i i,j; i mu,nu,al,be; i b1,b2,b3,b4; i a1,a2,a3,a4,a5,a6; i aa1,aa2,aa3,aa4,aa5,aa6,aa7; i bb1,bb2,bb3,bb4,bb5,bb6,bb7; * v pp,qp,Qp,Qm,k,kb,BQ; * s n; s I0; s PZ; s Com; s GT,T; s selv; s n1,n2; s [2-3]; s [5-6]; s [2+3]; s [5+6]; s eq,egt; s Qu,Qd,srt; s denk,denkb; s one,aux,int; s tau,x1,x2,z; s sw,swC,Gw,GwC; s gramd,restore; s l1,l2,l,lp,lv; s fws,fwt,fwsC,fwtC; s um,dm,ums,dms,QmS,QpS; s Gs,GsC,Gt,GtC,GsM2,GtM2; s Pws,Pwt,PwsC,PwtC,PwsM2,PwtM2; s [fws-fwt],[fwsC-fwtC],[Sigmas-Sigmat]; s Sigmas,SigmasC,Sigmat,SigmatC,SigmasM2; s y,s,rs,sp,t,tp,u,up,kp,km,zp,zm,tM,uM,X,zX,Xpo,Xph,tuM,tdM,Y; * f sl,sq,slC,sqC; f sum1_gg,sum1_zz,sum2; f wsub_gg,wsub_gz,wsub_zz; * cf es; cf redf; cf kf,qpf; cf Mods,Re; cf ae,au,ad; cf tv0,tv1,tv0C,tv1C; cf ve,vu,vd,ss,cs,csi; cf vvv,vvvC,wff,wffC,wffM2; cf I_uu_21,I_uu_22,I_uu_23,I_uu_24; cf I_dd_21,I_dd_22,I_dd_23,I_dd_24; cf I_nn_21,I_nn_22,I_nn_23,I_nn_24; cf I_un_21,I_un_22,I_un_23,I_un_24,I_un_25; cf I_dn_21,I_dn_22,I_dn_23,I_dn_24,I_dn_25; cf I_u_11,I_u_12,I_d_11,I_d_12,I_n_11,I_n_12; cf C00,B00t,B00s,B00g,C00C,B00tC,B00sC,B00gC; * .global * *---- * #procedure wtensor(compo) * * First W_{mu,nu} is constructed, gg or gz or zz * g w_'compo'= wsub_'compo'(mu,nu)*int; * id wsub_gg(mu?,nu?)= sum_(l1,1,4,sum1_gg(l1,mu,nu)); * id wsub_zz(mu?,nu?)= sum_(l1,5,9,sum1_zz(l1,mu,nu)); * id wsub_gz(mu?,nu?)= sum_(l1,1,4,sum1_zz(l1,mu,nu))+ sum_(l1,5,9,sum1_gg(l1,mu,nu)); * id sum1_gg(l?,mu?,nu?)= sum_(l2,1,4,sum2(l,l2,mu,nu)); id sum1_zz(l?,mu?,nu?)= sum_(l2,5,9,sum2(l,l2,mu,nu)); * id sum2(l?,lp?,mu?,nu?)= -sqC(i,l,nu)*(-i_*g_(i,k)+um*gi_(i))* sq(i,lp,mu)*(-i_*g_(i,kb)-dm*gi_(i))* slC(j,l,nu)*g_(j,pp)*sl(j,lp,mu)* (g_(j,pp)-g_(j,Qp)); * #call diagrams{dummy} * trace4,i; trace4,j; contract; * .store * #call kinematics{dummy} #call lin{'compo'} #call integration{'compo'} * #endprocedure * *--------------------------------------------------------------- * #procedure diagrams(dummy) * * The diagrams are constructed * id sl(i?,1,mu?)= i_/8*Gt* (tv0(mu,a1,a5)+Gs*(tv1(mu,a1,a5)-Sigmas*tv0(mu,a1,a5)))* es(T)*g_(i,a1)*g6_(i)/Pws/Pwt/s^2; id slC(i?,1,nu?)= i_/8*GtC* (tv0C(nu,b1,a6)+GsC*(tv1C(nu,b1,a6)-SigmasC*tv0C(nu,b1,a6)))* es(T)*g_(i,b1)*g6_(i)/PwsC/PwtC/s^2; * id sl(i?,5,mu?)= i_/32*Gt* (tv0(mu,aa1,aa5)+Gs*(tv1(mu,aa1,aa5)-Sigmas*tv0(mu,aa1,aa5)))* GT*PZ*g_(i,aa1)*g6_(i)/Pws/Pwt/s^3; id slC(i?,5,nu?)= i_/32*GtC* (tv0C(nu,bb1,aa6)+GsC*(tv1C(nu,bb1,aa6)-SigmasC*tv0C(nu,bb1,aa6)))* GT*PZ*g_(i,bb1)*g6_(i)/PwsC/PwtC/s^3; * al sl(i?,2,mu?)= i_/(8*y*s)*Gs*es(T)* g_(i,mu)*(g_(i,pp)+g_(i,Qm))*g_(i,a2)*g6_(i)/Pws/s; al slC(i?,2,nu?)= i_/(8*y*s)*GsC*es(T)* g_(i,b2)*g6_(i)*(g_(i,pp)+g_(i,Qm))*g_(i,nu)/PwsC/s; * al sl(i?,6,mu?)= -i_/(8*y*s)*Gs*GT*csi(T)/16*PZ* g_(i,mu)*(ve(T)*g6_(i)+ae(T)*g7_(i))* (g_(i,pp)+g_(i,Qm))*g_(i,aa2)*g6_(i)/Pws/s^2; al slC(i?,6,nu?)= -i_/(8*y*s)*GsC*GT*csi(T)/16*PZ* g_(i,bb2)*g6_(i)*(g_(i,pp)+g_(i,Qm))* g_(i,nu)*(ve(T)*g6_(i)+ae(T)*g7_(i))/PwsC/s^2; * al sl(i?,3,mu?)= i_/8*Qu*Gt*es(T)* g_(i,a3)*g6_(i)/Pwt/s/denk; al slC(i?,3,nu?)= i_/8*Qu*GtC*es(T)* g_(i,b3)*g6_(i)/PwtC/s/denk; * al sl(i?,7,mu?)= -i_/8*Gt*GT*csi(T)/16*PZ* g_(i,aa3)*g6_(i)/Pwt/s^2/denk; al slC(i?,7,nu?)= -i_/8*GtC*GT*csi(T)/16*PZ* g_(i,bb3)*g6_(i)/PwtC/s^2/denk; * al sl(i?,4,mu?)= -i_/8*Qd*Gt*es(T)* g_(i,a4)*g6_(i)/Pwt/s/denkb; al slC(i?,4,nu?)= -i_/8*Qd*GtC*es(T)* g_(i,b4)*g6_(i)/PwtC/s/denkb; * al sl(i?,8,mu?)= -i_/8*Gt*GT*cs(T)/16*PZ* g_(i,aa4)*g6_(i)/Pwt/s^2/denkb; al slC(i?,8,nu?)= -i_/8*GtC*GT*cs(T)/16*PZ* g_(i,bb4)*g6_(i)/PwtC/s^2/denkb; * al sl(i?,9,mu?)= i_/32/km*Gs*GT*csi(T)*PZ* g_(i,aa7)*g6_(i)*(g_(i,Qm)-g_(i,qp))* g_(i,mu)*g6_(i)/Pws/s^2; al slC(i?,9,nu?)= i_/32/km*GsC*GT*csi(T)*PZ* g_(i,nu)*g6_(i)*(g_(i,Qm)-g_(i,qp))* g_(i,bb7)*g6_(i)/PwsC/s^2; * id sq(i?,1,mu?)= g_(i,a5)*g6_(i); id sqC(i?,1,nu?)= -g_(i,a6)*g6_(i); * al sq(i?,5,mu?)= g_(i,aa5)*g6_(i); al sqC(i?,5,nu?)= -g_(i,aa6)*g6_(i); * al sq(i?,2,mu?)= g_(i,a2)*g6_(i); al sqC(i?,2,nu?)= -g_(i,b2)*g6_(i); * al sq(i?,6,mu?)= g_(i,aa2)*g6_(i); al sqC(i?,6,nu?)= -g_(i,bb2)*g6_(i); * al sq(i?,3,mu?)= g_(i,mu)*(g_(i,Qm)-g_(i,k)-i_*um*gi_(i))*g_(i,a3)*g6_(i); al sqC(i?,3,nu?)= g_(i,b3)*g6_(i)*(-(g_(i,Qm)-g_(i,k))+i_*um*gi_(i))*g_(i,nu); * al sq(i?,7,mu?)= g_(i,mu)*(vu(T)*g6_(i)+au(T)*g7_(i))* (g_(i,Qm)-g_(i,k)-i_*um*gi_(i))*g_(i,aa3)*g6_(i); al sqC(i?,7,nu?)= g_(i,bb3)*g6_(i)*(-(g_(i,Qm)-g_(i,k))+i_*um*gi_(i))* g_(i,nu)*(vu(T)*g6_(i)+au(T)*g7_(i)); * al sq(i?,4,mu?)= g_(i,a4)*g6_(i)*(g_(i,Qm)-g_(i,kb)+i_*dm*gi_(i))*g_(i,mu); al sqC(i?,4,nu?)= g_(i,nu)*(-(g_(i,Qm)-g_(i,kb))-i_*dm*gi_(i))*g_(i,b4)*g6_(i); * al sq(i?,8,mu?)= g_(i,aa4)*g6_(i)*(g_(i,Qm)-g_(i,kb)+i_*dm*gi_(i))* g_(i,mu)*(vd(T)*g6_(i)+ad(T)*g7_(i)) ; al sqC(i?,8,nu?)= g_(i,nu)*(vd(T)*g6_(i)+ad(T)*g7_(i))* (-(g_(i,Qm)-g_(i,kb))-i_*dm*gi_(i))*g_(i,bb4)*g6_(i); * al sq(i?,9,mu?)= g_(i,aa7)*g6_(i); al sqC(i?,9,nu?)= -g_(i,bb7)*g6_(i); * #endprocedure * .store * #procedure kinematics(dummy) * * Mostly kinematics * g ww_'compo'= w_'compo'; *nwrite statistics; * id Qu= 2/3; al Qd= -1/3; id srt^-2= 1/2; * id pp.pp= 0; al qp.qp= 0; al k.k= -ums; al kb.kb= -dms; al Qm.Qm= QmS; id um^2= ums; al dm^2= dms; * id Gs*GsC= GsM2; al Gt*GtC= GtM2; * id Pws^-1*PwsC^-1= 1/PwsM2; id Pwt^-1*PwtC^-1= 1/PwtM2; id Pws^-1= PwsC/PwsM2; id PwsC^-1= Pws/PwsM2; id Pwt^-1= PwtC/PwtM2; id PwtC^-1= Pwt/PwtM2; * * Triple-vertex is substituted * id tv0(mu?,al?,be?)= d_(mu,al)*(Qm(be)-Qp(be))+ d_(al,be)*(2*Qp(mu)+Qm(mu))- d_(mu,be)*(2*Qm(al)+Qp(al)); al tv0C(mu?,al?,be?)= d_(mu,al)*(Qm(be)-Qp(be))+ d_(al,be)*(2*Qp(mu)+Qm(mu))- d_(mu,be)*(2*Qm(al)+Qp(al)); id tv1(mu?,al?,be?)= sum_(lv,1,10,(vvv(lv,mu,al,be))); id tv1C(mu?,al?,be?)= sum_(lv,1,10,(vvvC(lv,mu,al,be))); * * Form factors are introduced * id vvv(1,mu?,al?,be?)= 4*wff(1)/rs*(d_(al,be)*Qp(mu)+ d_(mu,al)*Qm(be)-d_(mu,be)*(Qm(al)+Qp(al))); id vvv(2,mu?,al?,be?)= 2*wff(2)/rs*(d_(mu,al)*Qm(be)-d_(mu,be)*(Qm(al)+Qp(al))); id vvv(3,mu?,al?,be?)= 2*wff(3)/rs*(d_(mu,al)*Qm(be)+d_(mu,be)*(Qm(al)+Qp(al))); id vvv(4,mu?,al?,be?)= 2*wff(4)/rs/(X*y*s)*Qm(be)*(Qp(al)+Qm(al))*Qp(mu); id vvv(5,mu?,al?,be?)= wff(5)/rs*e_(Qm,mu,al,be); id vvv(6,mu?,al?,be?)= wff(6)/rs*(e_(Qm,mu,al,be)+2*e_(Qp,mu,al,be)); id vvv(7,mu?,al?,be?)= wff(7)/rs/(X*y*s)*e_(Qp,Qm,al,be)*(Qp(mu)+Qm(mu)); id vvv(8,mu?,al?,be?)= 2*wff(8)/rs/(X*y*s)*Qm(be)*Qm(mu)*(Qp(al)+Qm(al)); id vvv(9,mu?,al?,be?)= 2*wff(9)/rs*d_(al,be)*Qm(mu); id vvv(10,mu?,al?,be?)= -wff(10)/rs/(X*y*s)*e_(Qp,Qm,al,be)*Qp(mu); * id vvvC(1,mu?,al?,be?)= 4*wffC(1)/rs*(d_(al,be)*Qp(mu)+ d_(mu,al)*Qm(be)-d_(mu,be)*(Qm(al)+Qp(al))); id vvvC(2,mu?,al?,be?)= 2*wffC(2)/rs*(d_(mu,al)*Qm(be)-d_(mu,be)* (Qm(al)+Qp(al))); id vvvC(3,mu?,al?,be?)= 2*wffC(3)/rs*(d_(mu,al)*Qm(be)+d_(mu,be)* (Qm(al)+Qp(al))); id vvvC(4,mu?,al?,be?)= 2*wffC(4)/rs/(X*y*s)*Qm(be)*(Qp(al)+Qm(al))*Qp(mu); id vvvC(5,mu?,al?,be?)= -wffC(5)/rs*e_(Qm,mu,al,be); id vvvC(6,mu?,al?,be?)= -wffC(6)/rs*(e_(Qm,mu,al,be)+2*e_(Qp,mu,al,be)); id vvvC(7,mu?,al?,be?)= -wffC(7)/rs/(X*y*s)*e_(Qp,Qm,al,be)*(Qp(mu)+Qm(mu)); id vvvC(8,mu?,al?,be?)= 2*wffC(8)/rs/(X*y*s)*Qm(be)*Qm(mu)*(Qp(al)+Qm(al)); id vvvC(9,mu?,al?,be?)= 2*wffC(9)/rs*d_(al,be)*Qm(mu); id vvvC(10,mu?,al?,be?)= wffC(10)/rs/(X*y*s)*e_(Qp,Qm,al,be)*Qp(mu); * contract; * id Sigmas= 0; al SigmasC= 0; *id Sigmas*SigmasC= SigmasM2; * id BQ(mu?)= pp(mu)-qp(mu)+Qm(mu); id Qp(mu?)= pp(mu)-qp(mu); * id e_(a1?,Qp,a2?,a3?)= e_(a1,pp,a2,a3)-e_(a1,qp,a2,a3); id e_(a1?,a2?,Qp,a3?)= e_(a1,a2,pp,a3)-e_(a1,a2,qp,a3); id e_(a1?,a2?,a3?,Qp)= e_(a1,a2,a3,pp)-e_(a1,a2,a3,qp); * id Qp.Qm= pp.Qm-qp.Qm; id kb.Qp= kb.pp-kb.qp; id k.Qp= k.pp-k.qp; id pp.Qp= -pp.qp; id Qp.Qp= -2*pp.qp; * .store * #endprocedure * #procedure lin(compo) * * Linear independent invariants are introduced * g www_'compo'= ww_'compo'; *nwrite statistics; * contract; * id k.k= -ums; al kb.kb= -dms; * id denk^-1*denkb^-1= -1/2/(Qp.Qm)*(1/denk+1/denkb); * id pp.pp= 0; al qp.qp= 0; al k.k= -ums; al kb.kb= -dms; al Qm.Qm= QmS; * id denk^-1= -1/tM; id denkb^-1= -1/uM; * id e_(kb,a1?,a2?,a3?)= e_(pp,a1,a2,a3)-e_(qp,a1,a2,a3)+e_(Qm,a1,a2,a3)- e_(k,a1,a2,a3); id kb(mu?)= pp(mu)-qp(mu)+Qm(mu)-k(mu); id QpS= -2*pp.qp; id Qp.Qm= pp.Qm-qp.Qm; id kb.Qp= kb.pp-kb.qp; id k.Qp= k.pp-k.qp; id pp.Qp= -pp.qp; id Qp.Qp= -2*pp.qp; * id pp.Qm= -1/2*(QmS+y*s); al k.kb= 1/2*(-sp+ums+dms); al Qm.k= 1/2*(QmS+t-ums); al pp.kb= 1/2*(tp-dms); al Qm.kb= 1/2*(QmS+u-dms); al pp.k= 1/2*(up-ums); al pp.qp= 1/2*kp; al Qm.qp= 1/2*(QmS+km); al kb.qp= 1/2*(dms-zp); al k.qp= 1/2*(ums-zm); * id t= tau*y*s; al sp= x2*y*s; al km= z*y*s; al km^-1= 1/(z*y*s); al zm= -(x2-x1)*y*s; id QmS= X*y*s; * ratio,tM,t,ums; ratio,uM,u,dms; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g wwww_'compo'= www_'compo'; *nwrite statistics; * id kp= y*s * ( - 1 - X + x2 - z ); al u= y*s * ( - 1 - tau - 2*X - z ) + ums + dms; al up= y*s * ( - tau - X - x1 ) + 2*ums + dms; al tp= y*s * ( tau + X + x1 - x2 + z ) - ums; al zp= y*s * ( 1 - x1 ) + ums + dms; * id Qp.Qm^-1= -2/(zX*y*s); ratio,z,zX,aux; id aux= 1+2*X; id aux^-1= 1/2/Xph; ratio,X,Xph,aux; id aux= 1/2; al aux^-1= 2; * id k(mu?)= kf(mu); id qp(mu?)= qpf(mu); al e_(k,mu?,nu?,al?)= kf(a1)*e_(a1,mu,nu,al); al e_(qp,mu?,nu?,al?)= qpf(a1)*e_(a1,mu,nu,al); * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * #endprocedure * #procedure integration(compo) * * Integration starts * g WT1_'compo'= wwww_'compo'; *nwrite statistics; * id kf(mu?)*kf(nu?)*int= I_uu_21*pp(mu)*pp(nu)+I_uu_22*Qm(mu)*Qm(nu)+ I_uu_23*(pp(mu)*Qm(nu)+pp(nu)*Qm(mu))+ I_uu_24*d_(mu,nu); * .store * g WT2_'compo'= WT1_'compo'; *nwrite statistics; * id qpf(mu?)*qpf(nu?)*int= I_nn_21*pp(mu)*pp(nu)+I_nn_22*Qm(mu)*Qm(nu)+ I_nn_23*(pp(mu)*Qm(nu)+pp(nu)*Qm(mu))+ I_nn_24*d_(mu,nu); * .store * g WT3_'compo'= WT2_'compo'; *nwrite statistics; * id kf(mu?)*qpf(nu?)*int= I_un_21*pp(mu)*pp(nu)+I_un_22*Qm(mu)*Qm(nu)+ I_un_23*pp(mu)*Qm(nu)+I_un_24*pp(nu)*Qm(mu)+ I_un_25*d_(mu,nu); * .store * g WT4_'compo'= WT3_'compo'; *nwrite statistics; * id kf(mu?)*int= I_u_11*pp(mu)+I_u_12*Qm(mu); id qpf(mu?)*int= I_n_11*pp(mu)+I_n_12*Qm(mu); id int= I0; * * .store * g W_'compo'_int1= WT4_'compo'; *nwrite statistics; * id I_u_11 = + I0*ums*Xpo^-2*y^-1*s^-1 * ( 2 ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 1 ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 2 ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 2 ) + I0*Xpo^-2 * ( 2 - 2*tau - 2*x1 ) + I0*Xpo^-1 * ( - 3 + tau + 2*x1 ) + I0 * ( 1 ); al I_n_11 = + I0*Xpo^-2 * ( 2*x2 - 2*z ) + I0*Xpo^-1 * ( - 1 - 2*x2 + z ) + I0 * ( 1 ); al I_u_12 = + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 1 ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 1 ) + I0*Xpo^-1 * ( - 1 + tau + x1 ) + I0 * ( 1 ); al I_n_12 = + I0*Xpo^-1 * ( - x2 + z ) + I0 * ( 1 ); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g W_'compo'_int2= W_'compo'_int1; *nwrite statistics; * id I_uu_21 = + I0*ums*Xpo^-4*y^-1*s^-1 * ( 12 - 12*tau - 12*x1 ) + I0*ums*Xpo^-3*y^-1*s^-1 * ( - 24 + 12*tau + 18*x1 ) + I0*ums*Xpo^-2*y^-1*s^-1 * ( 16 - 2*tau - 6*x1 ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 4 ) + I0*dms*Xpo^-4*y^-1*s^-1 * ( 12 - 12*tau - 12*x1 ) + I0*dms*Xpo^-3*y^-1*s^-1 * ( - 30 + 18*tau + 24*x1 ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 24 - 6*tau - 12*x1 ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 6 ) + I0*Xpo^-4 * ( 6 + 12*tau*x1 - 12*tau + 6*tau^2 - 12*x1 + 6*x1^2 ) + I0*Xpo^-3 * ( - 18 - 18*tau*x1 + 24*tau - 6*tau^2 + 30*x1 - 12*x1^2 ) + I0*Xpo^-2 * ( 19 + 6*tau*x1 - 14*tau + tau^2 - 24*x1 + 6*x1^2 ) + I0*Xpo^-1 * ( - 8 + 2*tau + 6*x1 ) + I0 * ( 1 ); al I_nn_21 = + I0*Xpo^-4 * ( - 12*x2*z + 6*x2^2 + 6*z^2 ) + I0*Xpo^-3 * ( 18*x2*z - 6*x2 - 12*x2^2 + 6*z - 6*z^2 ) + I0*Xpo^-2 * ( 1 - 6*x2*z + 12*x2 + 6*x2^2 - 8*z + z^2 ) + I0*Xpo^-1 * ( - 2 - 6*x2 + 2*z ) + I0 * ( 1 ); al I_un_21 = + I0*ums*Xpo^-4*y^-1*s^-1 * ( 6*x2 - 6*z ) + I0*ums*Xpo^-3*y^-1*s^-1 * ( - 3 - 9*x2 + 6*z ) + I0*ums*Xpo^-2*y^-1*s^-1 * ( 3 + 3*x2 - z ) + I0*dms*Xpo^-4*y^-1*s^-1 * ( 6*x2 - 6*z ) + I0*dms*Xpo^-3*y^-1*s^-1 * ( - 3 - 12*x2 + 9*z ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 6 + 6*x2 - 3*z ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 3 ) + I0*Xpo^-4 * ( - 6*tau*x2 + 6*tau*z - 6*x1*x2 + 6*x1*z + 6*x2 - 6*z ) + I0*Xpo^-3 * ( - 3 + 9*tau*x2 - 6*tau*z + 3*tau + 12*x1*x2 - 9*x1*z + 3*x1 - 15*x2 + 12*z ) + I0*Xpo^-2 * ( 7 - 3*tau*x2 + tau*z - 4*tau - 6*x1*x2 + 3*x1*z - 5*x1 + 11*x2 - 7*z ) + I0*Xpo^-1 * ( - 5 + tau + 2*x1 - 2*x2 + z ) + I0 * ( 1 ); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g W_'compo'_int3= W_'compo'_int2; *nwrite statistics; * id I_uu_22 = + I0*ums*Xpo^-2*y^-1*s^-1 * ( 2 - 2*tau - 2*x1 ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 2 ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 2 - 2*tau - 2*x1 ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 2 ) + I0*Xpo^-2 * ( 1 + 2*tau*x1 - 2*tau + tau^2 - 2*x1 + x1^2 ) + I0*Xpo^-1 * ( - 2 + 2*tau + 2*x1 ) + I0 * ( 1 ); al I_nn_22 = + I0*Xpo^-2 * ( - 2*x2*z + x2^2 + z^2 ) + I0*Xpo^-1 * ( - 2*x2 + 2*z ) + I0 * ( 1 ); al I_un_22 = + I0*ums*Xpo^-2*y^-1*s^-1 * ( x2 - z ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 1 ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( x2 - z ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 1 ) + I0*Xpo^-2 * ( - tau*x2 + tau*z - x1*x2 + x1*z + x2 - z ) + I0*Xpo^-1 * ( - 1 + tau + x1 - x2 + z ) + I0 * ( 1 ); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g W_'compo'_int4= W_'compo'_int3; *nwrite statistics; * id I_uu_23 = + I0*ums*Xpo^-3*y^-1*s^-1 * ( - 6 + 6*tau + 6*x1 ) + I0*ums*Xpo^-2*y^-1*s^-1 * ( 8 - 2*tau - 4*x1 ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 3 ) + I0*dms*Xpo^-3*y^-1*s^-1 * ( - 6 + 6*tau + 6*x1 ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 10 - 4*tau - 6*x1 ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 4 ) + I0*Xpo^-3 * ( - 3 - 6*tau*x1 + 6*tau - 3*tau^2 + 6*x1 - 3*x1^2 ) + I0*Xpo^-2 * ( 7 + 4*tau*x1 - 8*tau + tau^2 - 10*x1 + 3*x1^2 ) + I0*Xpo^-1 * ( - 5 + 2*tau + 4*x1 ) + I0 * ( 1 ); al I_nn_23 = + I0*Xpo^-3 * ( 6*x2*z - 3*x2^2 - 3*z^2 ) + I0*Xpo^-2 * ( - 4*x2*z + 4*x2 + 3*x2^2 - 4*z + z^2 ) + I0*Xpo^-1 * ( - 1 - 4*x2 + 2*z ) + I0 * ( 1 ); al I_un_23 = + I0*ums*Xpo^-3*y^-1*s^-1 * ( - 3*x2 + 3*z ) + I0*ums*Xpo^-2*y^-1*s^-1 * ( 5/2 + 3/2*x2 - z ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 1/2 ) + I0*dms*Xpo^-3*y^-1*s^-1 * ( - 3*x2 + 3*z ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 5/2 + 3*x2 - 5/2*z ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 5/2 ) + I0*Xpo^-3 * ( 3*tau*x2 - 3*tau*z + 3*x1*x2 - 3*x1*z - 3*x2 + 3*z ) + I0*Xpo^-2 * ( 5/2 - 3/2*tau*x2 + tau*z - 5/2*tau - 3*x1*x2 + 5/2*x1*z - 5/2*x1 + 9/2*x2 - 4*z ) + I0*Xpo^-1 * ( - 7/2 + tau + 2*x1 - x2 + z ) + I0 * ( 1 ); ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g W_'compo'_int5= W_'compo'_int4; *nwrite statistics; * id I_uu_24 = + I0*ums*Xpo^-2 * ( - 1 + tau + x1 ) + I0*ums*Xpo^-1 * ( 1 - 1/2*x1 ) + I0*ums * ( - 1/2 ) + I0*dms*Xpo^-2 * ( - 1 + tau + x1 ) + I0*dms*Xpo^-1 * ( 3/2 - 1/2*tau - x1 ) + I0*dms * ( - 1/2 ) + I0*Xpo^-2*y*s * ( - 1/2 - tau*x1 + tau - 1/2*tau^2 + x1 - 1/2*x1^2 ) + I0*Xpo^-1*y*s * ( 1 + 1/2*tau*x1 - tau - 3/2*x1 + 1/2*x1^2 ) + I0*y*s * ( - 1/2 + 1/2*x1 ); al I_nn_24 = + I0*Xpo^-2*y*s * ( x2*z - 1/2*x2^2 - 1/2*z^2 ) + I0*Xpo^-1*y*s * ( - 1/2*x2*z + 1/2*x2 + 1/2*x2^2 - 1/2*z ) + I0*y*s * ( - 1/2*x2 ); al I_un_24 = + I0*ums*Xpo^-3*y^-1*s^-1 * ( - 3*x2 + 3*z ) + I0*ums*Xpo^-2*y^-1*s^-1 * ( 3/2 + 5/2*x2 - z ) + I0*ums*Xpo^-1*y^-1*s^-1 * ( - 1/2 ) + I0*dms*Xpo^-3*y^-1*s^-1 * ( - 3*x2 + 3*z ) + I0*dms*Xpo^-2*y^-1*s^-1 * ( 3/2 + 3*x2 - 3/2*z ) + I0*dms*Xpo^-1*y^-1*s^-1 * ( - 3/2 ) + I0*Xpo^-3 * ( 3*tau*x2 - 3*tau*z + 3*x1*x2 - 3*x1*z - 3*x2 + 3*z ) + I0*Xpo^-2 * ( 3/2 - 5/2*tau*x2 + tau*z - 3/2*tau - 3*x1*x2 + 3/2*x1*z - 3/2*x1 + 11/2*x2 - 4*z ) + I0*Xpo^-1 * ( - 5/2 + tau + x1 - 2*x2 + z ) + I0 * ( 1 ); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * .store * g W_'compo'_int6= W_'compo'_int5; *nwrite statistics; * id I_un_25 = + I0*ums*Xpo^-2 * ( - 1/2*x2 + 1/2*z ) + I0*ums*Xpo^-1 * ( 1/4 + 1/4*x2 ) + I0*ums * ( 1/4 ) + I0*dms*Xpo^-2 * ( - 1/2*x2 + 1/2*z ) + I0*dms*Xpo^-1 * ( 1/4 + 1/2*x2 - 1/4*z ) + I0*dms * ( - 1/4 ) + I0*Xpo^-2*y*s * ( 1/2*tau*x2 - 1/2*tau*z + 1/2*x1*x2 - 1/2*x1*z - 1/2 *x2 + 1/2*z ) + I0*Xpo^-1*y*s * ( 1/4 - 1/4*tau*x2 - 1/4*tau - 1/2*x1*x2 + 1/4*x1*z - 1/4*x1 + 3/4*x2 - 1/2*z ) + I0*y*s * ( - 1/4 ); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id ums*tM^-2= aux; id ums= 0; id aux= ums*tM^-2; id dms*uM^-2= aux; id dms= 0; id aux= dms*uM^-2; * id tM^-1= 1/(y*s)/tuM; id uM^-1= -1/(y*s)/tdM; * ratio,tuM,tau,aux; id aux= ums/(y*s); ratio,tdM,tau,aux; id aux= ums/(y*s)-z-1-2*X; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * ratio,z,zX,aux; id aux= 1+2*X; * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * .store * *save wrl$grp04:[giampiero]outputampgg.sav W_'compo'_int6; save wrl$grp04:[giampiero]outputampgz.sav W_'compo'_int6; *save wrl$grp04:[giampiero]outputampzz.sav W_'compo'_int6; * #endprocedure * #procedure totalgg(dummy) * * Now the full stuff * load wrl$grp04:[giampiero]outputampgg.sav; * g T_gg= PwsM2*PwtM2*W_gg_int6/(eq*I0); *nwrite statistics; * id es(T)*es(T)= eq; * id wff(n?)*wffC(n?)= wffM2(n); * id GtM2*GsM2*wff(2)*wffC(1)= GtM2*GsM2*(-wffC(2)*wff(1)+ 2*Re(wff(2)*wffC(1))); al GtM2*GsM2*wff(3)*wffC(1)= GtM2*GsM2*(-wffC(3)*wff(1)+ 2*Re(wff(3)*wffC(1))); al GtM2*GsM2*wff(4)*wffC(1)= GtM2*GsM2*(-wffC(4)*wff(1)+ 2*Re(wff(4)*wffC(1))); al GtM2*GsM2*wff(5)*wffC(1)= GtM2*GsM2*(-wffC(5)*wff(1)+ 2*Re(wff(5)*wffC(1))); al GtM2*GsM2*wff(6)*wffC(1)= GtM2*GsM2*(-wffC(6)*wff(1)+ 2*Re(wff(6)*wffC(1))); al GtM2*GsM2*wff(7)*wffC(1)= GtM2*GsM2*(-wffC(7)*wff(1)+ 2*Re(wff(7)*wffC(1))); al GtM2*GsM2*wff(8)*wffC(1)= GtM2*GsM2*(-wffC(8)*wff(1)+ 2*Re(wff(8)*wffC(1))); al GtM2*GsM2*wff(9)*wffC(1)= GtM2*GsM2*(-wffC(9)*wff(1)+ 2*Re(wff(9)*wffC(1))); al GtM2*GsM2*wff(10)*wffC(1)= GtM2*GsM2*(-wffC(10)*wff(1)+ 2*Re(wff(10)*wffC(1))); * al GtM2*GsM2*wff(3)*wffC(2)= GtM2*GsM2*(-wffC(3)*wff(2)+ 2*Re(wff(3)*wffC(2))); al GtM2*GsM2*wff(4)*wffC(2)= GtM2*GsM2*(-wffC(4)*wff(2)+ 2*Re(wff(4)*wffC(2))); al GtM2*GsM2*wff(5)*wffC(2)= GtM2*GsM2*(-wffC(5)*wff(2)+ 2*Re(wff(5)*wffC(2))); al GtM2*GsM2*wff(6)*wffC(2)= GtM2*GsM2*(-wffC(6)*wff(2)+ 2*Re(wff(6)*wffC(2))); al GtM2*GsM2*wff(7)*wffC(2)= GtM2*GsM2*(-wffC(7)*wff(2)+ 2*Re(wff(7)*wffC(2))); al GtM2*GsM2*wff(8)*wffC(2)= GtM2*GsM2*(-wffC(8)*wff(2)+ 2*Re(wff(8)*wffC(2))); al GtM2*GsM2*wff(9)*wffC(2)= GtM2*GsM2*(-wffC(9)*wff(2)+ 2*Re(wff(9)*wffC(2))); al GtM2*GsM2*wff(10)*wffC(2)= GtM2*GsM2*(-wffC(10)*wff(2)+ 2*Re(wff(10)*wffC(2))); * al GtM2*GsM2*wff(4)*wffC(3)= GtM2*GsM2*(-wffC(4)*wff(3)+ 2*Re(wff(4)*wffC(3))); al GtM2*GsM2*wff(5)*wffC(3)= GtM2*GsM2*(-wffC(5)*wff(3)+ 2*Re(wff(5)*wffC(3))); al GtM2*GsM2*wff(6)*wffC(3)= GtM2*GsM2*(-wffC(6)*wff(3)+ 2*Re(wff(6)*wffC(3))); al GtM2*GsM2*wff(7)*wffC(3)= GtM2*GsM2*(-wffC(7)*wff(3)+ 2*Re(wff(7)*wffC(3))); al GtM2*GsM2*wff(8)*wffC(3)= GtM2*GsM2*(-wffC(8)*wff(3)+ 2*Re(wff(8)*wffC(3))); al GtM2*GsM2*wff(9)*wffC(3)= GtM2*GsM2*(-wffC(9)*wff(3)+ 2*Re(wff(9)*wffC(3))); al GtM2*GsM2*wff(10)*wffC(3)= GtM2*GsM2*(-wffC(10)*wff(3)+ 2*Re(wff(10)*wffC(3))); * al GtM2*GsM2*wff(5)*wffC(4)= GtM2*GsM2*(-wffC(5)*wff(4)+ 2*Re(wff(5)*wffC(4))); al GtM2*GsM2*wff(6)*wffC(4)= GtM2*GsM2*(-wffC(6)*wff(4)+ 2*Re(wff(6)*wffC(4))); al GtM2*GsM2*wff(7)*wffC(4)= GtM2*GsM2*(-wffC(7)*wff(4)+ 2*Re(wff(7)*wffC(4))); al GtM2*GsM2*wff(8)*wffC(4)= GtM2*GsM2*(-wffC(8)*wff(4)+ 2*Re(wff(8)*wffC(4))); al GtM2*GsM2*wff(9)*wffC(4)= GtM2*GsM2*(-wffC(9)*wff(4)+ 2*Re(wff(9)*wffC(4))); al GtM2*GsM2*wff(10)*wffC(4)= GtM2*GsM2*(-wffC(10)*wff(4)+ 2*Re(wff(10)*wffC(4))); * al GtM2*GsM2*wff(6)*wffC(5)= GtM2*GsM2*(-wffC(6)*wff(5)+ 2*Re(wff(6)*wffC(5))); al GtM2*GsM2*wff(7)*wffC(5)= GtM2*GsM2*(-wffC(7)*wff(5)+ 2*Re(wff(7)*wffC(5))); al GtM2*GsM2*wff(8)*wffC(5)= GtM2*GsM2*(-wffC(8)*wff(5)+ 2*Re(wff(8)*wffC(5))); al GtM2*GsM2*wff(9)*wffC(5)= GtM2*GsM2*(-wffC(9)*wff(5)+ 2*Re(wff(9)*wffC(5))); al GtM2*GsM2*wff(10)*wffC(5)= GtM2*GsM2*(-wffC(10)*wff(5)+ 2*Re(wff(10)*wffC(5))); * al GtM2*GsM2*wff(7)*wffC(6)= GtM2*GsM2*(-wffC(7)*wff(6)+ 2*Re(wff(7)*wffC(6))); al GtM2*GsM2*wff(8)*wffC(6)= GtM2*GsM2*(-wffC(8)*wff(6)+ 2*Re(wff(8)*wffC(6))); al GtM2*GsM2*wff(9)*wffC(6)= GtM2*GsM2*(-wffC(9)*wff(6)+ 2*Re(wff(9)*wffC(6))); al GtM2*GsM2*wff(10)*wffC(6)= GtM2*GsM2*(-wffC(10)*wff(6)+ 2*Re(wff(10)*wffC(6))); * al GtM2*GsM2*wff(8)*wffC(7)= GtM2*GsM2*(-wffC(8)*wff(7)+ 2*Re(wff(8)*wffC(7))); al GtM2*GsM2*wff(9)*wffC(7)= GtM2*GsM2*(-wffC(9)*wff(7)+ 2*Re(wff(9)*wffC(7))); al GtM2*GsM2*wff(10)*wffC(7)= GtM2*GsM2*(-wffC(10)*wff(7)+ 2*Re(wff(10)*wffC(7))); * al GtM2*GsM2*wff(9)*wffC(8)= GtM2*GsM2*(-wffC(9)*wff(8)+ 2*Re(wff(9)*wffC(8))); al GtM2*GsM2*wff(10)*wffC(8)= GtM2*GsM2*(-wffC(10)*wff(8)+ 2*Re(wff(10)*wffC(8))); * al GtM2*GsM2*wff(10)*wffC(9)= GtM2*GsM2*(-wffC(10)*wff(9)+ 2*Re(wff(10)*wffC(9))); * id GtM2*Gs*PwsC*Sigmas= GtM2*(-GsC*Pws*SigmasC+2*Re(Gs*PwsC*Sigmas)); id GsM2*GtM2*wff(n?)*SigmasC= GsM2*GtM2*(-wffC(n)*Sigmas+2*Re(wff(n)*SigmasC)); * id GtM2*Gs*Sigmas= GtM2*(-GsC*SigmasC+2*Re(Gs*Sigmas)); id GsM2*Gt*Sigmas= GsM2*(-GtC*SigmasC+2*Re(Gt*Sigmas)); * id wff(n?)*Gs*GtM2*PwsC= GtM2*(-wffC(n)*GsC*Pws+2*Re(wff(n)*Gs*PwsC)); id wff(n?)*Gt*GsM2*PwtC= GsM2*(-wffC(n)*GtC*Pwt+2*Re(wff(n)*Gt*PwtC)); * id GsM2*GtC*PwtC*wffC(n?)= GsM2*(-Gt*Pwt*wff(n)+2*Re(Gt*Pwt*wff(n))); id GtM2*GsC*PwsC*wffC(n?)= GtM2*(-Gs*Pws*wff(n)+2*Re(Gs*Pws*wff(n))); * id Gt*GsM2*PwtC*Sigmas= -GtC*GsM2*Pwt*SigmasC+2*GsM2*Re(Gt*PwtC*Sigmas); id Gs*GtM2*PwsC*Sigmas= -GsC*GtM2*Pws*SigmasC+2*GtM2*Re(Gs*PwsC*Sigmas); * id Gs*GtM2*Sigmas= -GsC*GtM2*SigmasC+GtM2*Re(Gs*Sigmas); id Gt*GsM2*Sigmas= -GtC*GsM2*SigmasC+GsM2*Re(Gt*Sigmas); * id GsM2*GtC*PwtC= GsM2*(-Gt*Pwt+2*Re(Gt*Pwt)); id GtM2*GsC*PwsC= GtM2*(-Gs*Pws+2*Re(Gs*Pws)); * id GsC*PwsC*Gt*Pwt= -Gs*Pws*GtC*PwtC+2*Re(GsC*Gt*PwsC*Pwt); id GsC*Gt*Pws*PwtC= -Gs*GtC*PwsC*Pwt+2*Re(Gs*GtC*PwsC*Pwt); * id Gs*GtC*Pwt= -GsC*Gt*PwtC+2*Re(Gs*GtC*Pwt); * id GtM2*PwsC= GtM2*(-Pws+2*Re(Pws)); id GsM2*PwtC= GsM2*(-Pwt+2*Re(Pwt)); * id wff(n?)*Gs*GtM2= GtM2*(-GsC*wffC(n)+2*Re(Gs*wff(n))); id wff(n?)*Gt*GsM2= GsM2*(-GtC*wffC(n)+2*Re(Gt*wff(n))); * id Re(wffC(2)*wff(1))= Re(wff(2)*wffC(1)); al Re(wffC(3)*wff(1))= Re(wff(3)*wffC(1)); al Re(wffC(4)*wff(1))= Re(wff(4)*wffC(1)); al Re(wffC(5)*wff(1))= Re(wff(5)*wffC(1)); al Re(wffC(6)*wff(1))= Re(wff(6)*wffC(1)); al Re(wffC(7)*wff(1))= Re(wff(7)*wffC(1)); al Re(wffC(8)*wff(1))= Re(wff(8)*wffC(1)); al Re(wffC(9)*wff(1))= Re(wff(9)*wffC(1)); al Re(wffC(10)*wff(1))= Re(wff(10)*wffC(1)); * id Re(wffC(3)*wff(2))= Re(wff(3)*wffC(2)); al Re(wffC(4)*wff(2))= Re(wff(4)*wffC(2)); al Re(wffC(5)*wff(2))= Re(wff(5)*wffC(2)); al Re(wffC(6)*wff(2))= Re(wff(6)*wffC(2)); al Re(wffC(7)*wff(2))= Re(wff(7)*wffC(2)); al Re(wffC(8)*wff(2))= Re(wff(8)*wffC(2)); al Re(wffC(9)*wff(2))= Re(wff(9)*wffC(2)); al Re(wffC(10)*wff(2))= Re(wff(10)*wffC(2)); * id Re(wffC(4)*wff(3))= Re(wff(4)*wffC(3)); al Re(wffC(5)*wff(3))= Re(wff(5)*wffC(3)); al Re(wffC(6)*wff(3))= Re(wff(6)*wffC(3)); al Re(wffC(7)*wff(3))= Re(wff(7)*wffC(3)); al Re(wffC(8)*wff(3))= Re(wff(8)*wffC(3)); al Re(wffC(9)*wff(3))= Re(wff(9)*wffC(3)); al Re(wffC(10)*wff(3))= Re(wff(10)*wffC(3)); * id Re(wffC(5)*wff(4))= Re(wff(5)*wffC(4)); al Re(wffC(6)*wff(4))= Re(wff(6)*wffC(4)); al Re(wffC(7)*wff(4))= Re(wff(7)*wffC(4)); al Re(wffC(8)*wff(4))= Re(wff(8)*wffC(4)); al Re(wffC(9)*wff(4))= Re(wff(9)*wffC(4)); al Re(wffC(10)*wff(4))= Re(wff(10)*wffC(4)); * id Re(wffC(6)*wff(5))= Re(wff(6)*wffC(5)); al Re(wffC(7)*wff(5))= Re(wff(7)*wffC(5)); al Re(wffC(8)*wff(5))= Re(wff(8)*wffC(5)); al Re(wffC(9)*wff(5))= Re(wff(9)*wffC(5)); al Re(wffC(10)*wff(5))= Re(wff(10)*wffC(5)); * id Re(wffC(7)*wff(6))= Re(wff(7)*wffC(6)); al Re(wffC(8)*wff(6))= Re(wff(8)*wffC(6)); al Re(wffC(9)*wff(6))= Re(wff(9)*wffC(6)); al Re(wffC(10)*wff(6))= Re(wff(10)*wffC(6)); * id Re(wffC(8)*wff(7))= Re(wff(8)*wffC(7)); al Re(wffC(9)*wff(7))= Re(wff(9)*wffC(7)); al Re(wffC(10)*wff(7))= Re(wff(10)*wffC(7)); * id Re(wffC(9)*wff(8))= Re(wff(9)*wffC(8)); al Re(wffC(10)*wff(8))= Re(wff(10)*wffC(8)); * id Re(wffC(10)*wff(9))= Re(wff(10)*wffC(9)); * .store * #endprocedure * #procedure contractgg(dummy) * g Wd_gg= T_gg*d_(mu,nu); g Wpp_gg= T_gg*pp(mu)*pp(nu); * id rs^-2= -1/(X*y*s); id pp.pp= 0; al qp.qp= 0; al Qm.Qm= QmS; id Qp.Qm= pp.Qm-qp.Qm; id kb.Qp= kb.pp-kb.qp; id k.Qp= k.pp-k.qp; id pp.Qp= -pp.qp; id Qp.Qp= -2*pp.qp; * id pp.Qm= -1/2*(QmS+y*s); al k.kb= 1/2*(-sp+ums+dms); al Qm.k= 1/2*(QmS+t-ums); al pp.kb= 1/2*(tp-dms); al Qm.kb= 1/2*(QmS+u-dms); al pp.k= 1/2*(up-ums); al pp.qp= 1/2*kp; al Qm.qp= 1/2*(QmS+km); al kb.qp= 1/2*(dms-zp); al k.qp= 1/2*(ums-zm); * id t= tau*y*s; al sp= x2*y*s; al km= z*y*s; al km^-1= 1/(z*y*s); al zm= -(x2-x1)*y*s; id QmS= X*y*s; * ratio,tM,t,ums; ratio,uM,u,dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * id kp= y*s * ( - 1 - X + x2 - z ); al u= y*s * ( - 1 - tau - 2*X - z ) + ums + dms; al up= y*s * ( - tau - X - x1 ) + 2*ums + dms; al tp= y*s * ( tau + X + x1 - x2 + z ) - ums; al zp= y*s * ( 1 - x1 ) + ums + dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * .store * g W1_gg= -1/2*Wd_gg-2*X/Xpo^2*Wpp_gg/(y*s); g W2_gg= -1/2*Wd_gg-6*X/Xpo^2*Wpp_gg/(y*s); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * *-- id Re(wff(n?)*wffC(2))= 1/2*(Re(wff(n)*wffC([2+3]))+Re(wff(n)*wffC([2-3]))); id Re(wff(n?)*wffC(3))= 1/2*(Re(wff(n)*wffC([2+3]))-Re(wff(n)*wffC([2-3]))); id Re(wff(2)*wffC(2))= wffM2(2); id Re(wff(3)*wffC(3))= wffM2(3); * id Re(wff(2)*wffC(n?))= 1/2*(Re(wff([2+3])*wffC(n))+Re(wff([2-3])*wffC(n))); id Re(wff(3)*wffC(n?))= 1/2*(Re(wff([2+3])*wffC(n))-Re(wff([2-3])*wffC(n))); id Re(wff(2)*wffC(2))= wffM2(2); id Re(wff(3)*wffC(3))= wffM2(3); * id Re(wff(n?)*wffC(5))= 1/2*(Re(wff(n)*wffC([5+6]))+Re(wff(n)*wffC([5-6]))); id Re(wff(n?)*wffC(6))= 1/2*(Re(wff(n)*wffC([5+6]))-Re(wff(n)*wffC([5-6]))); id Re(wff(5)*wffC(5))= wffM2(5); id Re(wff(6)*wffC(6))= wffM2(6); * id Re(wff(5)*wffC(n?))= 1/2*(Re(wff([5+6])*wffC(n))+Re(wff([5-6])*wffC(n))); id Re(wff(6)*wffC(n?))= 1/2*(Re(wff([5+6])*wffC(n))-Re(wff([5-6])*wffC(n))); id Re(wff(5)*wffC(5))= wffM2(5); id Re(wff(6)*wffC(6))= wffM2(6); * id Re(wff(2)*X?*Y?)= 1/2*(Re(wff([2+3])*X*Y)+Re(wff([2-3])*X*Y)); id Re(wff(3)*X?*Y?)= 1/2*(Re(wff([2+3])*X*Y)-Re(wff([2-3])*X*Y)); id Re(wff(5)*X?*Y?)= 1/2*(Re(wff([5+6])*X*Y)+Re(wff([5-6])*X*Y)); id Re(wff(6)*X?*Y?)= 1/2*(Re(wff([5+6])*X*Y)-Re(wff([5-6])*X*Y)); * id Re(wff(2)*X?)= 1/2*(Re(wff([2+3])*X)+Re(wff([2-3])*X)); id Re(wff(3)*X?)= 1/2*(Re(wff([2+3])*X)-Re(wff([2-3])*X)); id Re(wff(5)*X?)= 1/2*(Re(wff([5+6])*X)+Re(wff([5-6])*X)); id Re(wff(6)*X?)= 1/2*(Re(wff([5+6])*X)-Re(wff([5-6])*X)); * id Re(wff([2+3])*wffC([2-3]))= Re(wff([2-3])*wffC([2+3])); id Re(wff([2+3])*wffC([5-6]))= Re(wff([5-6])*wffC([2+3])); id Re(wff([2-3])*wffC([5+6]))= Re(wff([5+6])*wffC([2-3])); id Re(wff([5+6])*wffC([5-6]))= Re(wff([5-6])*wffC([5+6])); * id Re(wff([2+3])*wffC([2+3]))= wffM2(2)+wffM2(3)+2*Re(wff(2)*wffC(3)); id Re(wff([2-3])*wffC([2-3]))= wffM2(2)+wffM2(3)-2*Re(wff(2)*wffC(3)); id Re(wff([5+6])*wffC([5+6]))= wffM2(5)+wffM2(6)+2*Re(wff(5)*wffC(6)); id Re(wff([5-6])*wffC([5-6]))= wffM2(5)+wffM2(6)-2*Re(wff(5)*wffC(6)); *-- * b i_,Gs,GsC,Gt,GtC,GsM2,GtM2,Re,Mods, zX,ums,dms,y,rs,s,tuM,tdM,wff,wffC,wffM2, Pws,PwsC,Pwt,PwtC,PwsM2,PwtM2,Sigmas,SigmasC,SigmasM2,Xpo, tau,X,z; print; * #endprocedure * #procedure totalgz(dummy) * * Now the full stuff * load wrl$grp04:[giampiero]outputampgz.sav; * g T_gz= PwsM2*PwtM2*W_gz_int6/(egt*I0); *nwrite statistics; * id es(T)*GT= egt; * id wff(n?)*wffC(n?)= wffM2(n); * id GtM2*GsM2*wff(2)*wffC(1)= GtM2*GsM2*(-wffC(2)*wff(1)+ 2*Re(wff(2)*wffC(1))); al GtM2*GsM2*wff(3)*wffC(1)= GtM2*GsM2*(-wffC(3)*wff(1)+ 2*Re(wff(3)*wffC(1))); al GtM2*GsM2*wff(4)*wffC(1)= GtM2*GsM2*(-wffC(4)*wff(1)+ 2*Re(wff(4)*wffC(1))); al GtM2*GsM2*wff(5)*wffC(1)= GtM2*GsM2*(-wffC(5)*wff(1)+ 2*Re(wff(5)*wffC(1))); al GtM2*GsM2*wff(6)*wffC(1)= GtM2*GsM2*(-wffC(6)*wff(1)+ 2*Re(wff(6)*wffC(1))); al GtM2*GsM2*wff(7)*wffC(1)= GtM2*GsM2*(-wffC(7)*wff(1)+ 2*Re(wff(7)*wffC(1))); al GtM2*GsM2*wff(8)*wffC(1)= GtM2*GsM2*(-wffC(8)*wff(1)+ 2*Re(wff(8)*wffC(1))); al GtM2*GsM2*wff(9)*wffC(1)= GtM2*GsM2*(-wffC(9)*wff(1)+ 2*Re(wff(9)*wffC(1))); al GtM2*GsM2*wff(10)*wffC(1)= GtM2*GsM2*(-wffC(10)*wff(1)+ 2*Re(wff(10)*wffC(1))); * al GtM2*GsM2*wff(3)*wffC(2)= GtM2*GsM2*(-wffC(3)*wff(2)+ 2*Re(wff(3)*wffC(2))); al GtM2*GsM2*wff(4)*wffC(2)= GtM2*GsM2*(-wffC(4)*wff(2)+ 2*Re(wff(4)*wffC(2))); al GtM2*GsM2*wff(5)*wffC(2)= GtM2*GsM2*(-wffC(5)*wff(2)+ 2*Re(wff(5)*wffC(2))); al GtM2*GsM2*wff(6)*wffC(2)= GtM2*GsM2*(-wffC(6)*wff(2)+ 2*Re(wff(6)*wffC(2))); al GtM2*GsM2*wff(7)*wffC(2)= GtM2*GsM2*(-wffC(7)*wff(2)+ 2*Re(wff(7)*wffC(2))); al GtM2*GsM2*wff(8)*wffC(2)= GtM2*GsM2*(-wffC(8)*wff(2)+ 2*Re(wff(8)*wffC(2))); al GtM2*GsM2*wff(9)*wffC(2)= GtM2*GsM2*(-wffC(9)*wff(2)+ 2*Re(wff(9)*wffC(2))); al GtM2*GsM2*wff(10)*wffC(2)= GtM2*GsM2*(-wffC(10)*wff(2)+ 2*Re(wff(10)*wffC(2))); * al GtM2*GsM2*wff(4)*wffC(3)= GtM2*GsM2*(-wffC(4)*wff(3)+ 2*Re(wff(4)*wffC(3))); al GtM2*GsM2*wff(5)*wffC(3)= GtM2*GsM2*(-wffC(5)*wff(3)+ 2*Re(wff(5)*wffC(3))); al GtM2*GsM2*wff(6)*wffC(3)= GtM2*GsM2*(-wffC(6)*wff(3)+ 2*Re(wff(6)*wffC(3))); al GtM2*GsM2*wff(7)*wffC(3)= GtM2*GsM2*(-wffC(7)*wff(3)+ 2*Re(wff(7)*wffC(3))); al GtM2*GsM2*wff(8)*wffC(3)= GtM2*GsM2*(-wffC(8)*wff(3)+ 2*Re(wff(8)*wffC(3))); al GtM2*GsM2*wff(9)*wffC(3)= GtM2*GsM2*(-wffC(9)*wff(3)+ 2*Re(wff(9)*wffC(3))); al GtM2*GsM2*wff(10)*wffC(3)= GtM2*GsM2*(-wffC(10)*wff(3)+ 2*Re(wff(10)*wffC(3))); * al GtM2*GsM2*wff(5)*wffC(4)= GtM2*GsM2*(-wffC(5)*wff(4)+ 2*Re(wff(5)*wffC(4))); al GtM2*GsM2*wff(6)*wffC(4)= GtM2*GsM2*(-wffC(6)*wff(4)+ 2*Re(wff(6)*wffC(4))); al GtM2*GsM2*wff(7)*wffC(4)= GtM2*GsM2*(-wffC(7)*wff(4)+ 2*Re(wff(7)*wffC(4))); al GtM2*GsM2*wff(8)*wffC(4)= GtM2*GsM2*(-wffC(8)*wff(4)+ 2*Re(wff(8)*wffC(4))); al GtM2*GsM2*wff(9)*wffC(4)= GtM2*GsM2*(-wffC(9)*wff(4)+ 2*Re(wff(9)*wffC(4))); al GtM2*GsM2*wff(10)*wffC(4)= GtM2*GsM2*(-wffC(10)*wff(4)+ 2*Re(wff(10)*wffC(4))); * al GtM2*GsM2*wff(6)*wffC(5)= GtM2*GsM2*(-wffC(6)*wff(5)+ 2*Re(wff(6)*wffC(5))); al GtM2*GsM2*wff(7)*wffC(5)= GtM2*GsM2*(-wffC(7)*wff(5)+ 2*Re(wff(7)*wffC(5))); al GtM2*GsM2*wff(8)*wffC(5)= GtM2*GsM2*(-wffC(8)*wff(5)+ 2*Re(wff(8)*wffC(5))); al GtM2*GsM2*wff(9)*wffC(5)= GtM2*GsM2*(-wffC(9)*wff(5)+ 2*Re(wff(9)*wffC(5))); al GtM2*GsM2*wff(10)*wffC(5)= GtM2*GsM2*(-wffC(10)*wff(5)+ 2*Re(wff(10)*wffC(5))); * al GtM2*GsM2*wff(7)*wffC(6)= GtM2*GsM2*(-wffC(7)*wff(6)+ 2*Re(wff(7)*wffC(6))); al GtM2*GsM2*wff(8)*wffC(6)= GtM2*GsM2*(-wffC(8)*wff(6)+ 2*Re(wff(8)*wffC(6))); al GtM2*GsM2*wff(9)*wffC(6)= GtM2*GsM2*(-wffC(9)*wff(6)+ 2*Re(wff(9)*wffC(6))); al GtM2*GsM2*wff(10)*wffC(6)= GtM2*GsM2*(-wffC(10)*wff(6)+ 2*Re(wff(10)*wffC(6))); * al GtM2*GsM2*wff(8)*wffC(7)= GtM2*GsM2*(-wffC(8)*wff(7)+ 2*Re(wff(8)*wffC(7))); al GtM2*GsM2*wff(9)*wffC(7)= GtM2*GsM2*(-wffC(9)*wff(7)+ 2*Re(wff(9)*wffC(7))); al GtM2*GsM2*wff(10)*wffC(7)= GtM2*GsM2*(-wffC(10)*wff(7)+ 2*Re(wff(10)*wffC(7))); * al GtM2*GsM2*wff(9)*wffC(8)= GtM2*GsM2*(-wffC(9)*wff(8)+ 2*Re(wff(9)*wffC(8))); al GtM2*GsM2*wff(10)*wffC(8)= GtM2*GsM2*(-wffC(10)*wff(8)+ 2*Re(wff(10)*wffC(8))); * al GtM2*GsM2*wff(10)*wffC(9)= GtM2*GsM2*(-wffC(10)*wff(9)+ 2*Re(wff(10)*wffC(9))); * id GtM2*Gs*PwsC*Sigmas= GtM2*(-GsC*Pws*SigmasC+2*Re(Gs*PwsC*Sigmas)); id GsM2*Gt*Pwt*SigmasC= GsM2*(-GtC*PwtC*Sigmas+2*Re(Gt*Pwt*SigmasC)); * id GsM2*GtM2*wff(n?)*SigmasC= GsM2*GtM2*(-wffC(n)*Sigmas+2*Re(wff(n)*SigmasC)); * id GtM2*Gs*Sigmas= GtM2*(-GsC*SigmasC+2*Re(Gs*Sigmas)); id GsM2*Gt*Sigmas= GsM2*(-GtC*SigmasC+2*Re(Gt*Sigmas)); * id wff(n?)*Gs*GtM2*PwsC= GtM2*(-wffC(n)*GsC*Pws+2*Re(wff(n)*Gs*PwsC)); id wff(n?)*Gt*GsM2*PwtC= GsM2*(-wffC(n)*GtC*Pwt+2*Re(wff(n)*Gt*PwtC)); * id GsM2*GtC*PwtC*wffC(n?)= GsM2*(-Gt*Pwt*wff(n)+2*Re(Gt*Pwt*wff(n))); id GtM2*GsC*PwsC*wffC(n?)= GtM2*(-Gs*Pws*wff(n)+2*Re(Gs*Pws*wff(n))); * id Gt*GsM2*PwtC*Sigmas= -GtC*GsM2*Pwt*SigmasC+2*GsM2*Re(Gt*PwtC*Sigmas); id Gt*GsM2*Pwt*Sigmas= -GtC*GsM2*PwtC*SigmasC+2*GsM2*Re(Gt*Pwt*Sigmas); id Gs*GtM2*PwsC*Sigmas= -GsC*GtM2*Pws*SigmasC+2*GtM2*Re(Gs*PwsC*Sigmas); id Gs*GtM2*Pws*Sigmas= -GsC*GtM2*PwsC*SigmasC+2*GtM2*Re(Gs*Pws*Sigmas); * id GsM2*GtC*PwtC*SigmasC= GsM2*(-Gt*Pwt*Sigmas+2*Re(Gt*Pwt*Sigmas)); id GtM2*GsC*PwsC*SigmasC= GtM2*(-Gs*Pws*Sigmas+2*Re(Gs*Pws*Sigmas)); * id Gt*GsM2*Pwt*Sigmas= -GtC*PwtC*GsM2*SigmasC+GsM2*Re(Gt*Pwt*Sigmas); id Gt*GsM2*PwtC*Sigmas= -GtC*Pwt*GsM2*SigmasC+GsM2*Re(Gt*PwtC*Sigmas); * id Gs*GtM2*Pws*Sigmas= -GsC*PwsC*GtM2*SigmasC+GtM2*Re(Gs*Pws*Sigmas); id Gs*GtM2*PwsC*Sigmas= -GsC*Pws*GtM2*SigmasC+GtM2*Re(Gs*PwsC*Sigmas); * id Gt*Pwt*SigmasC= -GtC*PwtC*Sigmas+2*Re(Gt*Pwt*SigmasC); id Gs*Pws*SigmasC= -GsC*PwsC*Sigmas+2*Re(Gs*Pws*SigmasC); * id Gt*PwtC*SigmasC= -GtC*Pwt*Sigmas+2*Re(Gt*PwtC*SigmasC); id Gs*PwsC*SigmasC= -GsC*Pws*Sigmas+2*Re(Gs*PwsC*SigmasC); * id Gs*GtM2*Sigmas= -GsC*GtM2*SigmasC+GtM2*Re(Gs*Sigmas); id Gt*GsM2*Sigmas= -GtC*GsM2*SigmasC+GsM2*Re(Gt*Sigmas); * id GsM2*GtC*PwtC= GsM2*(-Gt*Pwt+2*Re(Gt*Pwt)); id GtM2*GsC*PwsC= GtM2*(-Gs*Pws+2*Re(Gs*Pws)); * id GsC*PwsC*Gt*Pwt= -Gs*Pws*GtC*PwtC+2*Re(GsC*Gt*PwsC*Pwt); id GsC*Gt*Pws*PwtC= -Gs*GtC*PwsC*Pwt+2*Re(Gs*GtC*PwsC*Pwt); * id Gs*GtC*Pwt= -GsC*Gt*PwtC+2*Re(Gs*GtC*Pwt); * id GtM2*PwsC= GtM2*(-Pws+2*Re(Pws)); id GsM2*PwtC= GsM2*(-Pwt+2*Re(Pwt)); * id GsC*Gt*PwsC*PwtC= -Gs*GtC*Pws*Pwt+2*Re(Gs*GtC*Pws*Pwt); * id wff(n?)*Gs*GtM2= GtM2*(-GsC*wffC(n)+2*Re(Gs*wff(n))); id wff(n?)*Gt*GsM2= GsM2*(-GtC*wffC(n)+2*Re(Gt*wff(n))); * id Re(wffC(2)*wff(1))= Re(wff(2)*wffC(1)); al Re(wffC(3)*wff(1))= Re(wff(3)*wffC(1)); al Re(wffC(4)*wff(1))= Re(wff(4)*wffC(1)); al Re(wffC(5)*wff(1))= Re(wff(5)*wffC(1)); al Re(wffC(6)*wff(1))= Re(wff(6)*wffC(1)); al Re(wffC(7)*wff(1))= Re(wff(7)*wffC(1)); al Re(wffC(8)*wff(1))= Re(wff(8)*wffC(1)); al Re(wffC(9)*wff(1))= Re(wff(9)*wffC(1)); al Re(wffC(10)*wff(1))= Re(wff(10)*wffC(1)); * id Re(wffC(3)*wff(2))= Re(wff(3)*wffC(2)); al Re(wffC(4)*wff(2))= Re(wff(4)*wffC(2)); al Re(wffC(5)*wff(2))= Re(wff(5)*wffC(2)); al Re(wffC(6)*wff(2))= Re(wff(6)*wffC(2)); al Re(wffC(7)*wff(2))= Re(wff(7)*wffC(2)); al Re(wffC(8)*wff(2))= Re(wff(8)*wffC(2)); al Re(wffC(9)*wff(2))= Re(wff(9)*wffC(2)); al Re(wffC(10)*wff(2))= Re(wff(10)*wffC(2)); * id Re(wffC(4)*wff(3))= Re(wff(4)*wffC(3)); al Re(wffC(5)*wff(3))= Re(wff(5)*wffC(3)); al Re(wffC(6)*wff(3))= Re(wff(6)*wffC(3)); al Re(wffC(7)*wff(3))= Re(wff(7)*wffC(3)); al Re(wffC(8)*wff(3))= Re(wff(8)*wffC(3)); al Re(wffC(9)*wff(3))= Re(wff(9)*wffC(3)); al Re(wffC(10)*wff(3))= Re(wff(10)*wffC(3)); * id Re(wffC(5)*wff(4))= Re(wff(5)*wffC(4)); al Re(wffC(6)*wff(4))= Re(wff(6)*wffC(4)); al Re(wffC(7)*wff(4))= Re(wff(7)*wffC(4)); al Re(wffC(8)*wff(4))= Re(wff(8)*wffC(4)); al Re(wffC(9)*wff(4))= Re(wff(9)*wffC(4)); al Re(wffC(10)*wff(4))= Re(wff(10)*wffC(4)); * id Re(wffC(6)*wff(5))= Re(wff(6)*wffC(5)); al Re(wffC(7)*wff(5))= Re(wff(7)*wffC(5)); al Re(wffC(8)*wff(5))= Re(wff(8)*wffC(5)); al Re(wffC(9)*wff(5))= Re(wff(9)*wffC(5)); al Re(wffC(10)*wff(5))= Re(wff(10)*wffC(5)); * id Re(wffC(7)*wff(6))= Re(wff(7)*wffC(6)); al Re(wffC(8)*wff(6))= Re(wff(8)*wffC(6)); al Re(wffC(9)*wff(6))= Re(wff(9)*wffC(6)); al Re(wffC(10)*wff(6))= Re(wff(10)*wffC(6)); * id Re(wffC(8)*wff(7))= Re(wff(8)*wffC(7)); al Re(wffC(9)*wff(7))= Re(wff(9)*wffC(7)); al Re(wffC(10)*wff(7))= Re(wff(10)*wffC(7)); * id Re(wffC(9)*wff(8))= Re(wff(9)*wffC(8)); al Re(wffC(10)*wff(8))= Re(wff(10)*wffC(8)); * id Re(wffC(10)*wff(9))= Re(wff(10)*wffC(9)); * .store * #endprocedure * #procedure contractgz(dummy) * g Wd_gz= T_gz*d_(mu,nu); g Wpp_gz= T_gz*pp(mu)*pp(nu); g We_gz= T_gz*e_(mu,nu,Qm,pp); * contract; * id rs^-1= -1/(X*y*s); id pp.pp= 0; al qp.qp= 0; al Qm.Qm= QmS; id Qp.Qm= pp.Qm-qp.Qm; id kb.Qp= kb.pp-kb.qp; id k.Qp= k.pp-k.qp; id pp.Qp= -pp.qp; id Qp.Qp= -2*pp.qp; id qp.Qp= qp.pp; * id pp.Qm= -1/2*(QmS+y*s); al k.kb= 1/2*(-sp+ums+dms); al Qm.k= 1/2*(QmS+t-ums); al pp.kb= 1/2*(tp-dms); al Qm.kb= 1/2*(QmS+u-dms); al pp.k= 1/2*(up-ums); al pp.qp= 1/2*kp; al Qm.qp= 1/2*(QmS+km); al kb.qp= 1/2*(dms-zp); al k.qp= 1/2*(ums-zm); * id t= tau*y*s; al sp= x2*y*s; al km= z*y*s; al km^-1= 1/(z*y*s); al zm= -(x2-x1)*y*s; id QmS= X*y*s; * ratio,tM,t,ums; ratio,uM,u,dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * id kp= y*s * ( - 1 - X + x2 - z ); al u= y*s * ( - 1 - tau - 2*X - z ) + ums + dms; al up= y*s * ( - tau - X - x1 ) + 2*ums + dms; al tp= y*s * ( tau + X + x1 - x2 + z ) - ums; al zp= y*s * ( 1 - x1 ) + ums + dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * .store * g W1_gz= -1/2*Wd_gz-2*X/Xpo^2*Wpp_gz/(y*s); g W2_gz= -1/2*Wd_gz-6*X/Xpo^2*Wpp_gz/(y*s); g W3_gz= We_gz/(y*s)/Xpo; * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * *-- id Re(wff(n?)*wffC(2))= 1/2*(Re(wff(n)*wffC([2+3]))+Re(wff(n)*wffC([2-3]))); id Re(wff(n?)*wffC(3))= 1/2*(Re(wff(n)*wffC([2+3]))-Re(wff(n)*wffC([2-3]))); id Re(wff(2)*wffC(2))= wffM2(2); id Re(wff(3)*wffC(3))= wffM2(3); * id Re(wff(2)*wffC(n?))= 1/2*(Re(wff([2+3])*wffC(n))+Re(wff([2-3])*wffC(n))); id Re(wff(3)*wffC(n?))= 1/2*(Re(wff([2+3])*wffC(n))-Re(wff([2-3])*wffC(n))); id Re(wff(2)*wffC(2))= wffM2(2); id Re(wff(3)*wffC(3))= wffM2(3); * id Re(wff(n?)*wffC(5))= 1/2*(Re(wff(n)*wffC([5+6]))+Re(wff(n)*wffC([5-6]))); id Re(wff(n?)*wffC(6))= 1/2*(Re(wff(n)*wffC([5+6]))-Re(wff(n)*wffC([5-6]))); id Re(wff(5)*wffC(5))= wffM2(5); id Re(wff(6)*wffC(6))= wffM2(6); * id Re(wff(5)*wffC(n?))= 1/2*(Re(wff([5+6])*wffC(n))+Re(wff([5-6])*wffC(n))); id Re(wff(6)*wffC(n?))= 1/2*(Re(wff([5+6])*wffC(n))-Re(wff([5-6])*wffC(n))); id Re(wff(5)*wffC(5))= wffM2(5); id Re(wff(6)*wffC(6))= wffM2(6); * id Re(wff(2)*X?*Y?)= 1/2*(Re(wff([2+3])*X*Y)+Re(wff([2-3])*X*Y)); id Re(wff(3)*X?*Y?)= 1/2*(Re(wff([2+3])*X*Y)-Re(wff([2-3])*X*Y)); id Re(wff(5)*X?*Y?)= 1/2*(Re(wff([5+6])*X*Y)+Re(wff([5-6])*X*Y)); id Re(wff(6)*X?*Y?)= 1/2*(Re(wff([5+6])*X*Y)-Re(wff([5-6])*X*Y)); * id Re(wff(2)*X?)= 1/2*(Re(wff([2+3])*X)+Re(wff([2-3])*X)); id Re(wff(3)*X?)= 1/2*(Re(wff([2+3])*X)-Re(wff([2-3])*X)); id Re(wff(5)*X?)= 1/2*(Re(wff([5+6])*X)+Re(wff([5-6])*X)); id Re(wff(6)*X?)= 1/2*(Re(wff([5+6])*X)-Re(wff([5-6])*X)); * id Re(wff([2+3])*wffC([2-3]))= Re(wff([2-3])*wffC([2+3])); id Re(wff([2+3])*wffC([5-6]))= Re(wff([5-6])*wffC([2+3])); id Re(wff([2-3])*wffC([5+6]))= Re(wff([5+6])*wffC([2-3])); id Re(wff([5+6])*wffC([5-6]))= Re(wff([5-6])*wffC([5+6])); * id Re(wff([2+3])*wffC([2+3]))= wffM2(2)+wffM2(3)+2*Re(wff(2)*wffC(3)); id Re(wff([2-3])*wffC([2-3]))= wffM2(2)+wffM2(3)-2*Re(wff(2)*wffC(3)); id Re(wff([5+6])*wffC([5+6]))= wffM2(5)+wffM2(6)+2*Re(wff(5)*wffC(6)); id Re(wff([5-6])*wffC([5-6]))= wffM2(5)+wffM2(6)-2*Re(wff(5)*wffC(6)); *-- b i_,Gs,GsC,Gt,GtC,GsM2,GtM2,Re,Mods,ve,vu,vd,ae,au,ad,ss,cs,csi, zX,ums,dms,y,rs,s,tuM,tdM,wff,wffC,wffM2, Pws,PwsC,Pwt,PwtC,PwsM2,PwtM2,PZ,Sigmas,SigmasC,SigmasM2,Xpo; print; * #endprocedure * #procedure totalzz(dummy) * * Now the full stuff * load wrl$grp04:[giampiero]outputampzz.sav; * g T_zz= PwsM2*PwtM2*W_zz_int6/(GT^2*I0); *nwrite statistics; * id wff(n?)*wffC(n?)= wffM2(n); * id GtM2*GsM2*wff(2)*wffC(1)= GtM2*GsM2*(-wffC(2)*wff(1)+ 2*Re(wff(2)*wffC(1))); al GtM2*GsM2*wff(3)*wffC(1)= GtM2*GsM2*(-wffC(3)*wff(1)+ 2*Re(wff(3)*wffC(1))); al GtM2*GsM2*wff(4)*wffC(1)= GtM2*GsM2*(-wffC(4)*wff(1)+ 2*Re(wff(4)*wffC(1))); al GtM2*GsM2*wff(5)*wffC(1)= GtM2*GsM2*(-wffC(5)*wff(1)+ 2*Re(wff(5)*wffC(1))); al GtM2*GsM2*wff(6)*wffC(1)= GtM2*GsM2*(-wffC(6)*wff(1)+ 2*Re(wff(6)*wffC(1))); al GtM2*GsM2*wff(7)*wffC(1)= GtM2*GsM2*(-wffC(7)*wff(1)+ 2*Re(wff(7)*wffC(1))); al GtM2*GsM2*wff(8)*wffC(1)= GtM2*GsM2*(-wffC(8)*wff(1)+ 2*Re(wff(8)*wffC(1))); al GtM2*GsM2*wff(9)*wffC(1)= GtM2*GsM2*(-wffC(9)*wff(1)+ 2*Re(wff(9)*wffC(1))); al GtM2*GsM2*wff(10)*wffC(1)= GtM2*GsM2*(-wffC(10)*wff(1)+ 2*Re(wff(10)*wffC(1))); * al GtM2*GsM2*wff(3)*wffC(2)= GtM2*GsM2*(-wffC(3)*wff(2)+ 2*Re(wff(3)*wffC(2))); al GtM2*GsM2*wff(4)*wffC(2)= GtM2*GsM2*(-wffC(4)*wff(2)+ 2*Re(wff(4)*wffC(2))); al GtM2*GsM2*wff(5)*wffC(2)= GtM2*GsM2*(-wffC(5)*wff(2)+ 2*Re(wff(5)*wffC(2))); al GtM2*GsM2*wff(6)*wffC(2)= GtM2*GsM2*(-wffC(6)*wff(2)+ 2*Re(wff(6)*wffC(2))); al GtM2*GsM2*wff(7)*wffC(2)= GtM2*GsM2*(-wffC(7)*wff(2)+ 2*Re(wff(7)*wffC(2))); al GtM2*GsM2*wff(8)*wffC(2)= GtM2*GsM2*(-wffC(8)*wff(2)+ 2*Re(wff(8)*wffC(2))); al GtM2*GsM2*wff(9)*wffC(2)= GtM2*GsM2*(-wffC(9)*wff(2)+ 2*Re(wff(9)*wffC(2))); al GtM2*GsM2*wff(10)*wffC(2)= GtM2*GsM2*(-wffC(10)*wff(2)+ 2*Re(wff(10)*wffC(2))); * al GtM2*GsM2*wff(4)*wffC(3)= GtM2*GsM2*(-wffC(4)*wff(3)+ 2*Re(wff(4)*wffC(3))); al GtM2*GsM2*wff(5)*wffC(3)= GtM2*GsM2*(-wffC(5)*wff(3)+ 2*Re(wff(5)*wffC(3))); al GtM2*GsM2*wff(6)*wffC(3)= GtM2*GsM2*(-wffC(6)*wff(3)+ 2*Re(wff(6)*wffC(3))); al GtM2*GsM2*wff(7)*wffC(3)= GtM2*GsM2*(-wffC(7)*wff(3)+ 2*Re(wff(7)*wffC(3))); al GtM2*GsM2*wff(8)*wffC(3)= GtM2*GsM2*(-wffC(8)*wff(3)+ 2*Re(wff(8)*wffC(3))); al GtM2*GsM2*wff(9)*wffC(3)= GtM2*GsM2*(-wffC(9)*wff(3)+ 2*Re(wff(9)*wffC(3))); al GtM2*GsM2*wff(10)*wffC(3)= GtM2*GsM2*(-wffC(10)*wff(3)+ 2*Re(wff(10)*wffC(3))); * al GtM2*GsM2*wff(5)*wffC(4)= GtM2*GsM2*(-wffC(5)*wff(4)+ 2*Re(wff(5)*wffC(4))); al GtM2*GsM2*wff(6)*wffC(4)= GtM2*GsM2*(-wffC(6)*wff(4)+ 2*Re(wff(6)*wffC(4))); al GtM2*GsM2*wff(7)*wffC(4)= GtM2*GsM2*(-wffC(7)*wff(4)+ 2*Re(wff(7)*wffC(4))); al GtM2*GsM2*wff(8)*wffC(4)= GtM2*GsM2*(-wffC(8)*wff(4)+ 2*Re(wff(8)*wffC(4))); al GtM2*GsM2*wff(9)*wffC(4)= GtM2*GsM2*(-wffC(9)*wff(4)+ 2*Re(wff(9)*wffC(4))); al GtM2*GsM2*wff(10)*wffC(4)= GtM2*GsM2*(-wffC(10)*wff(4)+ 2*Re(wff(10)*wffC(4))); * al GtM2*GsM2*wff(6)*wffC(5)= GtM2*GsM2*(-wffC(6)*wff(5)+ 2*Re(wff(6)*wffC(5))); al GtM2*GsM2*wff(7)*wffC(5)= GtM2*GsM2*(-wffC(7)*wff(5)+ 2*Re(wff(7)*wffC(5))); al GtM2*GsM2*wff(8)*wffC(5)= GtM2*GsM2*(-wffC(8)*wff(5)+ 2*Re(wff(8)*wffC(5))); al GtM2*GsM2*wff(9)*wffC(5)= GtM2*GsM2*(-wffC(9)*wff(5)+ 2*Re(wff(9)*wffC(5))); al GtM2*GsM2*wff(10)*wffC(5)= GtM2*GsM2*(-wffC(10)*wff(5)+ 2*Re(wff(10)*wffC(5))); * al GtM2*GsM2*wff(7)*wffC(6)= GtM2*GsM2*(-wffC(7)*wff(6)+ 2*Re(wff(7)*wffC(6))); al GtM2*GsM2*wff(8)*wffC(6)= GtM2*GsM2*(-wffC(8)*wff(6)+ 2*Re(wff(8)*wffC(6))); al GtM2*GsM2*wff(9)*wffC(6)= GtM2*GsM2*(-wffC(9)*wff(6)+ 2*Re(wff(9)*wffC(6))); al GtM2*GsM2*wff(10)*wffC(6)= GtM2*GsM2*(-wffC(10)*wff(6)+ 2*Re(wff(10)*wffC(6))); * al GtM2*GsM2*wff(8)*wffC(7)= GtM2*GsM2*(-wffC(8)*wff(7)+ 2*Re(wff(8)*wffC(7))); al GtM2*GsM2*wff(9)*wffC(7)= GtM2*GsM2*(-wffC(9)*wff(7)+ 2*Re(wff(9)*wffC(7))); al GtM2*GsM2*wff(10)*wffC(7)= GtM2*GsM2*(-wffC(10)*wff(7)+ 2*Re(wff(10)*wffC(7))); * al GtM2*GsM2*wff(9)*wffC(8)= GtM2*GsM2*(-wffC(9)*wff(8)+ 2*Re(wff(9)*wffC(8))); al GtM2*GsM2*wff(10)*wffC(8)= GtM2*GsM2*(-wffC(10)*wff(8)+ 2*Re(wff(10)*wffC(8))); * al GtM2*GsM2*wff(10)*wffC(9)= GtM2*GsM2*(-wffC(10)*wff(9)+ 2*Re(wff(10)*wffC(9))); * id GtM2*Gs*PwsC*Sigmas= GtM2*(-GsC*Pws*SigmasC+2*Re(Gs*PwsC*Sigmas)); id GsM2*Gt*Pwt*SigmasC= GsM2*(-GtC*PwtC*Sigmas+2*Re(Gt*Pwt*SigmasC)); * id GsM2*GtM2*wff(n?)*SigmasC= GsM2*GtM2*(-wffC(n)*Sigmas+2*Re(wff(n)*SigmasC)); * id GtM2*Gs*Sigmas= GtM2*(-GsC*SigmasC+2*Re(Gs*Sigmas)); id GsM2*Gt*Sigmas= GsM2*(-GtC*SigmasC+2*Re(Gt*Sigmas)); * id wff(n?)*Gs*GtM2*PwsC= GtM2*(-wffC(n)*GsC*Pws+2*Re(wff(n)*Gs*PwsC)); id wff(n?)*Gt*GsM2*PwtC= GsM2*(-wffC(n)*GtC*Pwt+2*Re(wff(n)*Gt*PwtC)); * id GsM2*GtC*PwtC*wffC(n?)= GsM2*(-Gt*Pwt*wff(n)+2*Re(Gt*Pwt*wff(n))); id GtM2*GsC*PwsC*wffC(n?)= GtM2*(-Gs*Pws*wff(n)+2*Re(Gs*Pws*wff(n))); * id Gt*GsM2*PwtC*Sigmas= -GtC*GsM2*Pwt*SigmasC+2*GsM2*Re(Gt*PwtC*Sigmas); id Gt*GsM2*Pwt*Sigmas= -GtC*GsM2*PwtC*SigmasC+2*GsM2*Re(Gt*Pwt*Sigmas); id Gs*GtM2*PwsC*Sigmas= -GsC*GtM2*Pws*SigmasC+2*GtM2*Re(Gs*PwsC*Sigmas); id Gs*GtM2*Pws*Sigmas= -GsC*GtM2*PwsC*SigmasC+2*GtM2*Re(Gs*Pws*Sigmas); * id GsM2*GtC*PwtC*SigmasC= GsM2*(-Gt*Pwt*Sigmas+2*Re(Gt*Pwt*Sigmas)); id GtM2*GsC*PwsC*SigmasC= GtM2*(-Gs*Pws*Sigmas+2*Re(Gs*Pws*Sigmas)); * id Gt*GsM2*Pwt*Sigmas= -GtC*PwtC*GsM2*SigmasC+GsM2*Re(Gt*Pwt*Sigmas); id Gt*GsM2*PwtC*Sigmas= -GtC*Pwt*GsM2*SigmasC+GsM2*Re(Gt*PwtC*Sigmas); * id Gs*GtM2*Pws*Sigmas= -GsC*PwsC*GtM2*SigmasC+GtM2*Re(Gs*Pws*Sigmas); id Gs*GtM2*PwsC*Sigmas= -GsC*Pws*GtM2*SigmasC+GtM2*Re(Gs*PwsC*Sigmas); * id Gt*Pwt*SigmasC= -GtC*PwtC*Sigmas+2*Re(Gt*Pwt*SigmasC); id Gs*Pws*SigmasC= -GsC*PwsC*Sigmas+2*Re(Gs*Pws*SigmasC); * id Gt*PwtC*SigmasC= -GtC*Pwt*Sigmas+2*Re(Gt*PwtC*SigmasC); id Gs*PwsC*SigmasC= -GsC*Pws*Sigmas+2*Re(Gs*PwsC*SigmasC); * id Gs*GtM2*Sigmas= -GsC*GtM2*SigmasC+GtM2*Re(Gs*Sigmas); id Gt*GsM2*Sigmas= -GtC*GsM2*SigmasC+GsM2*Re(Gt*Sigmas); * id GsM2*GtC*PwtC= GsM2*(-Gt*Pwt+2*Re(Gt*Pwt)); id GtM2*GsC*PwsC= GtM2*(-Gs*Pws+2*Re(Gs*Pws)); * id GsC*PwsC*Gt*Pwt= -Gs*Pws*GtC*PwtC+2*Re(GsC*Gt*PwsC*Pwt); id GsC*Gt*Pws*PwtC= -Gs*GtC*PwsC*Pwt+2*Re(Gs*GtC*PwsC*Pwt); * id Gs*GtC*Pwt= -GsC*Gt*PwtC+2*Re(Gs*GtC*Pwt); * id GtM2*PwsC= GtM2*(-Pws+2*Re(Pws)); id GsM2*PwtC= GsM2*(-Pwt+2*Re(Pwt)); * id GsC*Gt*PwsC*PwtC= -Gs*GtC*Pws*Pwt+2*Re(Gs*GtC*Pws*Pwt); * id wff(n?)*Gs*GtM2= GtM2*(-GsC*wffC(n)+2*Re(Gs*wff(n))); id wff(n?)*Gt*GsM2= GsM2*(-GtC*wffC(n)+2*Re(Gt*wff(n))); * id Re(wffC(2)*wff(1))= Re(wff(2)*wffC(1)); al Re(wffC(3)*wff(1))= Re(wff(3)*wffC(1)); al Re(wffC(4)*wff(1))= Re(wff(4)*wffC(1)); al Re(wffC(5)*wff(1))= Re(wff(5)*wffC(1)); al Re(wffC(6)*wff(1))= Re(wff(6)*wffC(1)); al Re(wffC(7)*wff(1))= Re(wff(7)*wffC(1)); al Re(wffC(8)*wff(1))= Re(wff(8)*wffC(1)); al Re(wffC(9)*wff(1))= Re(wff(9)*wffC(1)); al Re(wffC(10)*wff(1))= Re(wff(10)*wffC(1)); * id Re(wffC(3)*wff(2))= Re(wff(3)*wffC(2)); al Re(wffC(4)*wff(2))= Re(wff(4)*wffC(2)); al Re(wffC(5)*wff(2))= Re(wff(5)*wffC(2)); al Re(wffC(6)*wff(2))= Re(wff(6)*wffC(2)); al Re(wffC(7)*wff(2))= Re(wff(7)*wffC(2)); al Re(wffC(8)*wff(2))= Re(wff(8)*wffC(2)); al Re(wffC(9)*wff(2))= Re(wff(9)*wffC(2)); al Re(wffC(10)*wff(2))= Re(wff(10)*wffC(2)); * id Re(wffC(4)*wff(3))= Re(wff(4)*wffC(3)); al Re(wffC(5)*wff(3))= Re(wff(5)*wffC(3)); al Re(wffC(6)*wff(3))= Re(wff(6)*wffC(3)); al Re(wffC(7)*wff(3))= Re(wff(7)*wffC(3)); al Re(wffC(8)*wff(3))= Re(wff(8)*wffC(3)); al Re(wffC(9)*wff(3))= Re(wff(9)*wffC(3)); al Re(wffC(10)*wff(3))= Re(wff(10)*wffC(3)); * id Re(wffC(5)*wff(4))= Re(wff(5)*wffC(4)); al Re(wffC(6)*wff(4))= Re(wff(6)*wffC(4)); al Re(wffC(7)*wff(4))= Re(wff(7)*wffC(4)); al Re(wffC(8)*wff(4))= Re(wff(8)*wffC(4)); al Re(wffC(9)*wff(4))= Re(wff(9)*wffC(4)); al Re(wffC(10)*wff(4))= Re(wff(10)*wffC(4)); * id Re(wffC(6)*wff(5))= Re(wff(6)*wffC(5)); al Re(wffC(7)*wff(5))= Re(wff(7)*wffC(5)); al Re(wffC(8)*wff(5))= Re(wff(8)*wffC(5)); al Re(wffC(9)*wff(5))= Re(wff(9)*wffC(5)); al Re(wffC(10)*wff(5))= Re(wff(10)*wffC(5)); * id Re(wffC(7)*wff(6))= Re(wff(7)*wffC(6)); al Re(wffC(8)*wff(6))= Re(wff(8)*wffC(6)); al Re(wffC(9)*wff(6))= Re(wff(9)*wffC(6)); al Re(wffC(10)*wff(6))= Re(wff(10)*wffC(6)); * id Re(wffC(8)*wff(7))= Re(wff(8)*wffC(7)); al Re(wffC(9)*wff(7))= Re(wff(9)*wffC(7)); al Re(wffC(10)*wff(7))= Re(wff(10)*wffC(7)); * id Re(wffC(9)*wff(8))= Re(wff(9)*wffC(8)); al Re(wffC(10)*wff(8))= Re(wff(10)*wffC(8)); * id Re(wffC(10)*wff(9))= Re(wff(10)*wffC(9)); * .store * #endprocedure * #procedure contractzz(dummy) * g Wd_zz= T_zz*d_(mu,nu); g Wpp_zz= T_zz*pp(mu)*pp(nu); g Wqq_zz= T_zz*Qm(mu)*Qm(nu); g Wpq_zz= T_zz*(pp(mu)*Qm(nu)+pp(nu)*Qm(mu)); g We_zz= T_zz*e_(mu,nu,Qm,pp); * contract; * id rs^-1= -1/(X*y*s); id pp.pp= 0; al qp.qp= 0; al Qm.Qm= QmS; id Qp.Qm= pp.Qm-qp.Qm; id kb.Qp= kb.pp-kb.qp; id k.Qp= k.pp-k.qp; id pp.Qp= -pp.qp; id Qp.Qp= -2*pp.qp; id qp.Qp= qp.pp; * id pp.Qm= -1/2*(QmS+y*s); al k.kb= 1/2*(-sp+ums+dms); al Qm.k= 1/2*(QmS+t-ums); al pp.kb= 1/2*(tp-dms); al Qm.kb= 1/2*(QmS+u-dms); al pp.k= 1/2*(up-ums); al pp.qp= 1/2*kp; al Qm.qp= 1/2*(QmS+km); al kb.qp= 1/2*(dms-zp); al k.qp= 1/2*(ums-zm); * id t= tau*y*s; al sp= x2*y*s; al km= z*y*s; al km^-1= 1/(z*y*s); al zm= -(x2-x1)*y*s; id QmS= X*y*s; * ratio,tM,t,ums; ratio,uM,u,dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * id kp= y*s * ( - 1 - X + x2 - z ); al u= y*s * ( - 1 - tau - 2*X - z ) + ums + dms; al up= y*s * ( - tau - X - x1 ) + 2*ums + dms; al tp= y*s * ( tau + X + x1 - x2 + z ) - ums; al zp= y*s * ( 1 - x1 ) + ums + dms; * id ums*tuM^-2= aux; id ums= 0; id aux= ums*tuM^-2; id dms*tdM^-2= aux; id dms= 0; id aux= dms*tdM^-2; * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * .store * g W1_zz= -1/2*Wd_zz-2*X/Xpo^2*Wpp_zz/(y*s)-Wpq_zz/(y*s)/Xpo; g W2_zz= -1/2*Wd_zz-6*X/Xpo^2*Wpp_zz/(y*s)-3*Wpq_zz/(y*s)/Xpo-Wqq_zz/(y*s)/Xpo; g W3_zz= We_zz/(y*s)/Xpo; g W4_zz= -2/Xpo*Wqq_zz/(y*s)-2*X/Xpo^2*Wpq_zz/(y*s); g W5_zz= -Wqq_zz/(y*s)/X-2/Xpo*Wpq_zz/(y*s); * ratio,X,Xpo,one; id one= 1; al one^-1= 1; * id cs(T)*csi(T)= 1; * b i_,Gs,GsC,Gt,GtC,GsM2,GtM2,Re,Mods,ve,vu,vd,ae,au,ad,ss,cs,csi, zX,ums,dms,y,rs,s,tuM,tdM,wff,wffC,wffM2, Pws,PwsC,Pwt,PwtC,PwsM2,PwtM2,PZ,Sigmas,SigmasC,SigmasM2,Xpo; print; * #endprocedure * */////////////////////////////////////////////////////////////////////// * *#call wtensor{gg} *#call totalgg{dummy} *#call contractgg{dummy} *---------------------------------------------------------------- *#call wtensor{gz} #call totalgz{dummy} #call contractgz{dummy} *---------------------------------------------------------------- *#call wtensor{zz} *#call totalzz{dummy} *#call contractzz{dummy} * .end