C Example of a gauge field theory. Lagrangian. BLOCK VERT{} S N,N_,M,m F VE4,VE3,PROP I al=N, be=N, ga=N, de=N, la=N, ka=N I l1=3,l2=3,l2=3,l3=3,l4=3,l5=3,l6=3,l7=3,l8=3,l9=3 V p,k,pp,kp,q,qs,qt,qu C F=fi triplet, W=vector boson triplet, Z=Higgs, X=FP ghost triplet. T TAP: F,U,W,Z T TFE: X T THI: Z=1:1,U=1:1 Antilist TAP X DEDE(al,be,ga,de)=2.*D(al,be)*D(ga,de) - D(al,de)*D(be,ga) - D(al,ga)*D(be,de) G 1 X FF(l1,al,l2,be;p) = NOM(p,M)*D(l1,l2) X WW(l1,al,l2,be;p) = NOM(p,M)*D(al,be)*D(l1,l2) X X_X(l1,al,l2,be;p) = NOM(p,M)*D(l1,l2) X WWW(l1,al,k,l2,be,p,l3,ga,q) = -i*Epf(l1,l2,l3)*D(al,ga)*(k(be)-q(be)) -i*Epf(l1,l2,l3)*D(be,ga)*(q(al)-p(al)) -i*Epf(l1,l2,l3)*D(al,be)*(p(ga)-k(ga)) X FFW(l2,be,p,l3,ga,q,l1,al,k) = 0.5*i*Epf(l1,l2,l3)*p(al) -0.5*i*Epf(l1,l2,l3)*q(al) X WWWW(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = -D(l4,l2)*D(l1,l3)*DEDE(al,ga,be,de)+D(l4,l1)*D(l3,l2)*DEDE(al,ga,be,de) -D(l4,l3)*D(l2,l1)*DEDE(al,be,ga,de)+D(l4,l1)*D(l2,l3)*DEDE(al,be,ga,de) X FFWW(l3,ga,k,l4,de,p,l1,al,q,l2,be,pp) = - 0.5*D(l1,l2)*D(l3,l4)*D(al,be) X FFFF(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.25*m^2/M^2*D(l1,l2)*D(l3,l4) - 0.25*m^2/M^2*D(l1,l3)*D(l2,l4) - 0.25*m^2/M^2*D(l1,l4)*D(l2,l3) X WX_X(l1,al,k,l2,be,p,l3,ga,q) = i*Epf(l1,l2,l3)*p(al) X FX_X(l1,al,k,l2,be,p,l3,ga,q) = 0.5*M*Epf(l1,l2,l3) G 2 X ZZ(l1,al,l2,be;p) = NOM(p,m) X FWZ(l2,be,p,l1,al,k,l3,ga,q) = 0.5*i*D(l1,l2)*p(al) -0.5*i*D(l1,l2)*q(al) X WWZ(l1,al,k,l2,be,p,l3,ga,q) = - M*D(l1,l2)*D(al,be) X FFZ(l1,al,k,l2,be,p,l3,ga,q) = - 0.5*m^2/M*D(l1,l2) X ZZZ(l1,al,k,l2,be,p,l3,ga,q) = - 1.5*m^2/M X WWZZ(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.5*D(l1,l2)*D(al,be) X FFZZ(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.25*m^2/M^2*D(l1,l2) X ZZZZ(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.75*m^2/M^2 X X_XZ(l1,al,k,l2,be,p,l3,ga,q) = - 0.5*M*D(l1,l2) G 3 C Tadpole counterterm. X NNZ(l1,al,k,l2,be,p,l3,ga,q) = - M*m^2*Et C Self-energy counter terms. X NWW(l1,al,k,l2,be,p,l3,ga,q) = - {2*M^2*Ew + 2*M^2*E1 - 2*pDq*Ew} * D(l2,l3)*D(be,ga) - 2*p(be)*q(ga)*D(l2,l3)*Ew X FFN(l2,be,p,l3,ga,q,l1,al,k) = 2*pDq*Eh*D(l2,l3) - 1/2*m^2*Et*D(l2,l3) X FNW(l2,be,p,l1,al,k,l3,ga,q) = M*(Ew+Eh+E1)*D(l2,l3)*i*p(ga) X NZZ(l1,al,k,l2,be,p,l3,ga,q) = m^2*{-2*Eh-1/2*Et+2*E2-2*E1} + 2*pDq*Eh G 4 C Three point counter terms. X WWWK = Eg+3*Ew X FFWK = Eg+Ew+2*Eh X FWZK = Eg+Ew+2*Eh X WWZK = Eg+2*Ew+Eh+E1 X FFZK = Eg+3*Eh-2*E2+E1 X ZZZK = Eg+3*Eh-2*E2+E1 C Four-point counter terms. X WWWWK = 2*Eg+4*Ew X FFWWK = 2*Eg+2*Ew+2*Eh X FFFFK = 2*Eg+4*Eh-2*E2 X WWZZK = 2*Eg+2*Ew+2*Eh X FFZZK = 2*Eg+4*Eh-2*E2 X ZZZZK = 2*Eg+4*Eh-2*E2 G 5 C New Higgs-like particle... Mass: as Higgs, i.e. m. Coupling: - 1/4* gu * U^2 * { (Z+2M/g)^2 + Fi^2 } Choice: gu = g^2 * m^2/4/M^2*gu Gotoif 2,_Sw0=0 X UU(l1,al,l2,be;p) = NOM(p,M) Goto 3 @2 X UU(l1,al,l2,be;p) = NOM(p,m) @3 X UUZ(l1,al,k,l2,be,p,l3,ga,q) = - 0.5*m^2/M*gu X FFUU(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.25*m^2/M^2*D(l1,l2)*gu X UUZZ(l1,al,k,l2,be,p,l3,ga,q,l4,de,pp) = - 0.25*m^2/M^2*gu G ENDBLOCK BLOCK FOUR{} C Four point topologies, including reducible graphs and tadpole types. Call: VIER("A,a,al,k,"B,b,p,p,"C,c,pp,pp,"D,d,kp,kp) The result needs additional contributions, obtained by crossing, as shown here: + VIER("A,a,al,k,"C,c,ga,pp,"B,b,be,p,"D,d,de,kp) + VIER("A,a,al,k,"B,b,be,p,"D,d,de,kp,"C,c,ga,pp) Id,VIER(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~,K4~,d~,de~,kp~)= Reduc(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp) + Redup(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp) + Tadp(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp) + DS(K1;J4;-J1;TAP,( DS(K2;J1;-J2;TAP,( DS(K3;J2;-J3;TAP,( A0*VIE(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J1,J2,J3,J4) * DC("F,TFE,-1,J1,J2,J3,J4) ))) ))) + DS(K1;K3;J7;-J5;TAP,( DS(K2;J5;-J6;TAP,(DC("F,TFE,-1,J5,J6,J7)* A1*VIE1(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J5,J6,J7) )) )) + DS(K2;K4;J8;-J9;TAP,( DS(K1;JA;-J8;TAP,(DC("F,TFE,-1,J8,J9,JA)* A2*VIE2(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J8,J9,JA) )) )) + DS(K1;K3;J0;-JB;Sym;J0;-JB;TAP,(DC("F,TFE,-1,J0,JB)* A3*VIE3(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,JB,J0) ) ) Id, VIE(K1~,a~,al~,k~,K2~,b~,be~,p~, K3~,c~,ga~,pp~,K4~,d~,de~,kp~,J1~,J2~,J3~,J4~)= VE3(K1,J4,-J1,*,a,al,k,*,l8,m8,q3,*,l1,m1,-q)* VE3(K2,J1,-J2,*,b,be,p,*,l2,m0,q,*,l3,m3,-q1)* VE3(K3,J2,-J3,*,c,ga,pp,*,l4,m4,q1,*,l5,m5,-q2)* VE3(K4,J3,-J4,*,d,de,kp,*,l6,m6,q2,*,l7,m7,-q3)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q1,*,l4,m4,-q1)* PROP(J3,-J3,*,l5,m5,q2,*,l6,m6,-q2)* PROP(J4,-J4,*,l7,m7,q3,*,l8,m8,-q3) Al,VIE1(K1~,a~,al~,k~,K2~,b~,be~,p~, K3~,c~,ga~,pp~,K4~,d~,de~,kp~,J1~,J2~,J3~)= VE4(K1,K3,J3,-J1,*,a,al,k,*,c,ga,pp,*,l6,m6,q4,*,l1,m1,-q)* VE3(K2,J1,-J2,*,b,be,p,*,l2,m0,q,*,l3,m3,-q1)* VE3(K4,J2,-J3,*,d,de,kp,*,l4,m4,q1,*,l5,m5,-q4)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q1,*,l4,m4,-q1)* PROP(J3,-J3,*,l5,m5,q4,*,l6,m6,-q4) Al,VIE2(K1~,a~,al~,k~,K2~,b~,be~,p~, K3~,c~,ga~,pp~,K4~,d~,de~,kp~,J1~,J2~,J3~)= VE4(K2,K4,J1,-J2,*,b,be,p,*,d,de,kp,*,l2,m0,q,*,l3,m3,-q4)* VE3(K1,J3,-J1,*,a,al,k,*,l6,m6,q3,*,l1,m1,-q)* VE3(K3,J2,-J3,*,c,ga,pp,*,l4,m4,q4,*,l5,m5,-q3)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4)* PROP(J3,-J3,*,l5,m5,q3,*,l6,m6,-q3) Al,VIE3(K1~,a~,al~,k~,K2~,b~,be~,p~, K3~,c~,ga~,pp~,K4~,d~,de~,kp~,J1~,J2~)= VE4(K1,K3,J2,-J1,*,a,al,k,*,c,ga,pp,*,l4,m4,q4,*,l1,m1,-q)* VE4(K2,K4,J1,-J2,*,b,be,p,*,d,de,kp,*,l2,m0,q,*,l3,m3,-q4)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4) Al,Reduc(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~,K4~,d~,de~,kp~) = DS(K2;K4;J4;TAP,(DS(-J4;J1;-J2;TAP,( DS(K1;J3;-J1;TAP,( DC("F,TFE,-1,J1,J2,J3)*R1(J4,J4)* RED1(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J1,J2,J3,J4) )) )) )) + DS(K1;K3;-J8;TAP,(DS(J8;-J5;J7;TAP,( DS(K2;J5;-J6;TAP,( DC("F,TFE,-1,J5,J6,J7)*R1(J8,J8)* RED2(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J5,J6,J7,J8) )) )) )) + DS(K1;K3;-J0;JA;Sym;-J0;JA;TAP,(DS(J0;-JA;-JB;TAP,( DC("F,TFE,-1,J0,JA)*R1(JB,JB)* RED3(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J0,JA,JB) )) )) + DS(K1;K3;-JE;TAP,(DS(JE;-JC;JD;Sym;-JC;JD;TAP,( DC("F,TFE,-1,JC,JD)*R1(JE,JE)* RED4(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,JC,JD,JE) )) )) + DS(K1;K3;-JI;TAP,(DS(JI;-JF;JG;Sym;-JF;JG;TAP,( DS(JF;-JG;-JH;TAP,(DC("F,TFE,-1,JF,JG)*R5(JI,JI)* RED5(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,JF,JG,JH,JI) )) )) )) + DS(K1;-JM;K3;TAP,(DS(JM;-JL;-JK;JK;Sym;-JK;JK;TAP,(R5(JM,JM)* RED6(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,JK,JL,JM) )) )) Al,Redup(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~,K4~,d~,de~,kp~) = DS(K2;K4;J3;TAP,( DS(-J2;J1;-J3;K3;Sym;-J2;J1;TAP,(R1(J3,J3)* RED3A(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J1,J2,J3) )) + DS(J5;-J4;-J3;K1;Sym;J5;-J4;TAP,(R1(J3,J3)* RED3B(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J4,J5,J3) )) )) + DS(K1;K3;J8;TAP,( DS(J7;-J6;-J8;K4;Sym;J7;-J6;TAP,(R1(J8,J8)* RED4A(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J6,J7,J8) )) + DS(JA;-J9;-J8;K2;Sym;JA;-J9;TAP,(R1(J8,J8)* RED4B(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J9,JA,J8) )) )) Al,Tadp(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~,K4~,d~,de~,kp~) = DS(K2;K4;J2;"Z;TAP,(DS("Z;J1;-J1;Sym;J1;-J1;TAP,( DC("F,TFE,-1,J1)* T1*TAD1(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J1,J2) )) )) + DS(K1;K3;-J4;"Z;TAP,(DS("Z;J3;-J3;Sym;J3;-J3;TAP,( DC("F,TFE,-1,J3)* T2*TAD2(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J3,J4) )) )) + DS(K1;-J6;K3;TAP,(DS(J6;-J7;"Z;TAP,(DS("Z;J5;-J5;Sym;J5;-J5;TAP,( DC("F,TFE,-1,J5)* T3*TAD3(K1,a,al,k,K2,b,be,p,K3,c,ga,pp,K4,d,de,kp,J5,J6,J7) )) )) )) Id,RED1(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~,J4~) = VE3(K1,-J1,J3,*,a,al,k,*,l1,m1,-q,*,l6,m6,q3)* VE3(J1,-J4,-J2,*,l2,m0,q,*,l7,m7,-qu,*,l3,m3,-q4)* VE3(K2,K4,J4,*,b,be,p,*,d,de,kp,*,l8,m8,qu)* VE3(K3,J2,-J3,*,c,ga,pp,*,l4,m4,q4,*,l5,m5,-q3)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4)* PROP(J3,-J3,*,l5,m5,q3,*,l6,m6,-q3)* PROP(J4,-J4,*,l7,m7,qu,*,l8,m8,-qu) Al,RED2(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~,J4~) = VE3(K1,-J4,K3,*,a,al,k,*,l7,m7,-qu,*,c,ga,pp)* VE3(J4,-J1,J3,*,l8,m8,qu,*,l1,m1,-q,*,l6,m6,q4)* VE3(K2,J1,-J2,*,b,be,p,*,l2,m0,q,*,l3,m3,-q1)* VE3(K4,J2,-J3,*,d,de,kp,*,l4,m4,q1,*,l5,m5,-q4)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q1,*,l4,m4,-q1)* PROP(J3,-J3,*,l5,m5,q4,*,l6,m6,-q4)* PROP(J4,-J4,*,l7,m7,qu,*,l8,m8,-qu) Al,RED3(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE4(K1,-J1,J2,K3,*,a,al,k,*,l1,m1,-q,*,l4,m4,q4,*,c,ga,pp)* VE3(J1,-J2,-J3,*,l2,m0,q,*,l3,m3,-q4,*,l5,m5,-qu)* VE3(K2,J3,K4,*,b,be,p,*,l6,m6,qu,*,d,de,kp)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED3A(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K2,K4,J3,*,b,be,p,*,d,de,kp,*,l6,m6,qu)* VE4(-J2,J1,-J3,K3,*,l3,m3,-q3,*,l2,m0,q,*,l5,m5,-qu,*,c,ga,pp)* VE3(K1,-J1,J2,*,a,al,k,*,l1,m1,-q,*,l4,m4,q3)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q3,*,l4,m4,-q3)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED3B(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K2,K4,J3,*,b,be,p,*,d,de,kp,*,l6,m6,qu)* VE4(J2,-J1,-J3,K1,*,l4,m4,q2,*,l1,m1,-q1,*,l5,m5,-qu,*,a,al,k)* VE3(K3,J1,-J2,*,c,ga,pp,*,l2,m0,q1,*,l3,m3,-q2)* PROP(J1,-J1,*,l1,m1,q1,*,l2,m0,-q1)* PROP(J2,-J2,*,l3,m3,q2,*,l4,m4,-q2)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED4(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K1,-J3,K3,*,a,al,k,*,l5,m5,-qu,*,c,ga,pp)* VE3(-J1,J2,J3,*,l1,m1,-q,*,l4,m4,q4,*,l6,m6,qu)* VE4(K2,J1,-J2,K4,*,b,be,p,*,l2,m0,q,*,l3,m3,-q4,*,d,de,kp)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED4A(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K1,K3,-J3,*,a,al,k,*,c,ga,pp,*,l5,m5,-qu)* VE4(J2,-J1,J3,K4,*,l4,m4,q1,*,l1,m1,q,*,l6,m6,qu,*,d,de,kp)* VE3(K2,J1,-J2,*,b,be,p,*,l2,m0,q,*,l3,m3,-q1)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q1,*,l4,m4,-q1)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED4B(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K1,K3,-J3,*,a,al,k,*,c,ga,pp,*,l5,m5,-qu)* VE4(J2,-J1,J3,K2,*,l4,m4,q3,*,l1,m1,q2,*,l6,m6,qu,*,b,be,p)* VE3(K4,J1,-J2,*,d,de,kp,*,l2,m0,q2,*,l3,m3,-q3)* PROP(J1,-J1,*,l1,m1,q2,*,l2,m0,-q2)* PROP(J2,-J2,*,l3,m3,q3,*,l4,m4,-q3)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Al,RED5(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~,J4~) = VE3(K1,-J4,K3,*,a,al,k,*,l7,m7,-qu,*,c,ga,pp)* VE3(J4,-J1,J2,*,l8,m8,qu,*,l1,m1,-q,*,l3,m3,q4)* VE3(J1,-J2,-J3,*,l2,m0,q,*,l4,m4,-q4,*,l5,m5,-qu)* VE3(K2,J3,K4,*,b,be,p,*,l6,m6,qu,*,d,de,kp)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,q4,*,l4,m4,-q4)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu)* PROP(J4,-J4,*,l7,m7,qu,*,l8,m8,-qu) Al,RED6(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K1,-J3,K3,*,a,al,k,*,l5,m5,-qu,*,c,ga,pp)* VE4(J3,-J2,-J1,J1,*,l6,m6,qu,*,l3,m3,-qu,*,l1,m1,-q,*,l2,m0,q)* VE3(K2,J2,K4,*,b,be,p,*,l4,m4,qu,*,d,de,kp)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q)* PROP(J2,-J2,*,l3,m3,qu,*,l4,m4,-qu)* PROP(J3,-J3,*,l5,m5,qu,*,l6,m6,-qu) Id,TAD1(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~) = VE4(K2,K4,J2,"Z,*,b,be,p,*,d,de,kp,*,l4,m4,qu,*,l5,m5,q0)* VE3(K1,K3,-J2,*,a,al,k,*,c,ga,pp,*,l3,m3,-qu)* VE3("Z,J1,-J1,*,l6,m6,-q0,*,l1,m1,-q,*,l2,m0,q)* PROP(J2,-J2,*,l3,m3,qu,*,l4,m4,-qu)* PROP("Z,"Z,*,l5,m5,q0,*,l6,m6,-q0)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q) Al,TAD2(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~) = VE4(K1,K3,-J2,"Z,*,a,al,k,*,c,ga,pp,*,l3,m3,-qu,*,l5,m5,q0)* VE3(K2,K4,J2,*,b,be,p,*,d,de,kp,*,l4,m4,qu)* VE3("Z,J1,-J1,*,l6,m6,-q0,*,l1,m1,-q,*,l2,m0,q)* PROP(J2,-J2,*,l3,m3,qu,*,l4,m4,-qu)* PROP("Z,"Z,*,l5,m5,q0,*,l6,m6,-q0)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q) Al,TAD3(K1~,a~,al~,k~,K2~,b~,be~,p~,K3~,c~,ga~,pp~, K4~,d~,de~,kp~,J1~,J2~,J3~) = VE3(K1,K3,-J2,*,a,al,k,*,c,ga,pp,*,l3,m3,-qu)* VE3(J2,-J3,"Z,*,l4,m4,qu,*,l7,m7,-qu,*,l5,m5,-q0)* VE3(K2,K4,J3,*,b,be,p,*,d,de,kp,*,l8,m8,qu)* VE3("Z,J1,-J1,*,l6,m6,-q0,*,l1,m1,-q,*,l2,m0,q)* PROP(J2,-J2,*,l3,m3,qu,*,l4,m4,-qu)* PROP(J3,-J3,*,l7,m7,qu,*,l8,m8,-qu)* PROP("Z,"Z,*,l5,m5,q0,*,l6,m6,-q0)* PROP(J1,-J1,*,l1,m1,q,*,l2,m0,-q) Id,Anti,TAP Al,Stats,0 Al,R1("Z,"Z)=R1Z Al,R5("Z,"Z)=R5Z Al,R1(J1~,J2~)=1 Al,R5(J1~,J2~)=1 Id,Compo,,VE4,VE3,PROP Id,VE4(FF~,l1~,al~,k~,l2~,be~,p~,l3~,ga~,pp~,l4~,la~,kp~)= FF(l1,al,k,l2,be,p,l3,ga,pp,l4,la,kp) Al,VE3(FF~,l1~,al~,k~,l2~,be~,q~,l3~,ga~,p~)= FF(l1,al,k,l2,be,q,l3,ga,p) Al,PROP(FF~,l1~,al~,q~,l2~,be~,k~)=FF(l1,al,l2,be,k) Al,Stats,1 ENDBLOCK BLOCK ETE1{} C Counterterms. Gotoif 2,_Sw0=0 Id,Et=i*Pi^2 * ( - 3/4 - 3/2*M^2*m^-2 + 9/2*M^2*m^-2*LogM2 - 3/4*M^-2*m^2 + 3/4*M^-2*m^2*Logm2 + 3/4*LogM2 - 1/4*gu + 1/4*LogM2*gu ) + i*Pi^2*N_^-1 * ( 3/2 + 9*M^2*m^-2 + 3/2*M^-2*m^2 + 1/2*gu) Goto 3 @2 Id,Et=i*Pi^2 * ( - 3/4 - 3/2*M^2*m^-2 + 9/2*M^2*m^-2*LogM2 - 3/4*M^-2*m^2 + 3/4*M^-2*m^2*Logm2 + 3/4*LogM2 - 1/4*M^-2*m^2*gu + 1/4*M^-2*m^2*Logm2*gu ) + i*Pi^2*N_^-1 * ( 3/2 + 9*M^2*m^-2 + 3/2*M^-2*m^2 + 1/2*M^-2*m^2*gu) @3 Al,E1= i*Pi^2 * ( 1/16*M^-2*m^2 + 5/12*Logm2) - 25/6*i*Pi^2*N_^-1 Goto 2,_Sw0=0 Al,E2 = i*Pi^2*( E2a*m^2/M^2 + E2al*m^2*Logm2/M^2 + E2b + E2bl*Logm2 + E2c*M^2/m^2 + E2cl*Logm2*M^2/m^2) + i*Pi^2*N_^-1 * ( - 8/3 - 9/2*M^2*m^-2 - 3/2*M^-2*m^2 - 1/8*M^-2*m^2*gu^2) Goto 3 @2 Id,E2 = i*Pi^2 * ( 7/16*M^-2*m^2 - 3/4*M^-2*m^2*Logm2 - 3/2 +7/6*Logm2 - 9/4*M^2/m^2*Logm2 - 9/16*m^2/M^2*[Pi/Sqrt(3)-2] - 1/16*M^-2*m^2*Logm2*gu^2 - 1/16*m^2/M^2*[Pi/Sqrt(3)-2]*gu^2) + i*Pi^2*N_^-1 * ( - 8/3 - 9/2*M^2*m^-2 - 3/2*M^-2*m^2 - 1/8*M^-2*m^2*gu^2) @3 Al,Eh=i*Pi^2*(3/2/N_ + m^2/M^2/16 + 1/8*Logm2) Al,Ew=i*Pi^2*(19/6/N_ - 1/24*Logm2) Al,Eg=- 43/6*i*Pi^2/N_ Gotoif 5,_Sw0=0 Id,E2a = 7/16 - 9/16*[Pi/Sqrt(3)-2] + gu^2/8 Al,E2al = - 3/4 - 1/16*gu^2 Al,E2b = - 3/2 Al,E2bl = 7/6 Al,E2c = 0 Al,E2cl = - 9/4 @5 ENDBLOCK BLOCK ASSIGN{} A N,N_,M,m,n,n1,n2,n3,n4,Div,Fact,Nom,Nohm F Fxx,Two,Three,Fq C q1 = q+p q2 = q+p+pp q3 = q-k q4 = q-k-pp q5 = q-k-p q6 = q+pp q7 = q+kp qu = k+pp qs = q-k-p qt = Crossing relations. p <-> pp pp <-> kp q1 -> q6 pDk -> ppDk q1 -> q1 pDk -> ppDk q2 -> q2 s -> u q2 -> q4 s -> s q3 -> q3 ppDk -> pDk q3 -> q3 ppDk -> kDkp q4 -> q5 u -> s q4 -> q2 u -> t q5 -> q4 pDpp -> pDpp q5 -> q5 pDpp -> pDkp q6 -> q1 t -> t q6 -> q7 t -> u q7 -> q7 q7 -> q6 V q,q1,q2,q3,q4,q5,q6,q7,qs,qu,qt I al=N,be=N,la=N,de=N,ga=N,la=N I a=3,b=3,c=3,d=3 X dede(al,be,ga,de)=D(al,be)*D(ga,de)+D(al,ga)*D(be,de)+D(al,de)*D(be,ga) C n1: -2 for every factor 1/(q^2+m^2) n2: number of factors m n3: degree of divergence with respect to integration variable q not counting n1 types. Integral is convergent if n3+4 < 0. X Fdiv(n1,n2,n3)= DT(-n3-4)*DT(n1+n2) + DT(n3+4-1)*DT(n1+n2+4+n3) C Series expansion for { Nohm/(1-x*Nohm) }^n4 C X Exp(n1,n2,n3,x,n4) = DT(-n3-4)*Nohm^n4*DS(J,0,n1+n2,(DB(n4+J-1,J)*x^J*Nohm^J)) + DT(n3+4-1)*Nohm^n4*DS(K,0,n1+n2+4+n3,(DB(n4+K-1,K)*x^K*Nohm^K)) ENDBLOCK BLOCK COUNT{} Id,Count,Div,q,1,NOM,-2,Nom,-2,Two,-4 Id,m^n~*Fxx(n1~,n2~,n3~,n4~)=m^n*Fxx(n1,n2+n,n3,n4) Id,[m2-M2]^n~*Fxx(n1~,n2~,n3~,n4~)=[m2-M2]^n*Fxx(n1,n2+2*n,n3,n4) Id,Div^n~*Fxx(n1~,n2~,n3~,n4~)=Fxx(n1,n2,n3+n,n4) ENDBLOCK BLOCK HCOUNT{} C Count behaviour with respect to m for large m. Eliminate if zero in that limit. IF Nohm^n~=Fxx(-2*n,0,0,n)*Nohm^n COUNT{} Id,Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3) ELSE Id,Count,0,m,1,[m2-M2],2 ENDIF ENDBLOCK BLOCK SHIFT{} IF Sh1 Al,qDq=qDq-2*qDp+pDp Al,Dotpr,q(al~)=q(al)-p(al) ENDIF IF Sh2 Al,qDq=qDq-2*qDp-2*qDpp+2*pDpp+pDp+ppDpp Al,Dotpr,q(al~)=q(al)-p(al) - pp(al) ENDIF IF Sh3 Al,qDq=qDq+2*qDk+kDk Al,Dotpr,q(al~)=q(al)+k(al) ENDIF IF Sh4 Al,qDq=qDq+2*qDk+2*qDpp+2*kDpp+kDk+ppDpp Al,Dotpr,q(al~)=q(al)+k(al)+pp(al) ENDIF IF Sh5 Al,qDq=qDq+2*qDk+2*qDp+2*kDp+kDk+pDp Al,Dotpr,q(al~)=q(al)+k(al)+p(al) ENDIF IF Sh6 Al,qDq=qDq-2*qDpp+ppDpp Al,Dotpr,q(al~)=q(al)-pp(al) ENDIF IF Sh7 Al,qDq=qDq+2*qDk+2*qDp+2*qDpp+kpDkp Al,Dotpr,q(al~)=q(al)+k(al)+p(al)+pp(al) ENDIF IF NOT Nohm Id,Sh1=1 Al,Sh2=1 Al,Sh3=1 Al,Sh4=1 Al,Sh5=1 Al,Sh6=1 Al,Sh7=1 ENDIF Id,pDp=-M^2 Al,kDk=-M^2 Al,ppDpp=-M^2 Al,kpDkp=-M^2 Id,Count,0,NOM,-2,Two,-4,Nom,-2,Nohm,-2,[m2-M2],2,p,1,k,1,pp,1,kp,1,q,1,m,1 *yep C Working out of shifted 1/(q^2+m^2)^n IF Nohm^n~*Sh1=Fxx(-2*n,0,0,n)*Sh1 OR Nohm^n~*Sh2=Fxx(-2*n,0,0,n)*Sh2 OR Nohm^n~*Sh3=Fxx(-2*n,0,0,n)*Sh3 OR Nohm^n~*Sh4=Fxx(-2*n,0,0,n)*Sh4 OR Nohm^n~*Sh5=Fxx(-2*n,0,0,n)*Sh5 OR Nohm^n~*Sh6=Fxx(-2*n,0,0,n)*Sh6 OR Nohm^n~*Sh7=Fxx(-2*n,0,0,n)*Sh7 COUNT{} Id,Sh1*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3)*Exp(n1,n2,n3,(2*qDp),n4) Al,Sh2*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3)* Exp(n1,n2,n3,(2*qDp+2*qDpp-2*pDpp),n4) Al,Sh3*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3)*Exp(n1,n2,n3,(-2*qDk),n4) Al,Sh4*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3) *Exp(n1,n2,n3,(-2*qDk-2*qDpp-2*kDpp),n4) Al,Sh5*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3) *Exp(n1,n2,n3,(-2*qDk-2*qDp-2*kDp),n4) Al,Sh6*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3)*Exp(n1,n2,n3,(2*qDpp),n4) Al,Sh7*Fxx(n1~,n2~,n3~,n4~)=Fdiv(n1,n2,n3)*Exp(n1,n2,n3,(2*qDkp),n4) ENDIF Id,pDp=-M^2 Al,kDk=-M^2 Al,ppDpp=-M^2 Al,kpDkp=-M^2 Al,qDkp=-qDk-qDp-qDpp Id,Count,0,NOM,-2,Two,-4,Nom,-2,Nohm,-2,[m2-M2],2,p,1,k,1,pp,1,kp,1,q,1,m,1 Id,Multi,Chsi^2=1 IF Chsi=1 Al,qDq=qDq Al,Dotpr,q(al~)=-q(al) ENDIF ENDBLOCK BLOCK STINT{} C Standard integrals. C Type Fn = 1/(q^2+M^2)^n Id,F(1,m2~) = 2*i*Pi^2*m2/N_ + i*Pi^2*m2*(-1+Log(m2)) Al,F(2,m2~) = - 2*i*Pi^2/N_ - i*Pi^2*Log(m2) Al,F(3,m2~) = 0.5*i*Pi^2/m2 Al,F(4,m2~) = i*Pi^2/6/m2^2 Al,F(5,m2~) = 1/12*i*Pi^2*m2^-3 Al,F(6,m2~) = 1/20*i*Pi^2*m2^-4 Al,F(7,m2~) = 1/30*i*Pi^2*m2^-5 Id,G(1,m2~) = - 0.5*i*Pi^2*m2^2/N_ + 3/8*i*Pi^2*m2^2 - 0.25*i*Pi^2*m2^2*Log(m2) Al,G(2,m2~) = i*Pi^2 * ( - 1/2*m2 + m2*N_^-1 ) + 0.5*m2*Log(m2)*i*Pi^2 Al,G(3,m2~) = i*Pi^2 * ( - 1/2*N_^-1 ) - 1/4*Log(m2)*i*Pi^2 Al,G(4,m2~) = 1/12*i*Pi^2*m2^-1 Al,G(5,m2~) = 1/48*i*Pi^2*m2^-2 Al,G(6,m2~) = 1/120*i*Pi^2*m2^-3 Al,G(7,m2~) = 1/240*i*Pi^2*m2^-4 Id,H(1,m2~) = 1/12*i*Pi^2*m2^3/N_ - 11/144*i*Pi^2*m2^3 + 1/24*i*Pi^2*m2^3*Log(m2) Al,H(2,m2~) = i*Pi^2 * ( 3/16*m2^2 - 1/4*m2^2*N_^-1 ) - 1/8*Log(m2)*i*Pi^2*m2^2 Al,H(3,m2~) = i*Pi^2 * ( - 1/8*m2 + 1/4*m2*N_^-1 ) + 1/8*Log(m2)*i*Pi^2 *m2 Al,H(4,m2~) = - 1/12*i*Pi^2*N_^-1 - 1/24*Log(m2)*i*Pi^2 Al,H(5,m2~) = i*Pi^2/96/m2 Al,H(6,m2~) = 1/480*i*Pi^2*m2^-2 Al,H(7,m2~) = 1/1200*i*Pi^2*m2^-3 C Type Fnm = 1/[(q^2+M^2)^n*(q^2+m^2)^m] Id,F(1,1,M2,m2) = - 2*i*Pi^2/N_ + i*Pi^2*{ 1 - m2*Log(m2)/[m2-M2] + M2*Log(M2)/[m2-M2]} Al,F(1,2,M2,m2) = i*Pi^2*{ 1/[m2-M2] - M2*Log(m2,M2)/[m2-M2]^2} Al,F(2,2,M2,m2) = - 2*i*Pi^2*[m2-M2]^-2 + Log(m2,M2)*i*Pi^2 * ( 2*M2*[m2-M2]^-3 + [m2-M2]^-2 ) Al,F(1,3,M2,m2) = 0.5*i*Pi^2*{ 1/[m2-M2]^2 + M2/m2/[m2-M2]^2 - 2*M2*Log(m2,M2)/[m2-M2]^3 } Al,F(2,3,M2,m2) = i*Pi^2 * ( 1/4*M2^-2*m2^-1 - 1/4*M2^-2*[m2-M2]^-1 + 1/4*M2^-1*[m2-M2]^-2 - 3/2*[m2-M2]^-3 ) + Log(m2,M2)*i*Pi^2 * ( 3/2*M2*[m2-M2]^-4 + 1/2*[m2-M2]^-3 ) Al,F(3,3,M2,m2) = i*Pi^2 * ( 1/4*M2^-3*m2^-1 - 1/4*M2^-3*[m2-M2]^-1 + 1/4*M2^-2*[m2-M2]^-2 + 3*[m2-M2]^-4 ) + Log(m2,M2)*i*Pi^2 * ( - 3*M2*[m2-M2]^-5 - 3/2*[m2-M2]^-4 ) Al,F(1,4,M2,m2) = i*Pi^2/6*{ 2/[m2-M2]^3 + 5*M2/m2/[m2-M2]^3 - M2^2/m2^2/[m2-M2]^3 - 6*M2*Log(m2,M2)/[m2-M2]^4 } Al,F(2,4,M2,m2) = + i*Pi^2 * ( - 2/3*M2^-3*m2^-1 + 2/3*M2^-3*[m2-M2]^-1 + 1/6*M2^-2*m2^-2 - 5/6*M2^-2*[m2-M2]^-2 + M2^-1*[m2-M2]^-3 - 4*[m2-M2]^-4 ) + Log(m2,M2)*i*Pi^2 * ( 4*M2*[m2-M2]^-5 + [m2-M2]^-4 ) Al,F(3,4,M2,m2) = i*Pi^2 * ( - M2^-4*m2^-1 + M2^-4*[m2-M2]^-1 + 1/6*M2^-3*m2^-2 - 7/6*M2^-3 *[m2-M2]^-2 + 4/3*M2^-2*[m2-M2]^-3 - M2^-1*[m2-M2]^-4 + 10* [m2-M2]^-5 ) + Log(m2,M2)*i*Pi^2 * ( - 10*M2*[m2-M2]^-6 - 4*[m2-M2]^-5 ) Al,F(4,4,M2,m2) = i*Pi^2 * ( - 2/3*M2^-4*m2^-1 + 2/3*M2^-4*[m2-M2]^-1 + 1/9*M2^-3*m2^-2 - 7/9*M2^-3*[m2-M2]^-2 + 8/9*M2^-2*[m2-M2]^-3 - 2/3*M2^-1* [m2-M2]^-4 + 20/3*[m2-M2]^-5 ) + Log(m2,M2)*i*Pi^2 * ( - 20/3*M2*[m2-M2]^-6 - 8/3*[m2-M2]^-5 ) C Type Gnm = q(mu)*q(nu)/[(q^2+M^2)^n*(q^2+m^2)^m] Function D(mu,nu) understood. Id,G(1,1,M2,m2) = + 0.5*i*Pi^2*(m2+M2)/N_ - 3*i*Pi^2*(m2+M2)/8 + 0.25*i*Pi^2*(m2^2*Log(m2) - M2^2*Log(M2))/[m2-M2] Al,G(1,2,M2,m2) = i*Pi^2*( 1/8 - 1/4*M2*[m2-M2]^-1 - 1/2*N_^-1 ) + 0.25*Log(m2,M2)*i*Pi^2*M2^2*[m2-M2]^-2 - 1/4*Log(m2)*i*Pi^2 Al,G(2,2,M2,m2) = i*Pi^2 * ( 1/2*M2*[m2-M2]^-2 + 1/4*[m2-M2]^-1 ) + Log(m2,M2)*i*Pi^2 * ( - 1/2*M2*[m2-M2]^-2 - 1/2*M2^2*[m2-M2]^-3 ) Al,G(1,3,M2,m2) = i*Pi^2*( - 1/4*M2*[m2-M2]^-2 + 1/8*[m2-M2]^-1 ) + 1/4*Log(m2,M2)*i*Pi^2*M2^2*[m2-M2]^-3 Al,G(2,3,M2,m2) = i*Pi^2 * ( 3/4*M2*[m2-M2]^-3 + 1/8*[m2-M2]^-2 ) + Log(m2,M2)*i*Pi^2 * ( - 1/2*M2*[m2-M2]^-3 - 3/4*M2^2*[m2-M2]^-4 ) Al,G(3,3,M2,m2) = + i*Pi^2 * ( - 3/2*M2*[m2-M2]^-4 - 3/4*[m2-M2]^-3 ) + Log(m2,M2)*i*Pi^2 * ( 3/2*M2*[m2-M2]^-4 + 3/2*M2^2*[m2-M2]^-5 + 1/4*[m2-M2]^-3 ) Al,G(1,4,M2,m2) = i*Pi^2 * ( - 1/4*M2*[m2-M2]^-3 + 1/12*M2^-1*m2^-1 - 1/12*M2^-1*[m2-M2]^-1 + 1/8*[m2-M2]^-2 ) + 1/4*Log(m2,M2)*i*Pi^2*M2^2*[m2-M2]^-4 Al,G(2,4,M2,m2) = i*Pi^2 * ( M2*[m2-M2]^-4 + 1/12*M2^-2*m2^-1 - 1/12*M2^-2*[m2-M2]^-1 + 1/12*M2^-1*[m2-M2]^-2 ) + Log(m2,M2)*i*Pi^2 * ( - 1/2*M2*[m2-M2]^-4 - M2^2*[m2-M2]^-5 ) Al,G(3,4,M2,m2) = i*Pi^2 * ( - 5/2*M2*[m2-M2]^-5 + 1/12*M2^-3*m2^-1 - 1/12*M2^-3* [m2-M2]^-1 + 1/12*M2^-2*[m2-M2]^-2 - 1/12*M2^-1*[m2-M2]^-3 - 3/4*[m2-M2]^-4 ) + Log(m2,M2)*i*Pi^2 * ( 2*M2*[m2-M2]^-5 + 5/2*M2^2*[m2-M2]^-6 + 1/4*[m2-M2]^-4 ) Al,G(4,4,M2,m2) = i*Pi^2 * ( 5*M2*[m2-M2]^-6 + 1/12*M2^-4*m2^-1 - 1/12*M2^-4*[m2-M2]^-1 + 1/12*M2^-3*[m2-M2]^-2 - 1/12*M2^-2*[m2-M2]^-3 + 1/6*M2^-1* [m2-M2]^-4 + 5/2*[m2-M2]^-5 ) + Log(m2,M2)*i*Pi^2 * ( - 5*M2*[m2-M2]^-6 - 5*M2^2*[m2-M2]^-7 - [m2-M2]^-5 ) C Type Hnm = q(mu)*q(nu)*q(al)*q(be)/[(q^2+M^2)^n*(q^2+m^2)^m] Function d(mu,nu,al,be) = D(mu,nu)*D(al,be) + D(mu,al)*D(nu,be) + D(mu,be)*D(nu,de) understood. Derived from H11(M2,m2) = {- m2*F1(m2) - M2*F1(M2) + m2*M2*F11(M2,m2)}/[N^2+2*N] Id,H(1,1,M2,m2) = i*Pi^2 * ( 11/144*M2*m2 - 1/12*M2*m2*N_^-1 + 11/144*M2^2 - 1/12*M2^2*N_^-1 + 11/144*m2^2 - 1/12*m2^2*N_^-1 ) - 1/24*Log(m2,M2)*i*Pi^2*M2^3*[m2-M2]^-1 + Log(m2)*i*Pi^2*( - 1/24*M2*m2 - 1/24*M2^2 - 1/24*m2^2 ) Al,H(1,2,M2,m2) = i*Pi^2 * ( - 5/144*M2 + 1/12*M2*N_^-1 + 1/24*M2^2*[m2-M2]^-1 - 1/9*m2 + 1/6*m2*N_^-1 ) -1/24*Log(m2,M2)*i*Pi^2*M2^3*[m2-M2]^-2 + Log(m2)*i*Pi^2* ( 1/24*M2 + 1/12*m2 ) Al,H(2,2,M2,m2) = i*Pi^2 * ( 5/144 - 1/12*M2*[m2-M2]^-1 - 1/12*M2^2*[m2-M2]^-2 - 1/12*N_^-1 ) + Log(m2,M2)*i*Pi^2 * ( 1/8*M2^2*[m2-M2]^-2 + 1/12*M2^3*[m2-M2]^-3 ) - 1/24*Log(m2)*i*Pi^2 Al,H(1,3,M2,m2) = i*Pi^2 * ( 1/72 - 1/48*M2*[m2-M2]^-1 + 1/24*M2^2*[m2-M2]^-2 - 1/12*N_^-1 ) -1/24*Log(m2,M2)*i*Pi^2*M2^3*[m2-M2]^-3 - 1/24*Log(m2)*i*Pi^2 Al,H(2,3,M2,m2) = i*Pi^2 * ( - 1/16*M2*[m2-M2]^-2 - 1/8*M2^2*[m2-M2]^-3 + 1/48*[m2-M2]^-1 ) + Log(m2,M2)*i*Pi^2 * ( 1/8*M2^2*[m2-M2]^-3 + 1/8*M2^3*[m2-M2]^-4 ) Al,H(3,3,M2,m2) = i*Pi^2 * ( 1/4*M2*[m2-M2]^-3 + 1/4*M2^2*[m2-M2]^-4 + 1/48*[m2-M2]^-2 ) + Log(m2,M2)*i*Pi^2 * ( - 1/8*M2*[m2-M2]^-3 - 3/8*M2^2*[m2-M2]^-4 - 1/4*M2^3* [m2-M2]^-5 ) Al,H(1,4,M2,m2) = + i*Pi^2 * ( - 1/48*M2*[m2-M2]^-2 + 1/24*M2^2*[m2-M2]^-3 + 1/72*[m2-M2]^-1 ) -1/24*Log(m2,M2)*i*Pi^2*M2^3*[m2-M2]^-4 Al,H(2,4,M2,m2) = + i*Pi^2 * ( - 1/24*M2*[m2-M2]^-3 - 1/6*M2^2*[m2-M2]^-4 + 1/144*[m2-M2]^-2 ) + Log(m2,M2)*i*Pi^2 * ( 1/8*M2^2*[m2-M2]^-4 + 1/6*M2^3*[m2-M2]^-5 ) Al,H(3,4,M2,m2) = i*Pi^2 * ( 7/24*M2*[m2-M2]^-4 + 5/12*M2^2*[m2-M2]^-5 + 1/72*[m2-M2]^-3 ) + Log(m2,M2)*i*Pi^2 * ( - 1/8*M2*[m2-M2]^-4 - 1/2*M2^2*[m2-M2]^-5 - 5/12*M2^3* [m2-M2]^-6 ) Al,H(4,4,M2,m2) = i*Pi^2 * ( - 5/6*M2*[m2-M2]^-5 - 5/6*M2^2*[m2-M2]^-6 - 11/72*[m2-M2]^-4 ) + Log(m2,M2)*i*Pi^2 * ( 1/2*M2*[m2-M2]^-5 + 5/4*M2^2*[m2-M2]^-6 + 5/6*M2^3*[m2-M2]^-7 + 1/24*[m2-M2]^-4 ) ENDBLOCK End