-J2;TAP,( DS(K2;J2;-J3;TAP,( DS(K3;J3;-J4;TAP,( VIE(K1,K2,K3,K4,L1,L2,L3,L4,J1,-J2,J2,-J3,J3,-J4,J4,-J1) * DC("F,TFE,-1,J1,J2) ))) ))) + DS(K1;K3;J5;-J6;TAP,( DS(K4;J6;-J7;TAP,( VIE1(K1,K2,K3,K4,L1,L2,L3,L4,J5,-J6,J6,-J7,J7,-J5) )) )) + DS(K2;K4;J8;-J9;TAP,( DS(K1;J9;-J0;TAP,( VIE2(K1,K2,K3,K4,L1,L2,L3,L4,J8,-J9,J9,-J0,J0,-J8) )) )) + DS(K1;K3;JA;-JB;Sym;JA;-JB;TAP,( VIE3(K1,K2,K3,K4,L1,L2,L3,L4,JA,-JB,JB,-JA) ) ) Id,Anti,TAP Id,VIE(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~, KA~,KB~)= VE3(K1,K5,K6,*,L1,P0,*,L5,P,*,L6,-P)* VE3(K2,K7,K8,*,L2,P0,*,L70,P,*,L8,-P)* VE3(K3,K9,K0,*,L3,P0,*,L9,P,*,L0,-P)* VE3(K4,KA,KB,*,L4,P0,*,LA,P,*,LB,-P)* PR8*D(L6,L70)*D(L8,L9)*D(L0,LA)*D(LB,L5) Al,VIE1(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE4(K1,K3,K5,K6,*,L1,*,L3,*,L5,*,L6)* VE3(K4,K7,K8,*,L4,P0,*,L71,P,*,L8,-P)* VE3(K2,K9,K0,*,L2,P0,*,L9,P,*,L0,-P)* PR6*D(L0,L5)*D(L6,L71)*D(L8,L9) Al,VIE2(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE4(K2,K4,K5,K6,*,L2,*,L4,*,L5,*,L6)* VE3(K1,K7,K8,*,L1,P0,*,L72,P,*,L8,-P)* VE3(K3,K9,K0,*,L3,P0,*,L9,P,*,L0,-P)* PR6*D(L0,L5)*D(L6,L72)*D(L8,L9) Al,VIE3(K1~,K2~,K3~,K4~,L1~,L2~,L3~,L4~,K5~,K6~,K7~,K8~)= VE4(K2,K4,K7,K8,*,L2,*,L4,*,L73,*,L8)* VE4(K1,K3,K5,K6,*,L1,*,L3,*,L5,*,L6)* PR4*D(L5,L8)*D(L6,L73) Id,Stats Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,Stats,1 C AL,PROP(AA+,L4+,Q+,L3+,P+)=AA(L4,L3,Q) Id,Count,-4,P,1,PR8,-8,PR6,-6,PR4,-4 Id,PR8*PDP**2=-DEL*TIPI2/EP Al,PR6*PDP=-DEL*TIPI2/EP Al,PR4=-DEL*TIPI2/EP Id,PR8*PDP*P(MU~)*P(NU~)=-0.25*DEL*TIPI2/EP*D(MU,NU) Al,PR6*P(MU~)*P(NU~)=-0.25*DEL*TIPI2/EP*D(MU,NU) Id,PR8*P(MU~)*P(NU~)*P(AL~)*P(BE~)=-DEL*TIPI2/EP/24*D4(MU,NU,AL,BE) Id,Symme,D4,1,2,3,4 Al,N=4 Al,PR8=0 B EP,TIPI2 *yep Id,D4(L1~,L2~,L3~,L4~)=D(L1,L2)*D(L3,L4)+D(L1,L3)*D(L2,L4) +D(L1,L4)*D(L2,L3) Al,C2MS2=2*C**2-1 Al,Multi,S**2=1-C**2 Keep 'TADP' Nprint 'TADP' *next SVERT{~,~,} Z 'TADP'='TADP' Id,CONTR(K1~,K2~,K3~,K4~)=CONT(K1,K2,K3,K4,/,"K)* VE4(K1,K2,K3,K4,*,L1,*,L2,*,L3,*,L4)/EP Id,Compo,,CONT,,VE4 Id,CONT(S~)=S Al,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) B EP,TIPI2 *yep CVERT{~,,~} SCVERT{~,,~} *yep Id,C2MS2=2*C**2-1 E1EZF{,,~,~,~} Id,Count,1,EP,-2,EZF,-2,E1F,-2 Id,Multi,S**2=1-C**2 P output *yep P input Id,DEL=-1. *next ENDBLOCK Z IAAUV=VIERP("A,"A,"U,"U_) WORK{IAAUV} Z IAFGV=VIERP("A,"F,"G,"U_) WORK{IAFGV} Z IAFHU=VIERP("A,"F,"G_,"U) WORK{IAFHU} Z IAGHW=VIERP("A,"G,"G_,"W) WORK{IAGHW} Z IAGVZ=VIERP("A,"G,"U_,"Z) WORK{IAGVZ} Z IAHUZ=VIERP("A,"G_,"U,"Z) WORK{IAHUZ} Z IAUVW=VIERP("A,"U,"U_,"W) WORK{IAUVW} Z IAAGH=VIERP("A,"A,"G,"G_) WORK{IAAGH} Z IAAUV=VIERP("A,"A,"U,"U_) WORK{IAAUV} Z IFGVW=VIERP("F,"G,"U_,"W) WORK{IFGVW} Z IFHUW=VIERP("F,"G_,"U,"W) WORK{IFHUW} Z IFFGH=VIERP("F,"F,"G,"G_) WORK{IFFGH} Z IFFUV=VIERP("F,"F,"U,"U_) WORK{IFFUV} Z IFFWW=VIERP("F,"F,"W,"W) WORK{IFFWW} Z IFFZZ=VIERP("F,"F,"Z,"Z) WORK{IFFZZ} Z IFFFF=VIERP("F,"F,"F,"F) WORK{IFFFF} Z IGHUV=VIERP("G,"G_,"U,"U_) WORK{IGHUV} Z IGHWW=VIERP("G,"G_,"W,"W) WORK{IGHWW} Z IGHZZ=VIERP("G,"G_,"Z,"Z) WORK{IGHZZ} Z IGVWZ=VIERP("G,"U_,"W,"Z) WORK{IGVWZ} Z IGGHH=VIERP("G,"G,"G_,"G_) WORK{IGGHH} Z IHUWZ=VIERP("G_,"U,"W,"Z) WORK{IHUWZ} Z IUUVV=VIERP("U,"U,"U_,"U_) WORK{IUUVV} Z IUVZZ=VIERP("U,"U_,"Z,"Z) WORK{IUVZZ} Z IUVWW=VIERP("U,"U_,"W,"W) WORK{IUVWW} Z IWWZZ=VIERP("W,"W,"Z,"Z) WORK{IWWZZ} Z IZZZZ=VIERP("Z,"Z,"Z,"Z) WORK{IZZZZ} Z IAFFW=VIERP("A,"F,"F,"W) WORK{IAFFW} Z IAWZZ=VIERP("A,"W,"Z,"Z) WORK{IAWZZ} *end C RO-parameter 4. Divergencies of one-loop diagrams, ghost external lines. C ONE-LOOP THREE-POINT DIAGRAMS WITH EXTERNAL GHOST LINES. C CALCULATION OF ONE-LOOP DIVERGENCIES. C COUNTERTERMS ARE ALSO CHECKED. C CDC CPU time: 16.09 sec. Oldnew i=I P ninput Read Roblocks.e VERT{,,~,,} V R,T,U,V *fix P ninput BLOCK WORK{TADP} P ninput Id,VERT(K1~,K2~,K3~)= DS(K1;J1;-J2;TAP,(DS(K2;-J1;J3;TAP,( DIB(K1,K2,K3,J1,-J1,J3,-J3,J2,-J2) )))) + CONTR(K1,K2,K3) Id,Anti,TAP Id,DIB(K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~)= VE3(K1,K4,K9,*,MU,Q,*,L4,P,*,L9,-R)* VE3(K2,K5,K6,*,NU,T,*,L5,-P,*,L6,V)* VE3(K3,K7,K8,*,AL,K,*,L7,-V,*,L8,R)* PROP(K4,K5,*,L4,P,*,L5,P)* PROP(K6,K7,*,L6,V,*,L7,V)* PROP(K8,K9,*,L8,R,*,L9,R) B EP,TIPI2 Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,P0(MU~)=0. Al,Dotpr,P0(MU~)=0. Id,Commu,NOM Id,NOM(P,M~)*NOM(R,M0~)*NOM(V,SM~)=1. Al,NOM(P,M~)*NOM(Q~,M0~)=F2(Q) Al,NOM(P,M~)=F1(M) Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 *yep Id,R(MU~)=P(MU)+Q(MU) Id,V(MU~)=P(MU)+Q(MU)+K(MU) Id,U(MU~)=P(MU)+K(MU) Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 Id,RDR=PDP+2.*PDQ Al,VDV=PDP-2.*PDT Al,PDR=PDP+PDQ Al,PDV=PDP-PDT Al,VDR=PDP+2.*PDQ+PDK-QDT Id,Count,3,P,2,R,2,V,2,F2,4,CONTR,4 Id,VDK=PDK Al,VDT=PDT Al,VDQ=PDQ Al,RDK=PDK Al,RDT=PDT Al,RDQ=PDQ Al,N=4 Al,C2MS2=2*C**2-1 *yep Id,P(MU~)*P(NU~)*P(AL~)=D3(MU,NU,AL,Q)*DEL*TIPI2/EP/6. +D3(MU,NU,AL,K)*DEL*TIPI2/EP/12. Id,P(MU~)*PDP=Q(MU)*DEL*TIPI2/EP+K(MU)*DEL*TIPI2/EP/2. Al,PDP=-DEL*TIPI2/EP Id,P(MU~)*P(NU~)=-0.25*D(MU,NU)*DEL*TIPI2/EP Id,P(MU~)*PDK=-0.25*K(MU)*DEL*TIPI2/EP Id,P(MU~)*PDQ=-0.25*Q(MU)*DEL*TIPI2/EP Id,P(MU~)*PDT=-0.25*DEL*TIPI2/EP*T(MU) Id,P(MU~)*F2(R)=0.5*DEL*TIPI2/EP*Q(MU) Id,P(MU~)*F2(U)=0.5*DEL*TIPI2/EP*K(MU) Id,P(MU~)*F2(V)=0.5*DEL*TIPI2/EP*(Q(MU)+K(MU)) Id,F2(Q~)=-DEL*TIPI2/EP *yep Id,T(MU~)=-K(MU)-Q(MU) Al,TDT=QDQ+KDK+2.*QDK Id,Dotpr,T(MU~)=-K(MU)-Q(MU) Id,D3(MU~,NU~,AL~,Q~)=D(MU,NU)*Q(AL)+D(MU,AL)*Q(NU)+D(NU,AL)*Q(MU) Id,Multi,S**2=1.-C**2 Keep 'TADP' Nprint 'TADP' *next SVERT{~,,~} Z 'TADP'='TADP'(AL,P,BE,Q,GA,K) Id,CONTR(K1~,K2~,K3~)=CONT(K1,K2,K3,/,"K) *VE3(K1,K2,K3,*,AL,P,*,BE,Q,*,GA,K)/EP Id,Compo,,CONT,,VE3 Id,CONT(S~)=S Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)=AA(MU,P0,L2,Q,L1,P) CVERT{~,~,} SCVERT{~,~,} Id,C2MS2=2*C**2-1 E1EZF{,,~,~,~} B EP,TIPI2 Id,Count,1,EP,-2,E1F,-2,EZF,-2 Id,Multi,S**2=1-C**2 Al,Q(MU~)=-P(MU)-K(MU) P output *yep Id,DEL=-1 *next P input ENDBLOCK P input Z IAOP(MU,Q,NU,T,AL,K)=VERT("A,"P_,"P) WORK{IAOP} Z IAXY(MU,Q,NU,T,AL,K)=VERT("A,"Y_,"Y) WORK{IAXY} Z IFOP(MU,Q,NU,T,AL,K)=VERT("F,"P_,"P) WORK{IFOP} Z IFXY(MU,Q,NU,T,AL,K)=VERT("F,"Y_,"Y) WORK{IFXY} Z IGPQ(MU,Q,NU,T,AL,K)=VERT("G,"P,"R_) WORK{IGPQ} Z IGRX(MU,Q,NU,T,AL,K)=VERT("G,"R,"Y_) WORK{IGRX} Z IGTX(MU,Q,NU,T,AL,K)=VERT("G,"T,"Y_) WORK{IGTX} Z IHOR(MU,Q,NU,T,AL,K)=VERT("G_,"P_,"R) WORK{IHOR} Z IHOT(MU,Q,NU,T,AL,K)=VERT("G_,"P_,"T) WORK{IHOT} Z IHQY(MU,Q,NU,T,AL,K)=VERT("G_,"R_,"Y) WORK{IHQY} Z IOPZ(MU,Q,NU,T,AL,K)=VERT("P_,"P,"Z) WORK{IOPZ} Z IOPW(MU,Q,NU,T,AL,K)=VERT("P_,"P,"W) WORK{IOPW} Z IORV(MU,Q,NU,T,AL,K)=VERT("P_,"R,"U_) WORK{IORV} Z IOTV(MU,Q,NU,T,AL,K)=VERT("P_,"T,"U_) WORK{IOTV} Z IPQU(MU,Q,NU,T,AL,K)=VERT("P,"R_,"U) WORK{IPQU} Z IPSU(MU,Q,NU,T,AL,K)=VERT("P,"T_,"U) WORK{IPSU} Z IQRZ(MU,Q,NU,T,AL,K)=VERT("R_,"R,"Z) WORK{IQRZ} Z IQTZ(MU,Q,NU,T,AL,K)=VERT("R_,"T,"Z) WORK{IQTZ} Z IQVY(MU,Q,NU,T,AL,K)=VERT("R_,"U_,"Y) WORK{IQVY} Z IRUX(MU,Q,NU,T,AL,K)=VERT("R,"U,"Y_) WORK{IRUX} Z ISVY(MU,Q,NU,T,AL,K)=VERT("T_,"U_,"Y) WORK{ISVY} Z ITUX(MU,Q,NU,T,AL,K)=VERT("T,"U,"Y_) WORK{ITUX} Z IWXY(MU,Q,NU,T,AL,K)=VERT("W,"Y_,"Y) WORK{IWXY} Z IXYZ(MU,Q,NU,T,AL,K)=VERT("Y_,"Y,"Z) WORK{IXYZ} *end C RO-parameter 5. Two-loop self-energy diagrams. C TWO-LOOP SELF-ENERGY DIAGRAMS. C THE DIAGRAMS ARE DIVIDED IN 8 TOPOLOGY CLASSES. C EACH CLASS IS WORKED OUT IN TERMS OF THE F211 ETC. C SUBSEQUENTLY THE F211 ETC ARE EXPANDED IN TERMS OF THE C HIGGS MASS SM. C CDC CPU time: 111.85 sec. Common A0A0,W0A0,W0W0,WPWM S PM=1,M,M0,SM,N,C,S,EP,AH Oldnew i=I P ninput Read Roblocks.e VERT{,,,~,~} X NUM(K1,K2)=1.-0.5*DK(K1,K2) X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3) +2/3*DK(K1,K2)*DK(K1,K3) X KUM(K1)=1-DK("Z,K1) C X KUM(K1)=1-DK(4,K1) X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5) F FP3,FP2,FP1,FQ2,FQ1,FK1 *fix P ninput BLOCK WORK{} P ninput Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,NOM(P,M~)*NOM(P,S~)*NOM(P,C~)=FP3(M,S,C) Al,NOM(P,M~)*NOM(P,S~)=FP2(M,S) Al,NOM(P,M~)=FP1(M) Al,NOM(Q,M~)*NOM(Q,S~)=FQ2(M,S) Al,NOM(Q,M~)=FQ1(M) Al,NOM(K,M~)=FK1(M) *yep Id,QDP=0.5*KDK-0.5*PDP-0.5*QDQ Al,QDK=-0.5*PDP+0.5*KDK+0.5*QDQ Al,PDK=-0.5*QDQ+0.5*KDK+0.5*PDP Id,Multi,S**2=1-C**2 Al,C2MS2=2*C**2-1 *yep C AT MOST FQ2, FK1, NOT FQ3 OR FK2 C AT MOST QDQ**2, KDK**2. Id,QDQ**2*FQ2(M~,M0~)=1.-(M**2+M0**2)*FQ1(M0)+M**4*FQ2(M,M0) Al,KDK**2*FK1(M~)=PDP+QDQ-M**2+M**4*FK1(M) Al,QDQ**2*FQ1(M~)=QDQ-M**2+M**4*FQ1(M) C NOW NO MORE QDQ**2 OR KDK**2. Id,QDQ*FQ2(M~,M0~)=FQ1(M0)-M**2*FQ2(M,M0) Al,QDQ*FQ1(M~)=1.-M**2*FQ1(M) Al,QDQ*FK1(M~)=PDP*FK1(M)+1.-M**2*FK1(M) Al,KDK*FK1(M~)=1.-M**2*FK1(M) Id,PDP**2*FP3(M~,M0~,S~)=FP1(S)-(M**2+M0**2)*FP2(M0,S) +M**4*FP3(M,M0,S) Al,PDP**2*FP2(M~,M0~)=1.-(M**2+M0**2)*FP1(M0)+M**4*FP2(M,M0) Al,PDP**2*FP1(M~)=PDP-M**2+M**4*FP1(M) Id,PDP*FP3(M~,M0~,S~)=FP2(M0,S)-M**2*FP3(M,M0,S) Al,PDP*FP2(M~,M0~)=FP1(M0)-M**2*FP2(M,M0) Al,PDP*FP1(M~)=1.-M**2*FP1(M) Id,FQ2(M~,M0~)=FP2(M,M0) Al,FQ1(M~)=FP1(M) Al,FK1(M~)=FP1(M) Id,Commu,FP3,FP2,FP1 *yep Id,FP3(M~,S~,C~)*FP2(M0~,SM~)=F32(M,S,C,M0,SM) Al,FP3(M~,S~,C~)*FP1(M0~)*FP1(SM~)=F311(M,S,C,M0,SM) Al,FP3(M~,S~,C~)*FP1(M0~)=F31(M,S,C,M0) Al,FP3(M~,S~,C~)=0 Id,FP2(M~,S~)*FP2(M0~,C~)*FP1(SM~)=F221(M,S,M0,C,SM) Al,FP2(M~,S~)*FP2(M0~,C~)=F22(M,S,M0,C) Al,FP2(M~,S~)*FP1(M0~)*FP1(C~)=F211(M,S,M0,C) Al,FP2(M~,S~)*FP1(M0~)=F21(M,S,M0) Al,FP2(M~,S~)=0 Id,FP1(M~)*FP1(S~)*FP1(C~)=F111(M,S,C) Al,FP1(M~)*FP1(S~)=F11(M,S) Al,FP1(M~)=0 *yep Id,F311(M~,S~,C~,M0~,SM~)=F311(M,S,C,M0,SM)*YYYY(C,SM) Al,F31(M~,S~,C~,M0~)=F31(M,S,C,M0)*XXXX(C,M0) Id,YYYY(SM,SM)=1./ATEL9**2 Al,YYYY(M~,SM)=1. Al,YYYY(SM,M~)=1./ATEL9**2 Al,YYYY(S~,C~)=1. Al,XXXX(SM,SM)=1. Al,XXXX(M~,SM)=ATEL9**2 Al,XXXX(SM,M~)=1./ATEL9**2 Al,XXXX(C~,S~)=1. Id,F221(M~,M0~,C~,S~,SM~)=F221(M,M0,C,S,SM)/ATEL9**2 Al,F21(M~,M0~,SM)=F21(M,M0,SM)*ATEL9**2 Al,F111(M~,M0~,SM)=F111(M,M0,SM)*ATEL9**2 Id,Count,1,ATEL9,1,SM,1 Id,ATEL9=1 Al,Multi,ATEL9**-1=1 C Nprint A0A0,W0A0,W0W0,WPWM ENDBLOCK BLOCK TOPO{} Id,TOPA(I1~,I2~)= DS(I1;J1;J4;Sym;J1;J4;TAP,( DS(J3;J2;-J1;TAP,( DS(-J2;-J5;I2;TAP,( DC("T,THI,-1,J1,J2,J3,J4,J5)* DIA(I1,I2,J1,-J1,J2,-J2,J3,-J3,J4,-J4,J5,-J5) )) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K7,*,MU,P0,*,L1,P,*,L7,-P)* VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)* VE3(K4,I2,K0,*,L4,Q,*,NU,-P0,*,L0,-Q)* VE3(K6,K8,K9,*,L6,-K,*,L8,P,*,L9,Q)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)* PROP(K7,K8,*,L7,P,*,L8,P)* PROP(K9,K0,*,L9,Q,*,L0,Q)*D(MU,NU)/N ENDBLOCK Z A0A0=TOPA("A,"A) TOPO{} WORK{} *next Z W0A0=TOPA("W,"A) TOPO{} WORK{} *next Z W0W0=TOPA("W,"W) TOPO{} WORK{} *next Z WPWM=TOPA("U,"U_) TOPO{} WORK{} *next BLOCK TOP1{} Id,TOPB(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;-J3;-J4;Sym;-J3;-J4;TAP,( DS(J3;J4;-J5;TAP,( DC("T,THI,-1,J1,J2,J3,J4,J5)* DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,-J3,J3,J4,-J4) )) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K3,*,MU,P0,*,L1,P,*,L3,-P)* VE3(K2,I2,K6,*,L2,-P,*,NU,-P0,*,L6,P)* VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)* VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,P,*,L4,P)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,K,*,L8,K)* PROP(K9,K0,*,L9,Q,*,L0,Q)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+TOPB("A,"A) TOP1{} WORK{} *next Z W0A0=W0A0+TOPB("W,"A) TOP1{} WORK{} *next Z W0W0=W0W0+TOPB("W,"W) TOP1{} WORK{} *next Z WPWM=WPWM+TOPB("U,"U_) TOP1{} WORK{} *next BLOCK TOP2{} Id,TOPC(I1~,I2~)= DS(I1;-J1;-J2;I2;Sym;J1;J2;TAP,( DS(J1;-J3;-J4;Sym;J3;J4;TAP,( DC("T,THI,-1,J1,J2,J3,J4)* DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3,J4,-J4) )) )) Id,Anti,TAP C DS(J1,1,8,(DS(J2,J1,8,( C DC(QN(I1),QN(I2),QH(J1),QH(J2))*(NUM(J1,J2))* C DS(J3,1,8,(DS(J4,J3,8,( C DC(QG(J1),QH(J3),QH(J4))*(NUM(J3,J4)*ZUM(J1,J2,J3,J4,3))* C DIA(I1,I2,CHH(J1),CHG(J1),CHH(J2),CHG(J2), C CHH(J3),CHG(J3),CHG(J4),CHH(J4) ) )))) )))) Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE4(I1,K1,K3,I2,*,MU,*,L1,*,L3,*,NU)* VE3(K2,K5,K8,*,L2,P,*,L5,-K,*,L8,Q)* VE3(K4,K6,K7,*,L4,-P,*,L6,K,*,L7,-Q)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,P,*,L4,P)* PROP(K5,K6,*,L5,K,*,L6,K)* PROP(K7,K8,*,L7,Q,*,L8,Q)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+TOPC("A,"A) TOP2{} WORK{} *next Z W0A0=W0A0+TOPC("W,"A) TOP2{} WORK{} *next Z W0W0=W0W0+TOPC("W,"W) TOP2{} WORK{} *next Z WPWM=WPWM+TOPC("U,"U_) TOP2{} WORK{} *next BLOCK TOP3{} Id,TOPD(I1~,I2~)= DS(I1;-J1;-J2;I2;Sym;J1;J2,TAP,( DS(J1;J2;-J3;J3;Sym;J3;-J3,TAP,( DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)= VE4(I1,K1,K3,I2,*,MU,*,L1,*,L3,*,NU)* VE4(K2,K4,K5,K6,*,L2,*,L4,*,L5,*,L6)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,P,*,L4,P)* PROP(K5,K6,*,L5,Q,*,L6,Q)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+TOPD("A,"A) TOP3{} WORK{} *next Z W0A0=W0A0+TOPD("W,"A) TOP3{} WORK{} *next Z W0W0=W0W0+TOPD("W,"W) TOP3{} WORK{} *next Z WPWM=WPWM+TOPD("U,"U_) TOP3{} WORK{} *next BLOCK TOP4{} Id,TOPE(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,( DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,P0,*,L1,-P,*,L5,P)* VE3(K2,I2,K8,*,L2,P,*,NU,-P0,*,L8,-P)* VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,P,*,L8,P)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+TOPE("A,"A) TOP4{} WORK{} *next Z W0A0=W0A0+TOPE("W,"A) TOP4{} WORK{} *next Z W0W0=W0W0+TOPE("W,"W) TOP4{} WORK{} *next Z WPWM=WPWM+TOPE("U,"U_) TOP4{} WORK{} *next BLOCK TOP5{} Id,TOPF(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J3;J2;J4;Sym;J3;J4,TAP,( DC("T,THI,-1,J1,J2,J3,J4)* DIA(I1,I2,-J1,J1,J3,-J3,-J2,J2,J4,-J4) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,P0,*,L1,P,*,L5,-P)* VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)* VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,K,*,L4,K)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,Q,*,L8,Q)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+2*TOPF("A,"A) TOP5{} WORK{} *next Z W0A0=W0A0+TOPF("W,"A)+TOPF("A,"W) TOP5{} WORK{} *next Z W0W0=W0W0+2*TOPF("W,"W) TOP5{} WORK{} *next Z WPWM=WPWM+TOPF("U,"U_)+TOPF("U_,"U) TOP5{} WORK{} *next BLOCK TOP6{} Id,TOPH(I1~,I2~)= DS(I1;-J1;-J2;-J3;Sym;-J1;-J2;-J3,TAP,( DC("T,THI,-1,J1,J2,J3)* DIA(I1,I2,-J1,J1,-J2,J2,-J3,J3) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)= VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)* VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)*D(MU,NU)/N ENDBLOCK Z A0A0=A0A0+TOPH("A,"A) TOP6{} WORK{} Print A0A0 *next Z W0A0=W0A0+TOPH("W,"A) TOP6{} WORK{} Print W0A0 *next Z W0W0=W0W0+TOPH("W,"W) TOP6{} WORK{} Print W0W0 *next Z WPWM=WPWM+TOPH("U,"U_) TOP6{} WORK{} Print WPWM *next Z A0A0=A0A0 Z W0A0=W0A0 Z W0W0=W0W0 Z WPWM=WPWM *yep P input Id,F22(M~,M0~,S~,C~)=F221(M,M0,S,C,AH) Al,F31(M~,M0~,S~,C~)=F311(M,M0,S,C,AH) Al,F21(M~,M0~,S~)=F211(M,M0,S,AH) Id,F221(M~,M~,M0~,M0~,SM~)=FF221(M,M,M0,M0,SM) Al,F221(M~,M~,C~,S~,SM~)=DIF(C,S)*F211(M,M,S,SM) -DIF(C,S)*F211(M,M,C,SM) Al,F221(C~,S~,M0~,M~,SM~)=DIF(C,S)*F211(M0,M,S,SM) -DIF(C,S)*F211(M0,M,C,SM) Id,FF221(M~,M~,C~,C~,S~)=F221(M,M,C,C,S) Al,F311(M~,M~,M~,C~,S~)=FF311(M,M,M,C,S) Al,F311(M~,SM~,M0~,C~,S~)=DIF(M,M0)*F211(SM,M0,C,S) -DIF(M,M0)*F211(M,SM,C,S) Id,FF311(M~,M~,M~,C~,S~)=F311(M,M,M,C,S) Al,F211(M~,M~,C~,S~)=FF211(M,M,C,S) Al,F211(C~,S~,M~,M0~)=DIF(C,S)*F111(S,M,M0) -DIF(C,S)*F111(C,M,M0) Id,FF211(M~,M~,C~,S~)=F211(M,M,C,S) Id,F111(M~,C~,AH)=F11(M,C) Al,F111(M~,C~,S~)=(EP-EP**2-1)*(M**2*F211(M,M,C,S) +C**2*F211(C,C,M,S)+S**2*F211(S,S,M,C)) Id,F11(PM,M~)=0 Al,F11(M~,PM)=0 Id,Symme,F211,3,4,F311,4,5,F111,1,2,3 Id,Symme,F211,1,2,F311,1,2,3,F11,1,2 Id,Asymm,DIF,1,2 *yep Id,DIF(M,SM)=-1./SM**2-M**2/SM**4-M**4/SM**6 Al,DIF(M0,SM)=-1./SM**2-M0**2/SM**4-M0**4/SM**6 Al,DIF(PM,M~)=-1./M**2 Al,DIF(M,M0)=-C**2/M**2/S**2 Id,Multi,M0**2=M**2/C**2 Al,Multi,M0**-2=C**2/M**2 Id,F221(M~,M0~,S~,C~,AH)=F22(M,M0,S,C) Al,F311(M~,M0~,S~,C~,AH)=F31(M,M0,S,C) Al,F211(M~,M0~,S~,AH)=F21(M,M0,S) Id,EP**2*N=4.*EP**2 Al,N=4+EP Al,EP**2*N**-1=0.25*EP**2 Al,EP*N**-1=EP/4.-EP**2/16. Al,N**-1=1/4-EP/16+EP**2/64 Id,EP**2*F22(M~,M0~,S~,C~)=-4.*PI**4 Al,EP**2*F31(M~,M0~,S~,C~)=0. Al,EP**2*F21(M~,M0~,S~)=4.*PI**4*S**2 Al,EP**2*F11(M~,M0~)=-4.*PI**4*M**2*M0**2 Al,EP**2*F221(M~,M0~,S~,C~,SM~)=0. Al,EP**2*F311(M~,M0~,S~,C~,SM~)=0. Al,EP**2*F211(M~,M0~,S~,C~)=-2.*PI**4 Id,EP*F3(M~,S~,C~)=0. Al,EP**2*F3(M~,S~,C~)=0 Al,EP*F2(M~,C~)=-2.*I*PI**2 Al,EP**2*F2(M~,C~)=0. Id,Multi,M0**2=M**2/C**2 *yep Id,Multi,C**2=1-S**2 *yep Id,Multi,S**2=1-C**2 Id,C**2*F211(M~,M0~,PM,SM~)=(1-S**2)*F211(M,M0,PM,SM) Al,C**2*F3(PM,M~,M0~)=(1-S**2)*F3(PM,M,M0) Al,C**2*F11(PM,M~)=(1-S**2)*F11(PM,M) *yep F21F22{} Id,F22(M~,M~,M0~,M0~)=F(2,M)*F(2,M0) Al,F21(M~,M~,M0~)=F(2,M)*F(1,M0) Al,F31(M~,M~,M~,M0~)=F(3,M)*F(1,M0) Al,F11(M~,M0~)=F(1,M)*F(1,M0) Id,F(1,PM)=0 F1t5{} Id,EP=0 B EP,I,PI2,TIPI2 Id,Count,1,SM,1 Id,LG(SM,M~)=LG(SM)-LG(M) Al,LG(M0,M~)=LG(M0)-LG(M) Al,LG(M,M0~)=LG(M)-LG(M0) Id,Multi,M0**2=M**2/C**2 Al,PI**4=-0.25*TIPI2**2 Id,Commu,LG *yep Id,C**-6*S**-4=1/C**6/S**2+1/C**4/S**4 Id,C**-6*S**-2=1/C**6+1/C**4/S**2 Id,C**-2*S**-2=1/C**2+1/S**2 Al,C**-2*S**-4=1/C**2+1/S**2+1/S**4 Al,C**-4*S**-2=1/C**4+1/C**2+1/S**2 Al,C**-4*S**-4=1/C**4+2/C**2+2/S**2+1/S**4 Id,Multi,C**2=1-S**2 Id,Multi,S**2=1-C**2 *begin Write comm2lp *end C RO-parameter 6. One-loop subtractions. RO-parameter result. C ONE-LOOP SUBTRACTIONS AND RO-PARAMETER CALCULATION. C NOT CONSIDERED ARE TADPOLE DIAGRAMS WITH INSERTED CORRECTIONS. C ALTHOUGH THEY ARE IMPORTANT FOR GAUGE INVARIANCE OF THE WW LINES, C THEY ARE NOT OF ANY CONSEQUENCE TO THE RO-PARAMETER. C BELOW THEY ARE MADE INACTIVE. C ENTER RESULT FROM TWO-LOOP SELF-ENERGY DIAGRAMS. C THESE ARE THE FILES A0A0, W0A0, W0W0 AND WPWM. C CDC CPU time 28.15 SEC. Oldnew i=I Enter comm2lp Common SWA,SPM,SWW,SAA P ninput Read Roblocks.e VERT{,,,~,~} SVERT{,,} X NUM(K1,K2)=1-0.5*DK(K1,K2) *fix P ninput BLOCK WORK{TADP} P ninput B ET,EP,I,PI2,DEL,TIPI2 Id,Compo,,VE4,VE3,PROP Id,Compo,,CONT Id,Adiso,CONT(S~)*CONT(C~)=S/EP+C/EP Al,CONT(S~)=S/EP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,NOM(P,M~)*NOM(P,M0~)*NOM(P,SM~)=F3(M,M0,SM) Al,NOM(P,M~)*NOM(P,M0~)=F2(M,M0) Al,NOM(P,M~)=F(1,M) Al,ZERO**2=0 *yep Id,F(1,PM)=0 Al,PM=0 Id,PDP**2*F3(M~,M0~,SM~)=F(1,SM)-(M**2+M0**2)*F2(M0,SM) +M**4*F3(M,M0,SM) Al,PDP*F3(M~,M0~,SM~)=F2(M0,SM)-M**2*F3(M,M0,SM) Al,PDP*F2(M~,M0~)=F(1,M0)-M**2*F2(M,M0) Id,F(1,PM)=0 Al,PM=0 Id,F3(M~,M0~,SM)=1/ATEL9**2*F3(M,M0,SM) Al,F(1,SM)=ATEL9**2*F(1,SM) Id,Count,-1,ATEL9,1,SM,1,E1,2,E2,2,ET,2,EZF,2 Id,Multi,M0**2=M**2/C**2 Al,ATEL9=1 Al,Multi,ATEL9**-1=1 Id,Multi,S**2=1.-C**2 *yep Id,Symme,F2,1,2,F3,1,2,3 Id,F3(M~,M~,M~)=F(3,M) Al,F3(M~,M~,SM~)=F3(SM,M,M) Id,F3(SM~,M0~,M~)=DIF(M0,SM)*(F2(SM,M)-F2(M0,M)) Id,F2(M~,M~)=F(2,M) Al,F2(M~,M0~)=DIF(M0,M)*(F(1,M)-F(1,M0)) Id,F(1,PM)=0 Al,PM=0 Id,Asymm,DIF,1,2 Id,DIF(PM,M~)=-1/M**2 Al,DIF(M,M0)=-C**2/M**2/S**2 Al,DIF(M~,SM)=-(1+M**2/SM**2+M**4/SM**4+M**6/SM**6)/SM**2 Id,F(1,SM)=ATEL9**2*F(1,SM) Al,F(3,SM)=F(3,SM)/ATEL9**2 Id,Count,-1,ATEL9,1,SM,1,E1,2,E2,2,ET,2,EZF,2 Id,Numer,ATEL9,1. F1t5{} Id,Once,PI**2=-I*TIPI2/2 Id,N**-1=0.25-EP/16+EP**2/64 Al,N=4+EP Id,EP=0 Id,Multi,M0**2=M**2/C**2 Id,Multi,M0**-1=C**2/M**2 Id,Multi,C**2=1.-S**2 Id,Multi,S**2=1.-C**2 *yep CVERT{,,~} SCVERT{,,~} Id,ZERO=0. Id,Count,1,SM,1,E1,2,E2,2,ET,2,EZF,2 Id,C2MS2=2*C**2-1 E1EZF{,,~,,} Id,PI**6=-PI2*TIPI2**2/4 Id,Commu,LG Id,EP=0 Id,Count,1,SM,1,ET,2 Id,C**-2*S**-4=1/S**4+1/S**2+1/C**2 Al,C**-2*S**-2=1/S**2+1/C**2 P input ENDBLOCK BLOCK SELF{} P ninput Id,SELF(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2,TAP,(DIB(I1,J1,-J1,J2,-J2,I2) )) + DS(I1;J3;-J3;I2;Sym;J3;-J3,TAP,(DIC(I1,J3,-J3,I2) )) + DS(I1;J4;-J5,TAP,(DS("N;J5;-J6,TAP,(DID(I1,I2,"N,J4,-J5,J5,-J6,J6,-J4) )))) + DS(I1;J7;-J8;I2;Sym;J7;-J8,TAP,(DIE(I1,I2,"N,J7,-J7,J8,-J8) )) Id,Anti,TAP Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)= VE3(I1,K1,K3,*,MU,P0,*,L1,-P,*,L3,P)* VE3(K2,I2,K4,*,L2,P,*,NU,-P0,*,L4,-P)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,P,*,L4,P) *D(MU,NU)/N *CONT(I1,K1,K3,/,"K)*CONT(K2,I2,K4,/,"K) Id,DIC(I1~,K1~,K2~,I2~)= VE4(I1,K1,K2,I2,*,MU,*,L1,*,L2,*,NU)* PROP(K1,K2,*,L1,P,*,L2,P) *D(MU,NU)/N *CONT(I1,K1,K2,I2,/,"K) Al,DID(I1~,I2~,I3~,K1~,K2~,K3~,K4~,K5~,K6~)= VE3(I1,K1,K2,*,MU,P0,*,L1,P,*,L2,-P)* VE3(I3,K3,K4,*,AL,K,*,L3,P,*,L4,-P)* VE3(I2,K5,K6,*,NU,-P0,*,L5,P,*,L6,-P)* PROP(K6,K1,*,L6,P,*,L1,P)* PROP(K2,K3,*,L2,P,*,L3,P)* PROP(K4,K5,*,L4,P,*,L5,P) *D(MU,NU)/N /EP Al,DIE(I1~,I2~,I3~,K1~,K2~,K3~,K4~)= VE4(I1,K1,K4,I2,*,MU,*,L1,*,L4,*,NU)* VE3(I3,K2,K3,*,AL,K,*,L2,P,*,L3,-P)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,P,*,L4,P) *D(MU,NU)/N /EP ENDBLOCK Z SWA=SELF("W,"A) SELF{} WORK{SWA} *next Z SPM=SELF("U,"U_) SELF{} WORK{SPM} *next P input Z SWW=SELF("W,"W) SELF{} WORK{SWW} *next P input Z SAA=SELF("A,"A) SELF{} WORK{SAA} *next S EP,TIPI2,N,PM,M,M0,SM,C,S F LG B EP,I,PI2,TIPI2 Z SAA=SAA Z SWA=SWA-4*M**2*S/C*E1F*TIPI2/EP**2 Z SWW=SWW-M**2*TIPI2/EP**2*(-E1F/C**4+43/12*ET/C**2 -55/6*E1F/C**2-E1F**2/C**2/TIPI2+8*E1F) Z SPM=SPM-M**2*TIPI2/EP**2*(-E1F/C**2+43/12*ET -7/6*E1F-E1F**2/TIPI2) E1EZF{~,~,,,} Id,EP=0 Id,Count,1,SM,1 Id,Commu,LG Id,C**-2*S**-2=1/S**2+1/C**2 Id,LG(M~,SM)=LG(M)-LG(SM) Al,LG(M~,M0)=LG(M)-LG(M0) Al,LG(M0~,M)=LG(M0)-LG(M) Id,Commu,LG *next S EP,TIPI2,N,PM,M,M0,SM,C,S B EP,I,PI2,TIPI2 F LG Z RWPWM=WPWM-SPM Z RW0W0=W0W0-SWW Id,C**-2*S**-2=1/S**2+1/C**2 Id,LG(M)=LG(M,SM)+LG(SM) Al,LG(M0)=LG(M0,SM)+LG(SM) Id,Commu,LG Id,LG(M~,SM)*LG(SM)=LG(SM)*LG(M,SM) *next S EP,TIPI2,N,PM,M,M0,SM,C,S B M,SM,C,S F LG Z RO=-(WPWM-C**2*W0W0-SPM+C**2*SWW)/TIPI2**2/PI**4/64/M**2 Id,Multi,TIPI2**-1=0.5/PI**2/I Id,Commu,LG Id,C**-2*S**-2=1/S**2+1/C**2 Id,LG(M)=LG(M,SM)+LG(SM) Al,LG(M0)=LG(M0,SM)+LG(SM) Id,Commu,LG Id,LG(M~,SM)*LG(SM)=LG(SM)*LG(M,SM) *yep Id,C**-2=1+S**2/C**2 *begin Write common *end C RO-parameter 7. Two-loop self-energy diagrams. A-A wave-function. Oldnew i=I P ninput Read Roblocks.e Common AAWF VERT{,,,~,~} C P input X NUM(K1,K2)=1.-0.5*DK(K1,K2) X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3) +2/3*DK(K1,K2)*DK(K1,K3) X KUM(K1)=1-DK(4,K1) X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5) S PM=1,EI=2,NP1,TRN V QL,PX,QX *fix Z AAWF=0 Nprint AAWF *next BLOCK WORK{AAWFA} C P ninput PROJ{,,~,} F21F51{} Id,Count,1,SM,1 *yep Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4 F1t5{} Id,EP=0 *yep NEXP{} Id,EP=0 B EP,I,PI2,TIPI2,LE2 Id,Count,1,SM,1 Id,LG(SM,M~)=LG(SM)-LG(M) Al,LG(M0,M~)=LG(M0)-LG(M) Al,LG(M,M0~)=LG(M)-LG(M0) Id,Multi,M0**2=M**2/C**2 Al,PI**4=-0.25*TIPI2**2 Id,Commu,LG Keep 'AAWFA' *next Z AAWF=AAWF+'AAWFA' Nprint AAWF B EP,I,PI2,TIPI2,LE2 ENDBLOCK BLOCK TOPO{} Id,TOPA(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2;TAP,( DS(-J1;J5;"Z;TAP,( DS(-J5;I2;-J4;TAP,( DIA(I1,I2,J1,-J1,J5,-J5,"Z,"Z,J2,-J2,J4,-J4) )) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)* VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)* VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)* VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)* PROP(K7,K8,*,L7,PL,*,L8,PL)* PROP(K9,K0,*,L9,QL,*,L0,QL)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PXDPX+2*PXDLE*E*(1-X)+LEDLE*E**2/3 Al,Dotpr,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E Al,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E Id,QLDQL=QXDQX-2*QXDLE*E*(1-X)+LEDLE*E**2/3 Al,Dotpr,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E Al,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E Id,PDP=PXDPX-2*X*PXDLE*E+LEDLE*E**2/3 Al,Dotpr,P(MU~)=PX(MU)-X*LE(MU)*E Al,P(MU~)=PX(MU)-X*LE(MU)*E Id,QDQ=QXDQX+2*X*QXDLE*E+LEDLE*E**2/3 Al,Dotpr,Q(MU~)=QX(MU)+X*LE(MU)*E Al,Q(MU~)=QX(MU)+X*LE(MU)*E Id,PXDPX=PDP Al,Dotpr,PX(MU~)=P(MU) Al,PX(MU~)=P(MU) Id,QXDQX=QDQ Al,Dotpr,QX(MU~)=Q(MU) Al,QX(MU~)=Q(MU) *yep Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-1/3*LEDLE*FP(3,M)*E**2 Id,Adiso,NOM(Q,M~)*NOM(QL,M~)=FQ(2,M)-4*QDLE*(X-Y)*FQ(3,M)*E -2/3*LEDLE*FQ(3,M)*E**2+2*QDLE**2*FQ(4,M)*E**2 Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,X**N~=1/(N+1) Al,Y**N~=1/(N+1) Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AAWFA=TOPA("A,"A) TOPO{} WORK{AAWFA} *next BDELETE TOPO BLOCK TOPO{} Id,TOPB(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;"Z;-J4;TAP,( DC("P,TAP,-1,"Z,J4)* DS(J1;I2;J5,TAP,( DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,"Z,"Z,J4,-J4) ))) ))) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K3,*,MU,-LE,*,L1,PL,*,L3,-P)* VE3(K2,I2,K6,*,L2,-PL,*,NU,LE,*,L6,P)* VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)* VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,P,*,L4,P)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,K,*,L8,K)* PROP(K9,K0,*,L9,Q,*,L0,Q)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AAWFB=TOPB("A,"A) TOPO{} WORK{AAWFB} *next BDELETE TOPO BLOCK TOPO{} Id,TOPE(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,( DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)* VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)* VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,P,*,L8,P)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Al,NOM(Q,M~)=FQ(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AAWFE=TOPE("A,"A) TOPO{} WORK{AAWFE} *next BDELETE TOPO BLOCK TOPO{} Id,TOPF(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS("Z;J2;J4;TAP,( DC("P,TAP,-1,"Z,J4)* DIA(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J4,-J4) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,-LE,*,L1,PL,*,L5,-P)* VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)* VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,K,*,L4,K)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,Q,*,L8,Q)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*FP(3,M)*E -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AAWFF=2*TOPF("A,"A) TOPO{} WORK{AAWFF} *next BDELETE TOPO BLOCK TOPO{} Id,TOPH(I1~,I2~)= DS(I1;-J1;-J2;"Z;Sym;-J1;-J2;"Z,TAP,( DIA(I1,I2,-J1,J1,-J2,J2,"Z,"Z) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)= VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)* VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM *yep Id,NOM(PL,M~)=FP(1,M)-2*PDLE*FP(2,M)*E -LEDLE*E**2*FP(2,M)+4*PDLE**2*E**2*FP(3,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AAWFH=TOPH("A,"A) TOPO{} WORK{AAWFH} Print AAWF *begin Write aawcomm *end C RO-parameter 8. Two-loop self-energy diagrams. A-W wave-function. Oldnew i=I Common AWWF P ninput Read Roblocks.e VERT{,,,~,~} S EI=2,NP1,TRN V QL,PX,QX X KROM(K1,K2)=DK(K1,5)*DK(K2,7)+DK(K1,7)*DK(K2,5) X NUM(K1,K2)=1.-0.5*DK(K1,K2) X NUM3(K1,K2,K3)=1-0.5*DK(K1,K2)-0.5*DK(K1,K3)-0.5*DK(K2,K3) +2/3*DK(K1,K2)*DK(K1,K3) X KUM(K1)=1-DK(4,K1) X ZUM(K1,K2,K3,K4,K5)=1-KUM(K1)*KUM(K2)*KUM(K3)*KUM(K4)*KUM(K5) *fix Z AWWF=0 Nprint AWWF *next BLOCK WORK{AWWFA} P ninput PROJ{,,~,} F21F51{} Id,Count,1,SM,1 *yep Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4 F1t5{} Id,EP=0 *yep NEXP{} Id,EP=0 B EP,I,PI2,TIPI2,LE2 Id,Count,1,SM,1 Id,LG(SM,M~)=LG(SM)-LG(M) Al,LG(M0,M~)=LG(M0)-LG(M) Al,LG(M,M0~)=LG(M)-LG(M0) Id,Multi,M0**2=M**2/C**2 Al,Multi,M0**-2=C**2/M**2 Al,Multi,PI**4=-0.25*TIPI2**2 Id,Commu,LG Keep 'AWWFA' *next Z AWWF=AWWF+'AWWFA' Nprint AWWF B EP,I,PI2,TIPI2,LE2 ENDBLOCK BLOCK TOPO{} Id,TOPA(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2;TAP,( DS(-J1;J5;"Z;TAP,( DS(-J5;I2;-J4;TAP,( DIA(I1,I2,J1,-J1,J5,-J5,"Z,"Z,J2,-J2,J4,-J4) )) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)* VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)* VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)* VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)* PROP(K7,K8,*,L7,PL,*,L8,PL)* PROP(K9,K0,*,L9,QL,*,L0,QL)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PXDPX+2*PXDLE*E*(1-X)+LEDLE*E**2/3 Al,Dotpr,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E Al,PL(MU~)=PX(MU)+LE(MU)*(1-X)*E Id,QLDQL=QXDQX-2*QXDLE*E*(1-X)+LEDLE*E**2/3 Al,Dotpr,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E Al,QL(MU~)=QX(MU)-LE(MU)*(1-X)*E Id,PDP=PXDPX-2*X*PXDLE*E+LEDLE*E**2/3 Al,Dotpr,P(MU~)=PX(MU)-X*LE(MU)*E Al,P(MU~)=PX(MU)-X*LE(MU)*E Id,QDQ=QXDQX+2*X*QXDLE*E+LEDLE*E**2/3 Al,Dotpr,Q(MU~)=QX(MU)+X*LE(MU)*E Al,Q(MU~)=QX(MU)+X*LE(MU)*E Id,PXDPX=PDP Al,Dotpr,PX(MU~)=P(MU) Al,PX(MU~)=P(MU) Id,QXDQX=QDQ Al,Dotpr,QX(MU~)=Q(MU) Al,QX(MU~)=Q(MU) *yep Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-1/3*LEDLE*FP(3,M)*E**2 Id,Adiso,NOM(Q,M~)*NOM(QL,M~)=FQ(2,M)-4*QDLE*(X-Y)*FQ(3,M)*E -2/3*LEDLE*FQ(3,M)*E**2+2*QDLE**2*FQ(4,M)*E**2 Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,X**N~=1/(N+1) Al,Y**N~=1/(N+1) Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AWWFA=TOPA("A,"W) TOPO{} WORK{AWWFA} *next BDELETE TOPO BLOCK TOPO{} Id,TOPAP(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2;TAP,( DS(-J1;J3;"Z;TAP,( DS("Z;I2;-J4;TAP,( DIA(I1,I2,J1,-J1,"Z,"Z,J3,-J3,J2,-J2,J4,-J4) )) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K7,*,MU,LE,*,L1,P,*,L7,-PL)* VE3(K2,K3,K5,*,L2,-P,*,L3,-Q,*,L5,K)* VE3(K4,I2,K0,*,L4,Q,*,NU,-LE,*,L0,-QL)* VE3(K6,K8,K9,*,L6,-K,*,L8,PL,*,L9,QL)* PROP(K1,K2,*,L1,P,*,L2,P)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)* PROP(K7,K8,*,L7,PL,*,L8,PL)* PROP(K9,K0,*,L9,QL,*,L0,QL)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E Id,QLDQL=QDQ-2*QDLE*E+LEDLE*E**2 Al,Dotpr,QL(MU~)=Q(MU)-LE(MU)*E Al,QL(MU~)=Q(MU)-LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*E*FP(3,M) -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M) Id,NOM(QL,M~)=FQ(1,M)+2*QDLE*E*FQ(2,M)-LEDLE*E**2*FQ(2,M) +4*QDLE**2*E**2*FQ(3,M) Al,NOM(K,M~)=FK(1,M) Al,NOM(Q,M~)=FQ(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 Id,Adiso,FQ(1,SM)*FQ(N~,M0)=DIFF**-N*FQ(1,SM)*(-1)**N *ATEL9 Id,DIFF**N~=SM**N*SM**N*(1-N*M0**2/SM**2) Id,Count,1,SM,1,P,1,Q,1,K,1,ATEL9,2 Id,Numer,ATEL9,1. ENDBLOCK Z AWWFA=TOPAP("A,"W) TOPO{} WORK{AWWFA} *next BDELETE TOPO BLOCK TOPO{} Id,TOPB(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;"Z;-J4;TAP,( DC("P,TAP,-1,"Z,J4)* DS(J1;I2;J5,TAP,( DIA(I1,I2,-J1,J1,-J2,J2,-J5,J5,"Z,"Z,J4,-J4) ))) ))) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~,K9~,K0~)= VE3(I1,K1,K3,*,MU,-LE,*,L1,PL,*,L3,-P)* VE3(K2,I2,K6,*,L2,-PL,*,NU,LE,*,L6,P)* VE3(K4,K7,K0,*,L4,P,*,L7,-K,*,L0,Q)* VE3(K5,K8,K9,*,L5,-P,*,L8,K,*,L9,-Q)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,P,*,L4,P)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,K,*,L8,K)* PROP(K9,K0,*,L9,Q,*,L0,Q)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AWWFB=TOPB("A,"W) TOPO{} WORK{AWWFB} *next BDELETE TOPO BLOCK TOPO{} Id,TOPE(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J2;-J4;J4;J3;Sym;-J4;J4;TAP,( DIA(I1,I2,-J1,J1,-J4,J4,-J2,J2,J3,-J3) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)* VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)* VE4(K6,K3,K4,K7,*,L6,*,L3,*,L4,*,L7)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,P,*,L8,P)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Al,NOM(Q,M~)=FQ(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AWWFE=TOPE("A,"W) TOPO{} WORK{AWWFE} *next BDELETE TOPO BLOCK TOPO{} Id,TOPF(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS("Z;J2;J4;TAP,( DC("P,TAP,-1,"Z,J4)* DIA(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J4,-J4) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,-LE,*,L1,PL,*,L5,-P)* VE4(K2,I2,K4,K8,*,L2,*,NU,*,L4,*,L8)* VE3(K3,K6,K7,*,L3,-K,*,L6,P,*,L7,Q)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,K,*,L4,K)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,Q,*,L8,Q)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,PLDPL=PDP+2*PDLE+LEDLE*E**2 Al,Dotpr,PL(MU~)=P(MU)+LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(PL,M~)=FP(2,M)-2*PDLE*FP(3,M)*E -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AWWFF=TOPF("A,"W)+TOPF("W,"A) TOPO{} WORK{AWWFF} *next BDELETE TOPO BLOCK TOPO{} Id,TOPFP(I1~,I2~)= DS(I2;-J1;"Z;TAP,( DS(J1;I1;-J3;-J4;TAP,( DIA(I1,I2,-J1,J1,J3,-J3,"Z,"Z,J4,-J4) )) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I2,K1,K5,*,NU,-LE,*,L1,QL,*,L5,-Q)* VE4(K2,I1,K4,K8,*,L2,*,MU,*,L4,*,L8)* VE3(K3,K6,K7,*,L3,-K,*,L6,Q,*,L7,P)* PROP(K1,K2,*,L1,QL,*,L2,QL)* PROP(K3,K4,*,L3,K,*,L4,K)* PROP(K5,K6,*,L5,Q,*,L6,Q)* PROP(K7,K8,*,L7,P,*,L8,P)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,QDLE=QDLE*E Al,KDLE=KDLE*E Al,PLDLE=PLDLE*E Al,QLDLE=QLDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Id,QLDQL=QDQ+2*QDLE+LEDLE*E**2 Al,Dotpr,QL(MU~)=Q(MU)+LE(MU)*E Al,QL(MU~)=Q(MU)+LE(MU)*E *yep Id,NOM(QL,M~)=FQ(1,M)-2*QDLE*E*FQ(2,M) -LEDLE*E**2*FQ(2,M)+4*QDLE**2*E**2*FQ(3,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(P,M~)=FP(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 Id,Adiso,FQ(1,SM)*FQ(N~,M0)=DIFF**-N*FQ(1,SM)*(-1)**N *ATEL9 Id,DIFF**N~=SM**N*SM**N*(1-N*M0**2/SM**2) Id,Count,1,SM,1,P,1,Q,1,K,1,ATEL9,2 Id,Numer,ATEL9,1. ENDBLOCK Z AWWFF=TOPFP("A,"W) TOPO{} WORK{AWWFF} *next BDELETE TOPO BLOCK TOPO{} Id,TOPH(I1~,I2~)= DS(I1;-J1;-J2;"Z;Sym;-J1;-J2;"Z,TAP,( DIA(I1,I2,-J1,J1,-J2,J2,"Z,"Z) )) Id,Anti,TAP Id,DIA(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~)= VE4(I1,K1,K3,K5,*,MU,*,L1,*,L3,*,L5)* VE4(I2,K2,K4,K6,*,NU,*,L2,*,L4,*,L6)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,Q,*,L4,Q)* PROP(K5,K6,*,L5,K,*,L6,K)*XX Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM *yep Id,NOM(PL,M~)=FP(1,M)-2*PDLE*FP(2,M)*E -LEDLE*E**2*FP(2,M)+4*PDLE**2*E**2*FP(3,M) Al,NOM(Q,M~)=FQ(1,M) Al,NOM(K,M~)=FK(1,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 ENDBLOCK Z AWWFH=TOPH("A,"W) TOPO{} WORK{AWWFH} Print AWWF *begin Write awwcomm *end C RO-parameter 9. Subtractions for A-A and A-W wave-functions. C SUBTRACTIONS, A-A AND A-W WAVEFUNCTIONS. C ENTER RESULTS FROM TWO-LOOP CALCULATIONS, AAWF AND AWWF. C DCDC CPU time 14.7 SEC. Oldnew i=I Enter aawcomm Enter awwcomm P ninput Read Roblocks.e VERT{,,~,~,~} SVERT{,,~} X NUM(K1,K2)=1-0.5*DK(K1,K2) *fix BLOCK WORK{} B E1,EZF,ET,EP,I,PI2,TIPI2,LE2 Id,Compo,,VE4,VE3,PROP Id,Compo,,CONT Id,Adiso,CONT(S~)*CONT(C~)=S/EP+C/EP Al,CONT(S~)=S/EP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,ZERO**2=0 Id,PDLE=PDLE*E Al,LEDLE=LEDLE*E**2 Al,PDPL=PDP+PDLE*E Al,PLDLE=PDLE*E+LEDLE*E**2 Al,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,LE(MU~)=LE(MU)*E Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Al,Adiso,NOM(P,M~)*NOM(PL,M~)= FP(2,M)-2*PDLE*FP(3,M)*E -LEDLE*E**2*FP(3,M)+4*PDLE**2*E**2*FP(4,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 PROJ{,,~,~} Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4 F1t5{} *yep CVERT{,~,~} SCVERT{,~,~} Id,ZERO=0. Id,Count,1,SM,1,E1,2,E2,2,ET,2,EZF,2 Id,C2MS2=1-2*S**2 E1EZF{,,~,~,~} Id,Count,1,SM,1,ET,2,E1F,2,EZF,2 Id,EP=0 *yep E1EZF{~,~,,,} Id,Count,1,SM,1 Id,EP=0 *yep NEXP{} Id,EP=0 B EP,I,PI2,TIPI2,LE2 Id,C**-2*S**-4=1/S**4+1/S**2+1/C**2 Al,C**-2*S**-2=1/S**2+1/C**2 Id,LG(SM,M~)=LG(SM)-LG(M) Al,LG(M0,M~)=LG(M0)-LG(M) Al,LG(M,M0~)=LG(M)-LG(M0) Id,Multi,M0**2=M**2/C**2 Al,PI**4=-0.25*TIPI2**2 Al,PI**2=-0.5*TIPI2*I Id,Commu,LG Id,C**2=1-S**2 ENDBLOCK BLOCK SELF{} Id,SELF(I1~,I2~)= DS(I1;J1;J2;Sym;J1;J2,TAP,( DIB(I1,J1,-J1,J2,-J2,I2) )) + DS(I1;J4;-J5;TAP,( DS("N;J5;-J6;TAP,( DID(I1,I2,"N,J4,-J5,J5,-J6,J6,-J4) )) )) Id,Anti,TAP Id,DIB(I1~,K1~,K2~,K3~,K4~,I2~)= VE3(I1,K1,K3,*,MU,LE,*,L1,-PL,*,L3,P)* VE3(K2,I2,K4,*,L2,PL,*,NU,-LE,*,L4,-P)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K3,K4,*,L3,P,*,L4,P) *XX *CONT(I1,K1,K3,/,"K)*CONT(K2,I2,K4,/,"K) Al,DID(I1~,I2~,I3~,K1~,K2~,K3~,K4~,K5~,K6~)= VE3(I1,K1,K2,*,MU,-LE,*,L1,PL,*,L2,-P)* VE3(I3,K3,K4,*,AL,K,*,L3,P,*,L4,-P)* VE3(I2,K5,K6,*,NU,LE,*,L5,P,*,L6,-PL)* PROP(K6,K1,*,L6,PL,*,L1,PL)* PROP(K2,K3,*,L2,P,*,L3,P)* PROP(K4,K5,*,L4,P,*,L5,P) *XX /EP ENDBLOCK P input Z AAWFC=SELF("A,"A) P ninput SELF{} WORK{} Keep AAWFC *next P input Z AWWFC=SELF("A,"W) P ninput SELF{} WORK{} Keep AAWFC,AWWFC *next P input B EP,I,PI2,TIPI2,LE2 Z TAAWF=AAWF-AAWFC Z TAWWF=AWWF-AWWFC *end C RO-parameter 10. Tadpoles in A-A wave-function. C A-A TWO-LOOP WAVE-FUNCTION. TADPOLE INSERTIONS. C THERE ARE MORE DIAGRAMS INVOLVING TADPOLES, NAMELY C WITH ONE 4-VERTEX AND ONE 3-VERTEX WHERE ONE OF THE C LINES OF THE 4-VERTEX CONNECTS TO A TADPOLE. C THESE DIAGRAMS CANCEL OUT IF ONE SUBTRACTS THE COUNTERDIAGRAMS C CONTAINING THE SAME TYPE OF DIAGRAMS, BUT THEY WERE COMPUTED C TO SEE IF WITH THIS ADDITION THE TWO-LOOP DIAGRAMS WHERE C GAUGE INVARIANT BY THEMSELVES, WHICH MUST BE. C CDC CPU TIME 2.5 SEC. Oldnew i=I P ninput Read Roblocks.e C P input VERT{,,~,,} F FSC S NP1,TRN *fix Z A0A0=0 Keep A0A0 Nprint A0A0 *next P ninput BLOCK WORK{A0A0A} P ninput Id,Compo,,VE4,VE3,PROP Id,VE4(AA~,L1~,L2~,L3~,L4~)=AA(L1,L2,L3,L4) Al,VE3(AA~,MU~,P0~,L2~,Q~,L1~,P~)= AA(MU,P0,L2,Q,L1,P) Al,PROP(AA~,L4~,Q~,L3~,P~)=AA(L4,L3,Q) Id,Commu,NOM Id,PDLE=PDLE*E Al,LEDLE=E**2*LEDLE Al,LE(MU~)=LE(MU)*E Al,PDPL=PDP+PDLE*E Al,PLDLE=PDLE*E+LEDLE*E**2 Al,PLDPL=PDP+2*PDLE*E+LEDLE*E**2 Al,PL(MU~)=P(MU)+LE(MU)*E *yep Id,Adiso,NOM(P,M~)*NOM(P,M~)*NOM(PL,M~)= FP(3,M)-2*PDLE*FP(4,M)*E -LEDLE*E**2*FP(4,M)+4*PDLE**2*E**2*FP(5,M) Id,E**1=0 Al,XX*E**2=1 Al,XX=0 PROJ{,,~,~} Id,FSC(N~,M~)=F(N,M)*M**N*M**N/M**4 F1t5{} Id,EP=0 *yep NEXP{} Id,EP=0 B EP,I,PI2,TIPI2,LE2,TADPO,TADGH Id,Count,1,SM,1,ET,2 Id,LG(SM,M~)=LG(SM)-LG(M) Al,LG(M0,M~)=LG(M0)-LG(M) Al,LG(M,M0~)=LG(M)-LG(M0) Id,Multi,M0**2=M**2/C**2 Al,PI**4=-0.25*TIPI2**2 Id,Commu,LG Keep A0A0,'A0A0A' *next Z A0A0=A0A0+'A0A0A' Nprint A0A0 Keep A0A0 B EP,I,PI2,TIPI2,LE2,TADPO,TADGH ENDBLOCK BLOCK TOPO{} P ninput Id,TOPE(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J1;I2;-J3;TAP,( DC("F,TFE,0,J1)* DIB(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J3,-J3) )) )) Id,Anti,TAP Id,DIB(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)* VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)* VE3(K6,K7,"Z,*,L6,-P,*,L7,P,*,L9,P0)/SM**2* M*SM**2*ET/EP*(-1)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,P,*,L8,P)*XX*TADPO ENDBLOCK P input Z A0A0E=TOPE("A,"A) TOPO{} WORK{A0A0E} C PRINT OUTPUT C PRINT A0A0 *yep E1EZF{~,~,,~,~} Id,EP=0 Id,Count,1,SM,1,ET,2 Id,PI**2=-0.5*I*TIPI2 *next BLOCK TOPOP{} P ninput Id,TOPE(I1~,I2~)= DS(I1;-J1;-J2;TAP,( DS(J1;I2;-J3;TAP,( -DC("F_,TFE,0,J1)* DIB(I1,I2,-J1,J1,"Z,"Z,-J2,J2,J3,-J3) )) )) Id,Anti,TAP Id,DIB(I1~,I2~,K1~,K2~,K3~,K4~,K5~,K6~,K7~,K8~)= VE3(I1,K1,K5,*,MU,LE,*,L1,-PL,*,L5,P)* VE3(K2,I2,K8,*,L2,PL,*,NU,-LE,*,L8,-P)* VE3(K6,K7,"Z,*,L6,-P,*,L7,P,*,L9,P0)/SM**2* M*SM**2*ET/EP*(-1)* PROP(K1,K2,*,L1,PL,*,L2,PL)* PROP(K5,K6,*,L5,P,*,L6,P)* PROP(K7,K8,*,L7,P,*,L8,P)*XX*TADGH ENDBLOCK Z A0A0E=TOPE("A,"A) TOPOP{} WORK{A0A0E} C PRINT OUTPUT Print A0A0 *yep E1EZF{~,~,,~,~} Id,EP=0 Id,Count,1,SM,1,ET,2 Id,PI**2=-0.5*I*TIPI2 C PRINT OUTPUT *yep Id,TADGH=TADPO *end C RO-parameter 11. Diagrams with tadpole insertions. C DIAGRAMS WITH ONE 4-VERTEX WITH TADPOLE AND ONE 3-VERTEX. C A-A WAVE-FUNCTION. C REST REFERS TO THE RESULT OF THE PREVIOUS PROGRAM, C SELF-ENERGY DIAGRAMS WITH TADPOLE INSERTION, C AND THE D(MU,NU) PART OF THE A-A WAVE-FUNCTION CALCULATION. C CDC CPU time 1 SEC. P ninput Read Roblocks.e C P input Oldnew,i=I I MU=N,NU=N S M,SM,LE2 B EP,TIPI2 F LG,F V LE Z XX=4*0.5*S**2*M*LE2*(-EP/N*F(3,M)-4/N*M**2*F(4,M)) *(-M*ET/EP) + REST Id,N**-1=1/4-EP/16+EP**2/64 F1t5{} E1EZF{~,~,,~,~} Id,EP=0 Al,PI**2=-0.5*I*TIPI2 Id,Count,2,SM,1,REST,2 P output *yep Id,REST=TIPI2**2*SM**2/M**2*S**2*LE2*( (1/16 + 21/16)/EP -1/6 - 37/48 +(1/16 + 5/8)*LG(M) +11/16*LG(SM) ) *end C RO-parameter 12. Counter-term Lagrangian for the standard model. C COUNTERLAGRANGIAN. TWO SCHOONSCHIP PROGRAMS, THE FIRST C TO PRODUCE THE REGULAR ONE-LOOP COUNTERTERMS, THE SECOND C TO PRODUCE THE QUADRATIC TERMS ARISING FROM THE ONE-LOOP C COUNTERTERMS. C CDC CPU time 10 SEC. Common DELL *fix P brackets S X,M,SM,AL,BET,C,S,E=3 S GG,AM,AN,AMN,AMM ,F3,F3M,FP,FMP,FM,FMM ,WMNP,WMMP,WMP,WNP ,WMNM,WMMM,WMM,WNM ,WMN0,WMM0,WM0,WN0,Z,ZM B GG,AM,AN,AMN,AMM ,F3,F3M,FP,FMP,FM,FMM ,WMNP,WMMP,WMP,WNP ,WMNM,WMMM,WMM,WNM ,WMN0,WMM0,WM0,WN0,Z,ZM Z DELL = (HAND + WMMP*WMMM - M*WMMP*FM - M*WMMM*FP + M**2*FM*FP + 0.5*WMM0**2 - M/C*WMM0*F3 + 0.5*M**2/C**2*F3**2 + 0.5*AMM**2 )*X Id HAND = - WMNP*WMNM - M**2*WMP*WMM - 0.5*WMN0**2 - 0.5*M**2*C**-2 *WM0**2 - 0.5*AMN**2 - FMP*FMM - M**2*FP*FM - 0.5*F3M**2 - 0.5*M**2*C**-2*F3**2 - 0.5*ZM**2 - 0.5*SM**2*Z**2 + GG*(-I*C*(WMN0*(WNP*WMM-WNM*WMP) - WM0*(WNP*WMNM-WNM*WMNP) + WN0*(WMP*WMNM-WMM*WMNP)) - I*S*(AMN*(WNP*WMM-WNM*WMP) - AM*(WNP*WMNM-WNM*WMNP) + AN*(WMP*WMNM-WMM*WMNP)) + GG*{-0.5*WMP*WMM*WNP*WNM + 0.5*WMP**2*WNM**2 + C**2*WM0*(WMP*WN0*WNM-WM0*WNP*WNM) + S**2*AM*WNM*(WMP*AN-AM*WNP) + S*C*AM*(WN0*(WMP*WNM+WNP*WMM) - 2.*WM0*WNP*WNM) } ) + GG*(-AL*M*Z*(Z**2+F3**2+2.*FP*FM) + GG*{-0.125*AL*(Z**4+F3**4+4.*FP**2*FM**2+4.*F3**2*FP*FM + 4.*Z**2*FP*FM + 2.*F3**2*Z**2) } - M*Z*WMP*WMM - 0.5*M*C**-2*Z*WM0**2 - 0.5*I*(WMP*(F3*FMM-FM*F3M) - WMM*(F3*FMP-FP*F3M)) + 0.5*(WMP*(Z*FMM-FM*ZM) + WMM*(Z*FMP-FP*ZM)) + 0.5*C**-1*(WM0*(Z*F3M-F3*ZM)) - I*S**2*C**-1*M*WM0*(WMP*FM-WMM*FP) + I*S*M*AM*(WMP*FM-WMM*FP) - I*(0.5*C**-1 - C)*WM0*(FP*FMM-FM*FMP) + I*S*AM*(FP*FMM-FM*FMP) + GG*{-0.25*WMP*WMM*(Z**2+F3**2+2.*FP*FM) - 0.125*C**-2*WM0**2*(Z**2+F3**2 + 2.*(2.*S**2-1.)**2*FP*FM) - S**2*AM**2*FP*FM - 0.5*S**2*C**-1*WM0*F3*(WMP*FM+WMM*FP) - 0.5*I*S**2/C*WM0*Z*(WMP*FM-WMM*FP) + 0.5*S*AM*F3*(WMP*FM+WMM*FP) + 0.5*I*S*AM*Z*(WMP*FM-WMM*FP) - S/C*(2.*C**2-1)*WM0*AM*FP*FM } ) Id,WMNP=WMNP*(1+E*EC) Al,WMMP=WMMP*(1+E*EC) Al,WMNM=WMNM*(1+E*EC) Al,WMMM=WMMM*(1+E*EC) Al,WMP=WMP*(1+E*EC) Al,WNP=WNP*(1+E*EC) Al,WMM=WMM*(1+E*EC) Al,WNM=WNM*(1+E*EC) Al,WMN0=WMN0*(1+E*E0) + E*E0A*AMN Al,WMM0=WMM0*(1+E*E0) + E*E0A*AMM Al,WM0=WM0*(1+E*E0) + E*E0A*AM Al,WN0=WN0*(1+E*E0) + E*E0A*AN Al,AMN=AMN*(1+E*EA) + E*EA0*WMN0 Al,AMM=AMM*(1+E*EA) + E*EA0*WMM0 Al,AM=AM*(1+E*EA) + E*EA0*WM0 Al,AN=AN*(1+E*EA) + E*EA0*WN0 Id,FMP=FMP*(1+E*EFC) Al,FP=FP*(1+E*EFC) Al,FMM=FMM*(1+E*EFC) Al,FM=FM*(1+E*EFC) Al,F3M=F3M*(1+E*EF3) Al,F3=F3*(1+E*EF3) Al,ZM=ZM*(1+E*EZ) Al,Z=Z*(1+E*EZ)+E*ETP Id,EFC=EZ Al,EF3=EZ *yep Id,GG=GG*(1+E*EG) Al,AL=AL*(1+E*EAL) Al,C=C*(1+E*ECO) Al,Multi,C**-1=C**-1*(1-E*ECO) Al,S=S*(1-E*ECO*C**2/S**2) Al,Multi,S**-1=S**-1*(1+E*ECO*C**2/S**2) Al,M=M*(1+E*EM) Al,SM=SM*(1+E*ESM) Nprint DELL *next B GG,AM,AN,AMN,AMM ,F3,F3M,FP,FMP,FM,FMM ,WMNP,WMMP,WMP,WNP ,WMNM,WMMM,WMM,WNM ,WMN0,WMM0,WM0,WN0,Z,ZM Z DELP=DELL Id,Multi,E**2=0 Id,X*E=1 Id,EAL=2*ESM-2*EM Al,ETP=M*ET*GG**-1 Al,AL=0.25*SM**2/M**2 C E1=EM+0.5*ET, E2=EM-ESM Id,EM=E1-0.5*ET Al,ESM=E1-E2-0.5*ET *yep C PRINT OUTPUT Id,Multi,S**2=1-C**2 Id WMP**2*WNM**2=WNP**2*WMM**2 Id WM0*WN0*WMM*WNP=WM0*WN0*WNM*WMP Al WM0*AN*WMM*WNP=WN0*AM*WNM*WMP Al WM0*AN*WMP*WNM=WN0*AM*WNP*WMM Al AM*AN*WMM*WNP=AM*AN*WNM*WMP Al WN0*AN*WMP*WMM=WM0*AM*WNP*WNM Al WN0**2*WMP*WMM=WM0**2*WNP*WNM Al AN**2*WMP*WMM=AM**2*WNP*WNM Oldnew,G=GAM,WNM=VN,WMM=VM,WMMM=VMM,WMNM=VMN Oldnew,WNP=UN,WMP=UM,WMMP=UMM,WMNP=UMN Oldnew,FMM=HM,FM=H,FMP=GM,FP=G,F3=F,F3M=FM B GG,AM,AN,AMN,AMM,F,FM,G,GM,H,HM,UMN,UMM ,UM,UN,VMN,VMM,VM,VN,WMN0,WMM0,WM0,WN0,Z,ZM *yep Id,EC=19/12 Al,E0=1/6+1.5*C**2-1/12/C**2 Al,E0A=-2*C*S Al,EA=1.5*S**2 Al,EA0=5*S*C+S/C/6 Al,EZ=0.5+0.25/C**2+EZF Al,EG=-43/12 Al,ECO=-S**2*(43-42*S**2)/12/C**2 C AL,E1=0.5/C**2-31/12+E1F C AL,E2=-25/12+0.75/C**2-1.5*M**2/SM**2 C -0.75*M**2/C**4/SM**2-0.75*SM**2/M**2 C +E2F C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2 C +0.75*SM**2/M**2 C +ETF C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2 C -3*SM**2/M**2/8 C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8 Al,AL=0.25*SM**2/M**2 Id,Multi,S**2=1-C**2 *begin C COUNTER LAGRANGIAN, QUADRATIC TERMS. Oldnew,GAM=G Names DELL S X,M,SM,AL,BET,C,S,E=3 S GG,AM,AN,AMN,AMM ,F3,F3M,FP,FMP,FM,FMM ,WMNP,WMMP,WMP,WNP ,WMNM,WMMM,WMM,WNM ,WMN0,WMM0,WM0,WN0,Z,ZM B GG,AM,AN,AMN,AMM ,F3,F3M,FP,FMP,FM,FMM ,WMNP,WMMP,WMP,WNP ,WMNM,WMMM,WMM,WNM ,WMN0,WMM0,WM0,WN0,Z,ZM Z DEPP=DELL Id,X*E**2=1 Al,E**1=0 Id,EAL=2*ESM-2*EM Al,ETP=M*ET*GG**-1 Al,AL=0.25*SM**2/M**2 C E1=EM+0.5*ET, E2=EM-ESM Id,EM=E1-0.5*ET Al,ESM=E1-E2-0.5*ET *yep C PRINT OUTPUT Id,Multi,S**2=1-C**2 Id WMP**2*WNM**2=WNP**2*WMM**2 Id WM0*WN0*WMM*WNP=WM0*WN0*WNM*WMP Al WM0*AN*WMM*WNP=WN0*AM*WNM*WMP Al WM0*AN*WMP*WNM=WN0*AM*WNP*WMM Al AM*AN*WMM*WNP=AM*AN*WNM*WMP Al WN0*AN*WMP*WMM=WM0*AM*WNP*WNM Al WN0**2*WMP*WMM=WM0**2*WNP*WNM Al AN**2*WMP*WMM=AM**2*WNP*WNM Oldnew,G=GAM,WNM=VN,WMM=VM,WMMM=VMM,WMNM=VMN Oldnew,WNP=UN,WMP=UM,WMMP=UMM,WMNP=UMN Oldnew,FMM=HM,FM=H,FMP=GM,FP=G,F3=F,F3M=FM B GG,AM,AN,AMN,AMM,F,FM,G,GM,H,HM,UMN,UMM ,UM,UN,VMN,VMM,VM,VN,WMN0,WMM0,WM0,WN0,Z,ZM Id,F=0 Al,FM=0 Al,Z=0 Al,ZM=0 Al,G=0 Al,GM=0 Al,H=0 Al,HM=0 Al,GG=0 Al,Multi,GG**-1=0 *yep Id,EC=19/12 Al,E0=1/6+1.5*C**2-1/12/C**2 Al,E0A=-2*C*S Al,EA=1.5*S**2 Al,EA0=5*S*C+S/C/6 Al,EZ=0.5+0.25/C**2+EZF Al,EG=-43/12 Al,ECO=-S**2*(43-42*S**2)/12/C**2 Al,E1=0.5/C**2-31/12+E1F Al,E2=-25/12+0.75/C**2-1.5*M**2/SM**2 -0.75*M**2/C**4/SM**2-0.75*SM**2/M**2 +E2F C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2 C +0.75*SM**2/M**2 C +ETF C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2 C -3*SM**2/M**2/8 C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8 Al,AL=0.25*SM**2/M**2 C ID,COUNT,1,SM,1,E1F,2,E2F,2,EZF,2,ET,2,X,2 Id,Multi,S**2=1-C**2 *end C RO-parameter 13. Counter terms for the Ghost Lagrangian, standard model. C GHOST COUNTER-LAGRANGIAN. C LAGRANGIAN WITH COUNTERTERMS GENERATED BY RENORMALIZED GAUGE C TRANSFORMATIONS. C INSTRUCTIONS FOR DIAGONILIZATION ARE GIVEN NEAR THE *END CARD. C FERMIONS DO NOT CONTRIBUTE TO GHOST INFINITIES. C A SECOND PROGRAM INDICATES AND CHECKS THE IDENTITIES C RESULTING FROM THIS REQUIREMENT. S XX,M,MP,LP,LPP,LNPP,LNP,LM,LMP,LNMP,LNM,L0,L0P,LN0P,LN0 ,LA,LAP,LNA,LNAP S E=2 Oldnew,G=GAM,DF=DFREZ B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN ,X,XN,Y,YN,Z Z GHOST=XX*( XN*DUN + M*X*DG +ON*DVN+M*O*DH +QN*DWN+M*Q*DF/C +SN*DAN) Id,DUN=(1-E*EC)*(I*BP*LPP*(CP*WNP+SP*ANP) -I*BP*(CP*L0P+SP*LAP)*UNP-LNPP) Al,DVN=(1-E*EC)*(-I*BP*LMP*(CP*WNP+SP*ANP) +I*BP*(CP*L0P+SP*LAP)*VNP-LNMP) Al,DWN=(1-E*E0)*(-I*BP*CP*LPP*VNP +I*BP*CP*LMP*UNP-LN0P) - E*E0A*(-I*GG*S*LP*VN+I*GG*S*LM*UN-LNA) Al,DAN=(1-E*EA)*(-I*BP*SP*LPP*VNP +I*BP*SP*LMP*UNP-LNAP) - E*EA0*(-I*GG*C*LP*VN+I*GG*C*LM*UN-LN0) Al,DG=(1-E*EZ)*(0.5*I*BP*LPP*FP -0.5*I*BP*((2*CP**2-1)*L0P/CP+2*SP*LAP)*GP -0.5*BP*ZP*LPP-MP*LPP) Al,DH=(1-E*EZ)*(-0.5*I*BP*LMP*FP +0.5*BP*I*((2*CP**2-1)*L0P/CP+2*SP*LAP)*HP -0.5*BP*ZP*LMP-MP*LMP) Al,DF=(1-E*EZ)*(-0.5*I*BP*(LPP*HP-LMP*GP) -0.5*BP*L0P*ZP/CP-MP*L0P/CP) Al,DZ=(1-E*EZ)*(0.5*BP*(LPP*HP*LMP*GP)+0.5*BP*FP*L0P/CP) Id,BP=GG*(1+E*EG) Al,MP=M*(1+E*EM) Al,LPP=LP*(1+E*ELC) Al,LMP=LM*(1+E*ELC) Al,CP=C*(1+E*ECO) Al,Multi,CP**-1=(1-E*ECO)/C Al,SP=S*(1-E*ECO*C**2/S**2) Al,WNP=(1+E*E0)*WN+E*E0A*AN Al,ANP=(1+E*EA)*AN+E*EA0*WN Al,L0P=(1+E*EL0)*L0+E*EL0A*LA Al,LAP=(1+E*ELA)*LA+E*ELA0*L0 Al,LN0P=(1+E*EL0)*LN0+E*EL0A*LNA Al,LNAP=(1+E*ELA)*LNA+E*ELA0*LN0 Al,LNPP=(1+E*ELC)*LNP Al,LNMP=(1+E*ELC)*LNM Id,ZP=(1+E*EZ)*Z+E*M*ET/GG Al,GP=(1+E*EZ)*G Al,HP=(1+E*EZ)*H Al,FP=(1+E*EZ)*F Al,UNP=(1+E*EC)*UN Al,VNP=(1+E*EC)*VN Id,XX*E=1 Id,L0=R Al,LN0=RN Al,LA=T Al,LNA=TN Al,LP=Y Al,LNP=YN Al,LM=P Al,LNM=PN Id,EM=E1-0.5*ET Al,ESM=E1-E2-0.5*ET Id,Multi,S**2=1-C**2 Keep GHOST *next B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN ,X,XN,Y,YN,Z Z GHO=GHOST Id,EC=19/12 Al,E0=1/6+1.5*C**2-1/12/C**2 Al,E0A=-2*C*S Al,EA=1.5*S**2 Al,EA0=5*S*C+S/C/6 Al,EZ=0.5+0.25/C**2+EZF Al,ELC=31/12 Al,EL0=1/6+5*C**2/2-1/12/C**2 Al,ELA=2.5*S**2 Al,EL0A=-C*S Al,ELA0=6*S*C+S/C/6 Al,EG=-43/12 Al,ECO=-S**2*(43-42*S**2)/12/C**2 C AL,ET=1.5*M**2/C**4/SM**2+0.25/C**2+0.5+3*M**2/SM**2 C +0.75*SM**2/M**2 C AL,EM=3/C**2/8-17/6-1.5*M**2/SM**2-0.75*M**2/C**4/SM**2 C -3*SM**2/M**2/8 C AL,ESM=-0.75-3/C**2/8+3*SM**2/M**2/8 Id,Multi,S**2=1-C**2 C PRINT OUTPUT C *YEP C PRINT INPUT C C THE FOLLOWING DIAGOLINIZES THE QUADRATIC PART. C ID,R=(1-S**2*EP)*R+C*S*T*EP C AL,RN=(1-S**2*EP)*RN+C*S*TN*EP C AL,T=-C*S*R*EP+(1-S**2*EP)*T C AL,TN=-C*S*EP*RN+(1-S**2*EP)*TN C AL,SN=SN+EP*SN-2*C*S*EP*QN C AL,Q=Q+2*S**2*EP*Q C AL,QN=QN+2*S**2*EP*QN C ID,XX*EP=1 C ID,EP=0 C ID,MULTI,S**2=1-C**2 C PRINT OUTPUT C *YEP C C THE FOLLOWING REMOVES THE DIVERGENCIES OF THE QUADRATIC PART C C BUT NOT OF THE MASS TERMS. C ID,Q=Q*(1-EP) C AL,QN=QN*(1-EP) C AL,O=O*(1-EP) C AL,ON=ON*(1-EP) C AL,SN=SN*(1-EP) C AL,X=X*(1-EP) C AL,XN=XN*(1-EP) C ID,XX*EP=1 C ID,EP=0 C ID,MULTI,S**2=1-C**2 Keep GHOST *next B GG,AN,F,G,H,O,ON,P,PN,Q,QN,R,RN,SN,T,TN,UN,VN,WN ,X,XN,Y,YN,Z Z GHO=GHOST Id,XX=0 *yep C REQUIRING NO INFINITIES IN QUADRATIC PART. Id,ELC=EC Al,ELA=EA Al,ELA0=EA0 Al,EL0A=E0A Al,EL0=E0 P output *yep C REQUIRING NO INFINITIES IN VERTICES. Id,EG=-EC Al,E0A=0 Al,ECO=E0-EC Al,E1=-EC+EZ Al,EA0=2*C*EC/S-2*C*E0/S Al,EA=-C**2*EC/S**2+C**2*E0/S**2+EC *end C RO-parameter 14. Rationalization. C RATIONALIZATION. P ninput S EI=2,N,M,M0,SM V P,Q,K B A1,A2,A3,A4,B1,B2,B3,B4,B5 Z XX= (A1*PDP + A2*PDP**2 + A3*PDP**3) *(B1*FP(1,M) + B2*FP(2,M) + B3*FP(3,M) + B4*FP(4,M) ) *(1+T) Id,T*PDP**K1~*FP(L1~,M~)=T*(-1)**K1*M**K1*M**K1* DS(IX,0,K1+(L1-1-K1)*DT(K1-L1+1),(M**-IX*M**-IX*FP(L1-IX,M)), (-(K1-IX+1)/IX) ) +T*EI*(-1)**K1*(-1)**L1*M**K1*M**K1/M**L1/M**L1* DT(K1-L1)*DB(K1-1,K1-L1)* DS(IX2,0,K1-L1, (PDP**IX2/M**IX2/M**IX2),(-(K1-L1-IX2+1)/(K1-IX2)) ) Id,T*PDP**2=T*QDQ**2+T*KDK**2+T*2*QDQ*KDK+T*4/N*QDQ*KDK Al,T*PDP=T*QDQ+T*KDK Id,PDP**3*FP(1,M~)=EI*QDQ**2+EI*KDK**2+2*EI*QDQ*KDK+4/N*EI*QDQ*KDK -M**2*EI*QDQ-M**2*EI*KDK+EI*M**4-M**6*FP(1,M) Al,PDP**3*FP(2,M~)=EI*KDK+EI*QDQ-2*EI*M**2 +3*M**4*FP(1,M)-M**6*FP(2,M) Id,2,PDP**2*FP(1,M~)=EI*QDQ+EI*KDK-EI*M**2+M**4*FP(1,M) Id,3,PDP**N~*FP(4,M~)=PDP**N/PDP*FP(3,M) -PDP**N/PDP*M**2*FP(4,M) Id,3,PDP**N~*FP(3,M~)=PDP**N/PDP*FP(2,M) -PDP**N/PDP*M**2*FP(3,M) Id,PDP**2*FP(2,M~)=EI-2*M**2*FP(1,M)+M**4*FP(2,M) Al,PDP*FP(2,M~)=FP(1,M)-M**2*FP(2,M) Al,PDP*FP(1,M~)=EI-M**2*FP(1,M) Id,FP(N~,M~)=AFP**N P output *yep Id,T=-1 C Id,NUMER,T,-1. *begin C C RATIONALIZATION. C XA=X+A, XB=X+B, BA=B-A. C EXPONENT OF XB POSITIVE, EXPONENT OF XA NEGATIVE. C Z XX=A1*XB**3*XA**-5 + A2*XB**3*XA**-4 + A3*XB**3*XA**-1 + A4*XB**4*XA**-2 + A5*XB**7*XA**-10 + A6*XB**10*XA**-5 - A1*XBP**3*XAP**-5 - A2*XBP**3*XAP**-4 - A3*XBP**3*XAP**-1 - A4*XBP**4*XAP**-2 - A5*XBP**7*XAP**-10 - A6*XBP**10*XAP**-5 B A1,A2,A3,A4,A5,A6 Id,XB**M~*XA**N~=BA**M*XA**N*DS(M0,0,-1-N,(BA**-M0*XA**M0), ((M-M0+1)/M0) ) + BA**M*BA**N*EI*DT(M+N)*DB(M-1,M+N)*DS(M1,0,M+N, (XB**M1*BA**-M1),((M+N-M1+1)/(M-M1)) ) Id,XBP=XAP+BAP *yep Id,XAP=XBP-BAP C ID,RATIO,XAP,XBP,BAP P output *yep Id,XBP=XB Al,BAP=BA Al,Multi,XAP**-1=XA**-1 Id,EI=1 C Id,NUMER,EI,1. *end C RO-parameter 15. Epsilon expansion and projection operators. S N,TRN,NP1,EP=3 Z TR1M1=2*N-N**2-N**3 Z X1=N**2*(N+1)*TRN Z X2=N*(N+1)*TRN Z X3=(N+1)*TRN Z X4=N**3*TRN Z X5=N**2*TRN Z X6=N*TRN Z X7=TRN Z X8=1/N Z X9=1/N**2 Z X0=N/OMN Id,TRN=-1/72*(1.-R+R**2) Id,N=4+EP Al,R=54/72*EP+13/72*EP**2 Al,Multi,N**-1=(1-EP/4+EP**2/16)/4 Al,OMN**-1=-1/3*(1-EP/3+EP**2/9) *next C PROJECTION OPERATORS AND EP-EXPANSION. S N,TRN,NP1,EP=3 I MU=N,NU=N,AL=N,BE=N,MUP=N,NUP=N Z XX=(EE*D(MU,NU)*D(AL,BE)+FF*D(MU,AL)*D(NU,BE) +GG*D(MU,BE)*D(NU,AL) ) *FACT Z YY=A1*AN/N + A2*AN**2/N**2 +A3*AOMN*N/OMN C PROJECTION OPERATOR FOR EE AND FF+GG PARTS. Id,FACT=TRN*(2*D(MU,NU)*D(AL,BE)-N*D(MU,AL)*D(NU,BE) -N*D(MU,BE)*D(NU,AL))*FGPRT +TRN*(-NP1*D(MU,NU)*D(AL,BE)+D(MU,AL)*D(NU,BE) +D(MU,BE)*D(NU,AL) )*EPART Id,N**2*NP1*TRN = - 10./9. + 1./18.*EP - 7./324.*EP**2 Al,N*NP1*TRN = - 5./18. + 1./12.*EP - 17./648.*EP**2 Al,NP1*TRN = - 5./72. + 11./288.*EP - 167./10368.*EP**2 Al,N**3*TRN = - 8./9. - 1./162.*EP**2 Al,N**2*TRN = - 2./9. + 1./18.*EP - 5./324.*EP**2 Al,N*TRN = - 1./18. + 1./36.*EP - 7./648.*EP**2 Al,TRN = - 1./72. + 1./96.*EP - 55./10368.*EP**2 Al,N*OMN** - 1 = - 4/3 + EP/9 - EP**2/27 Al,N = 4 + EP Al,N**-2 = 1/16 - EP/32 + 3*EP**2/256 Al,N**-1 = 1/4 - EP/16 + EP**2/64 Id,AN=4+EP Al,AOMN=(-3-EP)*(1/4-EP/16+EP**2/64) *end C RO-parameter 16. Differentiating F111. P stat F LG S SM,M,M0 X F1(M)=2*I*PI**2*M**2*(1/EP-0.5+0.5*LG(M) +EP*(1/4-LG(M)/4+LG(M)*LG(M)/8+PI**2/48)) X F2(M)=2*I*PI**2*(-1/EP-0.5*LG(M) -EP*(PI**2/48+LG(M)*LG(M)/8)) X F3(M)=I*PI**2/2/M**2+I*EP*PI**2/2/M**2/2*LG(M) X F4(M)=I*PI**2/6/M**4 -1/12*I*EP*PI**2/M**4*(1-LG(M)) X F5(M)=I*PI**2/M**6*(1/12-EP/16+EP*LG(M)/24) X FX211(M,M0,SM)= +PI**4*(-1./2.-3.*SM**(-4)*M**2*M0**2-1./4.*SM**(-4)*M**4-9./4.* SM**(-4)*M0**4-SM**(-2)*M**2-SM**(-2)*M0**2-2.*EP**(-2)+EP**(-1) ) +PI**6*(1./12.+2./3.*SM**(-4)*M**2*M0**2+1./3.*SM**(-4)*M0**4+1. /3.*SM**(-2)*M0**2) +LG(SM)*PI**4*(-4.*SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M**4-5./2. *SM**(-4)*M0**4-SM**(-2)*M**2-SM**(-2)*M0**2) +LG(SM)*LG(SM)*PI**4*(1./2.+2.*SM**(-4)*M**2*M0**2+SM**(-4)*M0** 4+SM**(-2)*M0**2) -1./2.*LG(SM)*LG(M)*PI**4 +LG(SM)*LG(M0)*PI**4*(-2.*SM**(-4)*M**2*M0**2-SM**(-4)*M0**4-SM* *(-2)*M0**2) +LG(M)*PI**4*(1.+3.*SM**(-4)*M**2*M0**2+1./2.*SM**(-4)*M**4+SM** (-2)*M**2-2.*EP**(-1)) +LG(M)*LG(SM)*PI**4*(-1./2.-2.*SM**(-4)*M**2*M0**2-SM**(-4)*M0** 4-SM**(-2)*M0**2) -1./2.*LG(M)*LG(M)*PI**4 +LG(M)*LG(M0)*PI**4*(2.*SM**(-4)*M**2*M0**2+SM**(-4)*M0**4+SM**( -2)*M0**2) +LG(M0)*PI**4*(SM**(-4)*M**2*M0**2+5./2.*SM**(-4)*M0**4+SM**(-2) *M0**2) X FX112(M,M0,SM)= +PI**4*(-1./2.+3.*SM**(-6)*M**2*M0**4+3.*SM**(-6)*M**4*M0**2+1./ 9.*SM**(-6)*M**6+1./9.*SM**(-6)*M0**6+SM**(-4)*M**2*M0**2+1./4.* SM**(-4)*M**4+1./4.*SM**(-4)*M0**4+SM**(-2)*M**2+SM**(-2)*M0**2- 2.*EP**(-2)+EP**(-1)) +PI**6*(-1./4.-2./3.*SM**(-6)*M**2*M0**4-2./3.*SM**(-6)*M**4*M0* *2-1./3.*SM**(-4)*M**2*M0**2) +LG(SM)*PI**4*(1.+5.*SM**(-6)*M**2*M0**4+5.*SM**(-6)*M**4*M0**2+ 1./3.*SM**(-6)*M**6+1./3.*SM**(-6)*M0**6+2.*SM**(-4)*M**2*M0**2+ 1./2.*SM**(-4)*M**4+1./2.*SM**(-4)*M0**4+SM**(-2)*M**2+SM**(-2)* M0**2-2.*EP**(-1)) +LG(SM)*LG(SM)*PI**4*(-1.-2.*SM**(-6)*M**2*M0**4-2.*SM**(-6)*M** 4*M0**2-SM**(-4)*M**2*M0**2) +LG(SM)*LG(M0)*PI**4*(2.*SM**(-6)*M**2*M0**4+2.*SM**(-6)*M**4*M0 **2+SM**(-4)*M**2*M0**2) +LG(M)*PI**4*(-SM**(-6)*M**2*M0**4-4.*SM**(-6)*M**4*M0**2-1./3.* SM**(-6)*M**6-SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M**4-SM**(-2)*M **2) +LG(M)*LG(SM)*PI**4*(2.*SM**(-6)*M**2*M0**4+2.*SM**(-6)*M**4*M0* *2+SM**(-4)*M**2*M0**2) +LG(M)*LG(M0)*PI**4*(-2.*SM**(-6)*M**2*M0**4-2.*SM**(-6)*M**4*M0 **2-SM**(-4)*M**2*M0**2) +LG(M0)*PI**4*(-4.*SM**(-6)*M**2*M0**4-SM**(-6)*M**4*M0**2-1./3. *SM**(-6)*M0**6-SM**(-4)*M**2*M0**2-1./2.*SM**(-4)*M0**4-SM**(-2 )*M0**2) X FX111(M,M0,SM)= +PI**4*(7./2.*SM**2+2.*SM**2*EP**(-2)-3.*SM**2*EP**(-1)+9./4.*SM **(-4)*M**2*M0**4+9./4.*SM**(-4)*M**4*M0**2+5./36.*SM**(-4)*M**6 +5./36.*SM**(-4)*M0**6+SM**(-2)*M**2*M0**2+3./4.*SM**(-2)*M**4+3 ./4.*SM**(-2)*M0**4+5./2.*M**2+2.*M**2*EP**(-2)-3.*M**2*EP**(-1) +5./2.*M0**2+2.*M0**2*EP**(-2)-3.*M0**2*EP**(-1)) +PI**6*(1./4.*SM**2-1./3.*SM**(-4)*M**2*M0**4-1./3.*SM**(-4)*M** 4*M0**2-1./3.*SM**(-2)*M**2*M0**2-1./12.*M**2-1./12.*M0**2) +LG(SM)*PI**4*(-3.*SM**2+2.*SM**2*EP**(-1)+3./2.*SM**(-4)*M**2*M 0**4+3./2.*SM**(-4)*M**4*M0**2+1./6.*SM**(-4)*M**6+1./6.*SM**(-4 )*M0**6+1./2.*SM**(-2)*M**4+1./2.*SM**(-2)*M0**4-M**2-M0**2) +LG(SM)*LG(SM)*PI**4*(SM**2-SM**(-4)*M**2*M0**4-SM**(-4)*M**4*M0 **2-SM**(-2)*M**2*M0**2-1./2.*M**2-1./2.*M0**2) +LG(SM)*LG(M)*PI**4*(2.*SM**(-4)*M**2*M0**4+SM**(-4)*M**4*M0**2+ SM**(-2)*M**2*M0**2+1./2.*M**2) +LG(SM)*LG(M0)*PI**4*(-SM**(-4)*M**2*M0**4+1./2.*M0**2) +LG(M)*PI**4*(-3./2.*SM**(-4)*M**4*M0**2-1./6.*SM**(-4)*M**6-1./ 2.*SM**(-2)*M**4-2.*M**2+2.*M**2*EP**(-1)) +LG(M)*LG(SM)*PI**4*(-SM**(-4)*M**2*M0**4+1./2.*M**2) +LG(M)*LG(M)*PI**4*(1./2.*M**2) +LG(M)*LG(M0)*PI**4*(SM**(-4)*M**2*M0**4) +LG(M0)*PI**4*(-3./2.*SM**(-4)*M**2*M0**4-1./6.*SM**(-4)*M0**6-1 ./2.*SM**(-2)*M0**4-2.*M0**2+2.*M0**2*EP**(-1)) +LG(M0)*LG(SM)*PI**4*(2.*SM**(-4)*M**2*M0**4+SM**(-4)*M**4*M0**2 +SM**(-2)*M**2*M0**2+1./2.*M0**2) +LG(M0)*LG(M)*PI**4*(-2.*SM**(-4)*M**2*M0**4-SM**(-4)*M**4*M0**2 -SM**(-2)*M**2*M0**2) +LG(M0)*LG(M0)*PI**4*(1./2.*M0**2) *fix BLOCK DIFF{} B PI Id,I=i Id,DM*M**N~=N*M**N/M**2/2+M**N*DM Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0 Al,DSM*SM**N~=N*SM**N/SM**2/2+SM**N*DSM Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0 Al,Adiso,DSM*LG(SM)*LG(SM)=2*LG(SM)/SM**2+LG(SM)*LG(SM)*DSM Al,DM*LG(M)=1/M**2+LG(M)*DM Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0 Al,DSM*LG(SM)=1/SM**2+LG(SM)*DSM Id,DM*XX=0 Al,DM0*XX=0 Al,DSM*XX=0 Al,XX=1 Id,Commu,LG Id,EP=0 ENDBLOCK Z CH1=FX211(M,M0,SM)+DM*FX111(M,M0,SM)*XX Z CH2=FX112(M,M0,SM)+DSM*FX111(M,M0,SM)*XX Z CH3=FX211(M0,M,SM)+DM0*FX111(M,M0,SM)*XX Z CH4=-(1+EP)*FX211(M,M0,SM)+2*M02*DM0*FX211(M,M0,SM)*XX -FX112(M,M0,SM)+F2(M)*F2(SM)-MM0SM*DSM*FX211(M,M0,SM)*XX DIFF{} Id,M02=M0**2 Al,MM0SM=M**2-M0**2-SM**2 *end C RO-parameter 17. Differentiating F211. P stats F LG S M,M0,SM *fix B PI Z F311(M,M0,SM)=-1/2*DM*FX211(M,M,M0,SM)*XX Z F221(M,M0,SM)=-DM0*FX211(M,M,M0,SM)*XX Z F211(M,M0,SM)=FX211(M,M,M0,SM) Id,FX211(M~,M~,M0~,SM)=PI**4*(-2/EP**2+(1-2*LG(M))/EP -0.5+PI**2/12+LG(M)-LG(M)*LG(M)+0.5*LG(SM,M)*LG(SM,M) +(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4*LG(SM,M)*LG(SM,M) -(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4*LG(SM,M)*LG(M0,M) -(M**2*SM**2+M0**2*SM**2+4*M**2*M0**2+5/2*M0**4+0.5*M**4) /SM**4*LG(SM,M) + (M0**2*SM**2+M**2*M0**2+5/2*M0**4)/SM**4 *LG(M0,M) - (M**2+M0**2)/SM**2 - (1/4*M**4+3*M**2*M0**2+9/4*M0**4)/SM**4 +PI**2/3*(M0**2*SM**2+2*M**2*M0**2+M0**4)/SM**4 ) Id,LG(SM~,M)=LG(SM)-LG(M) Id,DM*M**N~=N*M**N/M**2/2+M**N*DM Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0 Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0 Al,DM*LG(M)=1/M**2+LG(M)*DM Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0 Id,DM*XX=0 Al,DM0*XX=0 Al,XX=1 Id,Commu,LG Keep F311,F221,F211 Punch F311,F221,F211 *next B PI Z F411(M,M0,SM)=-1/3*DM*F311(M,M0,SM)*XX Z F321(M,M0,SM)=-1/2*DM*F221(M,M0,SM)*XX Id,DM*M**N~=N*M**N/M**2/2+M**N*DM Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0 Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0 Al,DM*LG(M)=1/M**2+LG(M)*DM Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0 Id,DM*XX=0 Al,DM0*XX=0 Al,XX=1 Id,Commu,LG Keep F311,F221,F411,F321,F211 Punch F411,F321 *next B PI Z F511(M,M0,SM)=-1/4*DM*F411(M,M0,SM)*XX Z F421(M,M0,SM)=-1/3*DM*F321(M,M0,SM)*XX Id,DM*M**N~=N*M**N/M**2/2+M**N*DM Al,DM0*M0**N~=N*M0**N/M0**2/2+M0**N*DM0 Id,Adiso,DM*LG(M)*LG(M)=2*LG(M)/M**2+LG(M)*LG(M)*DM Al,Adiso,DM0*LG(M0)*LG(M0)=2*LG(M0)/M0**2+LG(M0)*LG(M0)*DM0 Al,DM*LG(M)=1/M**2+LG(M)*DM Al,DM0*LG(M0)=1/M0**2+LG(M0)*DM0 Id,DM*XX=0 Al,DM0*XX=0 Al,XX=1 Id,Commu,LG Keep F311,F221,F411,F321,F421,F211,F511 Punch F421,F511 *next B PI Z FF211=F211(M,M,SM) Z FF311=F311(M,M,SM) Z FF411=F411(M,M,SM) Z FF511=F511(M,M,SM) Z FF221=F221(M,M,SM) Z FF321=F321(M,M,SM) Z FF421=F421(M,M,SM) Id,Commu,LG *end C RO-parameter 18. Expansion of F211(SM,M1,M2) for large SM. C A=M1**2/SM**2, B=M2**2/SM**2. LGA=LOG(A), LGB=LG(B). C S2=PI**2/6. E=EXPANSION PARAMETER, COUNTS ORDER IN A,B. E**7=0. C THE FORMULA USED IS: C F(A,B)=-1/2*LOG(A)**2-SP((A-B)/A) C + FAC1*( SP((B-A)/X1)-SP((A-B)/(1-X1))-SP(1-1/X1)+SP(-X1/(1-X1)) ) C + FAC2*( SAME, BUT X1 REPLACED BY X2 ) C FAC1=(B-X1)/ROOT, FAC2=(X2-B)/ROOT C X1=(1+B-A+ROOT)/2, X2=(1+B-A-ROOT)/2. C ROOT=SQRT((A-B)**2+1-2*(A+B)) C X1,2 SOLUTION OF X**2+(A-B-1)*X+B=0 C THUS X1*X2=B, (1-X1)*(1-X2)=A, X1+X2=1+B-A. C NOTE THAT FAC1+FAC2=-1. C FOR THIS EXPANSION THE EQUATION WAS REWRITTEN AS C F(A,B)=-1/2*LOG(A)**2-SP((A-B)/A)+SP((A-B)*(1-X2)/A) C +S2*(1-A-B)/ROOT C + FAC1*(SP((B-A)*X2/B)-2*SP(-(1-X1)*X2/B) C -1/2*LOG((1-X1)*X2/B)**2 ) C + FAC2*(-1/2*LOG(1-(B-A)*X1/B)**2-SP((A-B)*(1-X1)/A) C +2*SP(-X2*(1-X1)/A)+1/2*LOG(X2*(1-X1)/A)**2 ) C THE TERMS LOG(A)**2 AND LOG(B)**2 CANCEL OUT. C THE EXPRESSIONS BELOW REFER TO THE EXPANSION OF THE C INDIVIDUAL TERMS, FOR INSTANCE EXP(2) REFERS TO THE C EXPRESSION CONTAINING S2. C C THE FUNCTION F211 IS GIVEN BY C F211=PI**4*(-2/EP**2+1/EP*(1-2*GA-2*LOG(SM**2) C -1/2-PI**2/12+GA-GA**2+(1-2*GA)*LOG(SM**2) C -LOG(SM**2)**2-F(A,B) ) C EP=N-4, GA=EULERS CONSTANT. GA MAY BE ABSORBED IN C A REDIFINITION OF THE UNITS IN THE LOG, WHICH WAS C ALREADY DONE WITH FACTORS LOG(PI). (READ LOG(PI*SM**2) C EVERYWHERE). C THE WORK WAS DIVIDED IN TWO PARTS. PART 1 = COMPUTING THE C VARIOUS ARGUMENTS OF THE FUNCTIONS TO BE EXPANDED. THIS C INCLUDED WORKING OUT THE ROOT, ALSO GIVEN HERE. GIVEN X1 AND C X2 THE OTHER ARGUMENTS ARE COMPUTED ACCORDING TO THE CARDS C BELOW MADE INACTIVE. PART 2 IS COMPUTING THE EXPRESSIONS. C PRINT NINPUT C C C IN THIS PART X1, X2 ETC ARE COMPUTED TO ORDER E**7. THIS C C IS NECESSARY TO OBTAIN THE ARGUMENTS OF THE VARIOUS FUNCTIONS C C TO ORDER E**6. C C SCREEN C N R C COMMON XX(0),XX1(0),XX2(0) C S E=8,A,B C X X(A)=E**2*(A**2+B**2-2*A*B)-2*E*(A+B) C *FIX C Z XX(0)=1. C *NEXT C DO K1=1,7 C Z XX('K1')=X(A)*XX('K1'-1) C B E C NPRINT XX('K1') C *NEXT C ENDDO C Z WO=1+XX(1)/2-XX(2)/8+XX(3)/16-5*XX(4)/128 C +7*XX(5)/256-21*XX(6)/1024 C +33/2048*XX(7) C Z WOI=1.-XX(1)/2+3*XX(2)/8-5*XX(3)/16+35*XX(4)/128 C -63*XX(5)/256+231*XX(6)/1024 C -429/2048*XX(7) C B E C KEEP WO,WOI C *NEXT C Z X1=0.5+0.5*B*E-0.5*A*E+0.5*WO C Z X2=0.5+0.5*B*E-0.5*A*E-0.5*WO C B E C PUNCH X1,X2 C KEEP WO,WOI,X1,X2 C *NEXT C B E C Z OMX1A=1/A/E-X1/A/E C Z X2B=X2/B/E C Z BMX2A=B/A-X2/A/E C PUNCH OMX1A,X2B,BMX2A C B E C KEEP X1,X2,WOI C *NEXT C S E=7 C Z FAC1=(B*E-X1)*WOI C Z FAC2=(X2-B*E)*WOI C B E C PUNCH FAC1,FAC2 C *END Common EXP(0),Exp(0) S LOMX,LGA,LGB C X X1=1-E*A-A*B*E**2-E**3*A*B**2-E**3*A**2*B C +E**4*(-A*B**3-3.*A**2*B**2-A**3*B) C +E**5*(-A*B**4-6.*A**2*B**3-6.*A**3*B**2-A**4*B) C +E**6*(-A*B**5-10.*A**2*B**4-20.*A**3*B**3-10.*A**4*B**2-A**5*B) C +E**7*(-A*B**6-15.*A**2*B**5-50.*A**3*B**4-50.*A**4*B**3-15.*A** C 5*B**2-A**6*B) C X X2=E*B+E**2*A*B+E**3*A*B**2+E**3*A**2*B C +E**4*(A*B**3+3.*A**2*B**2+A**3*B) C +E**5*(A*B**4+6.*A**2*B**3+6.*A**3*B**2+A**4*B) C +E**6*(A*B**5+10.*A**2*B**4+20.*A**3*B**3+10.*A**4*B**2+A**5*B) C +E**7*(A*B**6+15.*A**2*B**5+50.*A**3*B**4+50.*A**4*B**3+15.*A**5 C *B**2+A**6*B) C X OMX1A=1 + E*B C +E**2*(A*B+B**2) C +E**3*(3.*A*B**2+A**2*B+B**3) C +E**4*(6.*A*B**3+6.*A**2*B**2+A**3*B+B**4) C +E**5*(10.*A*B**4+20.*A**2*B**3+10.*A**3*B**2+A**4*B+B**5) C +E**6*(15.*A*B**5+50.*A**2*B**4+50.*A**3*B**3+15.*A**4*B**2+A**5 C *B+B**6) C X X2B=1+E*A C +E**2*(A*B+A**2) C +E**3*(A*B**2+3.*A**2*B+A**3) C +E**4*(A*B**3+6.*A**2*B**2+6.*A**3*B+A**4) C +E**5*(A*B**4+10.*A**2*B**3+20.*A**3*B**2+10.*A**4*B+A**5) C +E**6*(A*B**5+15.*A**2*B**4+50.*A**3*B**3+50.*A**4*B**2+15.*A**5 C *B+A**6) C X BMX2A=-B*E C +E**2*(-A*B-B**2) C +E**3*(-3.*A*B**2-A**2*B-B**3) C +E**4*(-6.*A*B**3-6.*A**2*B**2-A**3*B-B**4) C +E**5*(-10.*A*B**4-20.*A**2*B**3-10.*A**3*B**2-A**4*B-B**5) C +E**6*(-15.*A*B**5-50.*A**2*B**4-50.*A**3*B**3-15.*A**4*B**2-A** C 5*B-B**6) X FAC1=-1-A*B*E**2 +E**3*(-2.*A*B**2-2.*A**2*B) +E**4*(-3.*A*B**3-9.*A**2*B**2-3.*A**3*B) +E**5*(-4.*A*B**4-24.*A**2*B**3-24.*A**3*B**2-4.*A**4*B) +E**6*(-5.*A*B**5-50.*A**2*B**4-100.*A**3*B**3-50.*A**4*B**2-5.*A **5*B) X FAC2=E**2*A*B +E**3*(2.*A*B**2+2.*A**2*B) +E**4*(3.*A*B**3+9.*A**2*B**2+3.*A**3*B) +E**5*(4.*A*B**4+24.*A**2*B**3+24.*A**3*B**2+4.*A**4*B) +E**6*(5.*A*B**5+50.*A**2*B**4+100.*A**3*B**3+50.*A**4*B**2+5.*A **5*B) X ARG1=E*B+A*B*E**2 +E**3*(A*B**2+A**2*B) +E**4*(A*B**3+3.*A**2*B**2+A**3*B) +E**5*(A*B**4+6.*A**2*B**3+6.*A**3*B**2+A**4*B) +E**6*(A*B**5+10.*A**2*B**4+20.*A**3*B**3+10.*A**4*B**2+A**5*B) X ARG3=-A*E+E*B +E**2*(A*B-A**2) +E**3*(A*B**2-A**3) +E**4*(A*B**3+2.*A**2*B**2-2.*A**3*B-A**4) +E**5*(A*B**4+5.*A**2*B**3-5.*A**4*B-A**5) +E**6*(A*B**5+9.*A**2*B**4+10.*A**3*B**3-10.*A**4*B**2-9.*A**5*B -A**6) X ARG4=-A*E +E**2*(-A*B-A**2) +E**3*(-A*B**2-3.*A**2*B-A**3) +E**4*(-A*B**3-6.*A**2*B**2-6.*A**3*B-A**4) +E**5*(-A*B**4-10.*A**2*B**3-20.*A**3*B**2-10.*A**4*B-A**5) +E**6*(-A*B**5-15.*A**2*B**4-50.*A**3*B**3-50.*A**4*B**2-15.*A** 5*B-A**6) X ARG5=E*A+E*B +E**2*(3.*A*B+A**2+B**2) +E**3*(6.*A*B**2+6.*A**2*B+A**3+B**3) +E**4*(10.*A*B**3+20.*A**2*B**2+10.*A**3*B+A**4+B**4) +E**5*(15.*A*B**4+50.*A**2*B**3+50.*A**3*B**2+15.*A**4*B+A**5+B* *5) +E**6*(21.*A*B**5+105.*A**2*B**4+175.*A**3*B**3+105.*A**4*B**2+2 1.*A**5*B+A**6+B**6) X ARG6=-E*A+B*E +E**2*(-A*B+B**2) +E**3*(-A**2*B+B**3) +E**4*(2.*A*B**3-2.*A**2*B**2-A**3*B+B**4) +E**5*(5.*A*B**4-5.*A**3*B**2-A**4*B+B**5) +E**6*(9.*A*B**5+10.*A**2*B**4-10.*A**3*B**3-9.*A**4*B**2-A**5*B +B**6) X ARG8=-B*E +E**2*(-A*B-B**2) +E**3*(-3.*A*B**2-A**2*B-B**3) +E**4*(-6.*A*B**3-6.*A**2*B**2-A**3*B-B**4) +E**5*(-10.*A*B**4-20.*A**2*B**3-10.*A**3*B**2-A**4*B-B**5) +E**6*(-15.*A*B**5-50.*A**2*B**4-50.*A**3*B**3-15.*A**4*B**2-A** 5*B-B**6) S E=7 *fix C B E C Z ARG1=X2 C Z ARG3=(B-A)*X2/B C Z ARG4=1-X2B C Z ARG5=OMX1A*X2B - 1 C Z ARG6=(B-A)*(1-X1)/A C Z ARG7=(A-B)*E*OMX1A C Z ARG8=BMX2A C Punch ARG1,ARG3,ARG4,ARG5,ARG6,ARG8 C *end Z SP(1)=-LOMX/X Z XX2(1)=-ARG1 B E Nprint SP,XX2 Keep SP,XX2 *next DO K1=2,6 P input Z SP('K1')=DIFX*SP('K1'-1)*YY/'K1' Z XX2('K1')=-XX2('K1'-1)*ARG1 Id,DIFX*LOMX=-1/OMX+LOMX*DIFX Id,DIFX*OMX**N~=-N*OMX**N/OMX+OMX**N*DIFX Id,DIFX*X**N~=N*X**N/X+X**N*DIFX Id,DIFX*YY=0 Al,YY=1 Id,X**N~*OMX**-1=DS(J1,1,-N,(X**-J1))+1/OMX B E Nprint SP,XX2 Keep SP,XX2 *next ENDDO DO K2=1,6 P input Z SP('K2')=SP('K2')*X**'K2' ENDDO Id,X**N~*OMX**M~=XOMX**-M*X**N*X**M Id,X=(A-B)/A Al,XOMX=(A-B)/B Id,LOMX=LGB-LGA B LGA,LGB Keep SP,XX2 Nprint SP *next B E,LGA,LGB Z EXP(1)=DS(J3,1,6,(SP(J3)*XX2(J3)) ) *next B E,S2 Z EXP(2)=S2*(FAC2-FAC1) *next B E Z TOT(3)=0 Z TOT(4)=0 Z TOT(7)=0 Z TOT(8)=0 Z SP(3)=ARG3 Z SP(4)=ARG4 Z SP(7)=-ARG6 Z SP(8)=ARG8 Keep TOT,SP Nprint TOT,SP *next DO K3=2,6 B E Z TOT(3)=TOT(3)+SP(3) Z TOT(4)=TOT(4)+SP(4) Z TOT(7)=TOT(7)+SP(7) Z TOT(8)=TOT(8)+SP(8) Z SP(3)=SP(3)*ARG3*('K3'-1)**2/'K3'**2 Z SP(4)=SP(4)*ARG4*('K3'-1)**2/'K3'**2 Z SP(7)=-SP(7)*ARG6*('K3'-1)**2/'K3'**2 Z SP(8)=SP(8)*ARG8*('K3'-1)**2/'K3'**2 Keep TOT,SP Nprint TOT,SP *next ENDDO B E Z EXP(3)=FAC1*(TOT(3)+SP(3)) Z EXP(4)=-2*FAC1*(TOT(4)+SP(4)) Z EXP(7)=-FAC2*(TOT(7)+SP(7)) Z EXP(8)=2*FAC2*(TOT(8)+SP(8)) *next Z Exp(3)=EXP(3) Z Exp(4)=EXP(4) Z Exp(7)=EXP(7) Delete EXP(3),EXP(4),EXP(7) *next B E,LGA,LGB Z XX(5)=ARG5 Z XX(6)=ARG6 Z TOT(5)=0 Z TOT(6)=0 Keep XX,TOT Nprint XX,TOT *next DO K5=2,6 Z TOT(5)=TOT(5)+XX(5) Z TOT(6)=TOT(6)+XX(6) Z XX(5)=-XX(5)*ARG5*('K5'-1)/'K5' Z XX(6)=-XX(6)*ARG6*('K5'-1)/'K5' B E Keep TOT,XX Nprint TOT,XX *next ENDDO B E Z TOT(5)=TOT(5)+XX(5) Z TOT(6)=TOT(6)+XX(6) Keep TOT Nprint TOT *next Z TOT(15)=TOT(5)*TOT(5) Z TOT(16)=TOT(6)*TOT(6) Keep TOT Nprint TOT B E *next Z EXP(5)=-0.5*FAC1*(2*LGA*TOT(5)+TOT(15)) Z EXP(6)=-0.5*FAC2*(-2*LGA*LGB+2*ABLG*TOT(6)+TOT(16) ) Z EXP(9)=+0.5*FAC2*(2*LGB*TOT(5)+TOT(15)) Id,ABLG=LGA-LGB B E,LGA,LGB *next Z EXP(3)=Exp(3) Z EXP(4)=Exp(4) Z EXP(7)=Exp(7) Delete Exp(3),Exp(4),Exp(7) *next B E,LGA,LGB,S2 Z TOTAL=DS(J0,1,9,(EXP(J0))) P outp *yep C Id,Numer,E,1. Id,E=1 B S2,LGA,LGB *end C RO-parameter 19. Higher orders of F211(M,M0,SM) expansion for large SM. C THE HIGHER ORDERS ARE MADE SUCH THAT THE RELATION C -(N-3)*F211-2*M0**2*F221-F112+F2(M)*F2(M)+(M**2-M0**2-SM**2)*F212=0 C IS SATISFIED. START WITH THE COEFFICIENT OF LGA*LGB, ETC. F LG S M,M0,SM,LGA,LGB C THIS IS F211/PI**4 X F211=-1./2.-A-3.*A*B-1./4.*A**2-B-9./4.*B**2 -47/18*B**3-9*B**2*A-11/2*B*A**2-1/9*A**3 -401/144*B**4-20*B**3*A-107/4*B**2*A**2-74/9*B*A**3-1/16*A**4 -5197/1800*B**5-2296/63*B**4*A-177/2*B**3*A**2-569/9*B**2*A**3 -797/72*B*A**4-1/25*A**5 +LGA*(1.+A+3.*A*B+1./2.*A**2 +5*B**2*A+7*B*A**2+1/3*A**3 +7*B**3*A+51/2*B**2*A**2+35/3*B*A**3+1/4*A**4 +9*B**4*A+62*B**3*A**2+224/3*B**2*A**3 +101/6*B*A**4+1/5*A**5 ) +LGA*LGB*(2.*A*B+B+B**2 +B**3+6*B**2*A+3*B*A**2 +B**4+12*B**3*A+18*B**2*A**2+4*B*A**3 +B**5+20*B**4*A+60*B**3*A**2+40*B**2*A**3 +5*B*A**4 ) -1./2.*LGA**2 +LGB*(A*B+B+5./2.*B**2 +10/3*B**3+8*B**2*A+B*A**2 +47/12*B**4+23*B**3*A+33/2*B**2*A**2+B*A**3 +131/30*B**5+142/3*B**4*A+82*B**3*A**2+28*B**2*A**3 +B*A**4 ) +PI**2*(1./12.+2./3.*A*B+1./3.*B+1./3.*B**2 +1/3*B**3+2*B**2*A+B*A**2 +1/3*B**4+4*B**3*A+6*B**2*A**2+4/3*B*A**3 +1/3*B**5+20/3*B**4*A+20*B**3*A**2+40/3*B**2*A**3 +5/3*B*A**4 ) -2.*EP**(-2) +EP**(-1) -2.*EP**(-1)*LGA +LG(SM) -2.*LG(SM)*LGA -2.*LG(SM)*EP**(-1) -LG(SM)*LG(SM) C THIS IS F2(M)*F2(SM)/PI**4 X F22=-1./2.*LGA**2 -1./6.*PI**2 -4.*EP**(-2) -2.*EP**(-1)*LGA -2.*LG(SM)*LGA -4.*LG(SM)*EP**(-1) -2.*LG(SM)*LG(SM) X FFF(A,B)=-A-A*B-3.*A*B**2-11./2.*A*B**3-74./9.*A*B**4-797./72.*A*B* *5-1./4.*A**2-3.*A**2*B-49./4.*A**2*B**2-35.*A**2*B**3-2851./36. *A**2*B**4-1./9.*A**3-11./2.*A**3*B-35.*A**3*B**2-2531./18.*A**3 *B**3-1./16.*A**4-74./9.*A**4*B-2851./36.*A**4*B**2-1./25.*A**5- 797./72.*A**5*B-1./36.*A**6-B-1./4.*B**2-1./9.*B**3-1./16.*B**4- 1./25.*B**5-1./36.*B**6 +LGA*(A+A*B+A*B**2+A*B**3+A*B**4+A*B**5+1./2.*A**2+4.*A**2*B+21. /2.*A**2*B**2+20.*A**2*B**3+65./2.*A**2*B**4+1./3.*A**3+8.*A**3* B+40.*A**3*B**2+370./3.*A**3*B**3+1./4.*A**4+38./3.*A**4*B+310./ 3.*A**4*B**2+1./5.*A**5+107./6.*A**5*B+1./6.*A**6) +LGA*LGB*(A*B+2.*A*B**2+3.*A*B**3+4.*A*B**4+5.*A*B**5+2.*A**2*B+ 9.*A**2*B**2+24.*A**2*B**3+50.*A**2*B**4+3.*A**3*B+24.*A**3*B**2 +100.*A**3*B**3+4.*A**4*B+50.*A**4*B**2+5.*A**5*B) +LGB*(A*B+4.*A*B**2+8.*A*B**3+38./3.*A*B**4+107./6.*A*B**5+A**2* B+21./2.*A**2*B**2+40.*A**2*B**3+310./3.*A**2*B**4+A**3*B+20.*A* *3*B**2+370./3.*A**3*B**3+A**4*B+65./2.*A**4*B**2+A**5*B+B+1./2. *B**2+1./3.*B**3+1./4.*B**4+1./5.*B**5+1./6.*B**6) +S2*(1.+2.*A*B+4.*A*B**2+6.*A*B**3+8.*A*B**4+10.*A*B**5+4.*A**2* B+18.*A**2*B**2+48.*A**2*B**3+100.*A**2*B**4+6.*A**3*B+48.*A**3* B**2+200.*A**3*B**3+8.*A**4*B+100.*A**4*B**2+10.*A**5*B)+0. *fix B EP,LGA,LGB,PI,SM Z F112=-2/EP**2+(1-2*LG(SM))/EP-1/2-PI**2/12+LG(SM)-LG(SM)*LG(SM) -FFF(A,B) Z F221=-DM0*F211*XX Z F212=DM*FFF(A,B)*XX Z FF211=F211 Id,DM=DFA/SM**2 Al,DM0=DFB/SM**2 Al,EP=0 Id,DFB*B**N~=N*B**N/B+B**N*DFB Al,DFA*A**N~=N*A**N/A+A**N*DFA Id,DFB*LGB**2=2*LGB/B+LGB**2*DFB Al,DFA*LGA**2=2*LGA/A+LGA**2*DFA Al,DFB*LGB=1/B+LGB*DFB Al,DFA*LGA=1/A+LGA*DFA Id,DFB*XX=0 Al,DFA*XX=0 Al,XX=1 Id,Multi,M**2=A*SM**2 Al,Multi,M0**2=B*SM**2 Id,LG(M)=LGA+LG(SM) Al,LG(M0)=LGB+LG(SM) Id,Commu,LG Id,S2=PI**2/6 Keep F112,F221,F212 *next B EP,LGA,LGB,PI,SM Z CH1=-(1+EP)*F211-2*M0**2*F221-F112+F22+(M**2-M0**2-SM**2)*F212 Id,Multi,M**2=A*SM**2 Al,Multi,M0**2=B*SM**2 Id,EP=0 Id,Commu,LG *end C RO-parameter 20. Expansion of F211(SM,SM,M) for large SM. C S X=13,B=7 C *FIX C Z XX(1)=X C KEEP XX C *NEXT C DO K2=2,12 C Z XX(K2)=XX(K2-1)*X C ID,X**2=B*X-B C KEEP XX C PUNCH XX(K2) C *NEXT C ENDDO C *END Common Exp,Expp S B=7,LGB,ROOT,FACT S X1=13,X2=13 X FB=1+B+B**2+B**3+B**4*B**5+B**6 D POW(N,X)=X, (-B+B*X), (-B*X-B**2+B**2*X), (+B**2-2.*B**2*X-B**3+B**3*X), (+B**2*X+2.*B**3-3.*B**3*X-B**4+B**4*X), (-B**3+3.*B**3*X+3.*B**4-4.*B**4*X-B**5+B**5*X), (-B**3*X-3.*B**4+6.*B**4*X+4.*B**5-5.*B**5*X-B**6+B**6*X), (+B**4-4.*B**4*X-6.*B**5+10.*B**5*X+5.*B**6-6.*B**6*X), (+B**4*X+4.*B**5-10.*B**5*X-10.*B**6+15.*B**6*X), (-B**5+5.*B**5*X+10.*B**6-20.*B**6*X), (-B**5*X-5.*B**6+15.*B**6*X), (+B**6-6.*B**6*X), B**6*X,0. *fix Z TOT=0. Z TOTP=0. Z SPE=-X1*FB Z SPEP=X2-X2**2 Keep TOT,SPE,TOTP,SPEP Nprint TOT,SPE,TOTP,SPEP *next DO K1=2,12 Z TOT=TOT+SPE Z TOTP=TOTP+SPEP Z SPE=-SPE*X1*FB*('K1'-1)**2/'K1'**2 Z SPEP=SPEP*(X2-X2**2)*('K1'-1)**2/'K1'**2 Nprint TOT,SPE,TOTP,SPEP Keep TOT,SPE,TOTP,SPEP *next ENDDO Z TOT=TOT+SPE Z TOTP=TOTP+SPEP Nprint TOT,TOTP Keep TOT,TOTP *next N 20,R20 B LGB,ROOT,FACT X SP(X)=X+X**2/4+X**3/9+X**4/16+X**5/25+X**6/36+X**7/49 +X**8/64+X**9/81+X**10/100+X**11/121+X**12/144 X LGP(X)=-X-X**2/2-X**3/3-X**4/4-X**5/5-X**6/6-X**7/7 -X**8/8-X**9/9-X**10/10-X**11/11-X**12/12 C TOT=SPENCE(-X1/(1-B)), TOTP=SPENCE(X2-X2**2). C POWERS OF X1 AND X2 HAVE BEEN COMPUTED USING X**2=B*X-B. Z EXP=FACT*(-TOT+TOTP+2*SP(X2)-S2 +(LGP(B)+LGP(X2))*(LGB+LGP(X2)) +0.5*LGP(X1)*LGP(X1)-0.5*LGP(B)*LGP(B) ) +SP(B)+LGB*LGP(B)-S2 *yep Id,X1**N~=POW(N,X1) Al,X2**N~=POW(N,X2) *yep Id,X1=0.5*B+0.5*ROOT Al,X2=0.5*B-0.5*ROOT Al,FACT=B/ROOT-1 Id,ROOT=0. Al,ROOT**-1=0 Keep EXP Punch EXP *next B EP,LGB,PI F LG C COMPUTE NOW F211(SM,SM,M), WITH B=M**2/SM**2. Z F211=PI**4*(-2/EP**2+(1-2*GA-2*LG(SM))/EP -1/2-PI**2/12+GA-GA**2+(1-2*GA)*LG(SM)-LG(SM)*LG(SM) -EXP ) Z Exp=EXP C GA=EULERS CONSTANT, CAN BE ABSORBED INTO LOG DEFINITION. Id,GA=0 Keep F211 *next Z Expp=F211 *begin Write Exp Write Expp *end