*FORM by J.Vermaseren,version 3.1(Oct 17 2002) Run at: Mon Mar 14 20:13:26 2005 * * This FORM code processes the result produced by the (PQint) code: * * Simplifications and sums over sea and valence quark indices are * * implemented. Includes the possiblilty of producing output intended for * * fortran functions and LaTeX. * * ************************************************************************** * * comp 1 : Simplification of the pseudoscalar meson mass to NNLO * * comp 2 : Simplification of the pseudoscalar meson decay constant to NNLO * * #define comp "1" * #define nfl "2" * * * The parameters (mode) and (type) select the values of (dval) and (dsea), * * according to the tables below: * * * nfl = 2: * * dval + dsea Mode Type * ***************************** * * 1 + 1 1 1 * * 1 + 2 2 1 * * 2 + 1 4 1 * * 2 + 2 5 1 * * * nfl = 3: * * dval + dsea Mode Type * ***************************** * * 1 + 1 2 1 * * 1 + 2 4 1 * * 1 + 3 5 1 * * 2 + 1 2 2 * * 2 + 2 4 2 * * 2 + 3 5 2 * * #define mode "4" * #define type "1" * * #define pout "0" * #define nsim "0" * * #- * Sigma2 loaded * Sigma4 loaded * Sigma6 loaded * *Time = 0.37 sec Generated terms = 1 * M0p2 Terms in output = 1 * Bytes used = 24 * *Time = 0.37 sec Generated terms = 5 * M0p4 Terms in output = 5 * Bytes used = 182 * *Time = 0.37 sec Generated terms = 182 * M0p6 Terms in output = 182 * Bytes used = 7106 L M0p2timo21 = + X12 ; L M0p4timo21 = + F0^-2*L4r * ( - 16*X12*X33 ) + F0^-2*L5r * ( - 8*X12^2 ) + F0^-2*L6r * ( + 32*X12*X33 ) + F0^-2*L8r * ( + 16*X12^2 ) + Ab(Xpp)*F0^-2 * ( - 1/2*R(Xpp,Xqq)*X12 ); L M0p6timo21 = + F0^-4*pi16*L0r * ( + 4*X11*X12*X22 + 2*X12*X33^2 + 8*X12^2*X33 - 8*X12^3 ) + F0^-4*pi16*L1r * ( + 4*X12^3 ) + F0^-4*pi16*L2r * ( + 6*X12*X33^2 + 2*X12^3 ) + F0^-4*pi16*L3r * ( + 3*X11*X12*X22 + X12*X33^2 + 6*X12^2*X33 - 8*X12^3 ) + F0^-4*pi16^2 * ( + 17/96*X11*X12*X22 + 47/96*X12*X33^2 + 35/144*X12^2*X33 - 17/72*X12^3 ) + F0^-4*L4r*L5r * ( + 256*X12^2*X33 ) + F0^-4*L4r*L6r * ( - 512*X12*X33^2 ) + F0^-4*L4r*L8r * ( - 256*X12^2*X33 ) + F0^-4*L4r*L11r * ( + 128*X12^2*X33 ) + F0^-4*L4r^2 * ( + 256*X12*X33^2 ) + F0^-4*L5r*L6r * ( - 256*X12^2*X33 ) + F0^-4*L5r*L8r * ( - 128*X12^3 ) + F0^-4*L5r*L11r * ( + 64*X12^3 ) + F0^-4*L5r^2 * ( + 64*X12^3 ) + F0^-4*L6r*L11r * ( - 256*X12^2*X33 ) + F0^-4*L8r*L11r * ( - 128*X12^3 ) + F0^-4*K17r * ( - 32*X12^3 ) + F0^-4*K18r * ( - 64*X12^2*X33 ) + F0^-4*K19r * ( - 8*Xpp^2*X12 ) + F0^-4*K20r * ( - 32*X12^2*X33 ) + F0^-4*K21r * ( - 32*X12*X33^2 ) + F0^-4*K22r * ( - 64*X12*X33^2 ) + F0^-4*K23r * ( - 16*X11*X12*X22 ) + F0^-4*K25r * ( + 24*Xpp^2*X12 ) + F0^-4*K26r * ( + 32*X12*X33^2 + 64*X12^2*X33 ) + F0^-4*K27r * ( + 192*X12*X33^2 ) + F0^-4*K39r * ( + 32*X12^3 ) + F0^-4*K40r * ( + 64*X12^2*X33 ) + Ab(Xpp)*F0^-4*pi16 * ( - 1/24*Xqq*X12 - 1/8*X12*X33 + 1/4*R(Xpp,Xqq)*X12*X33 + 1/12*R(Xpp,Xqq)*X12^2 ) + Ab(Xpp)*F0^-4*L0r * ( - 2*Xpp*X12 - 8*R(Xpp,Xqq)*Xpp*X12 - 2*RD(Xpp)*X12 ) + Ab(Xpp)*F0^-4*L3r * ( - 5*Xpp*X12 - 2*R(Xpp,Xqq)*Xpp*X12 - 5*RD(Xpp)*X12 ) + Ab(Xpp)*F0^-4*L4r * ( + 16*R(Xpp,Xqq)*X12*X33 ) + Ab(Xpp)*F0^-4*L5r * ( + 4*Xpp*X12 + 8*R(Xpp,Xqq)*Xpp*X12 ) + Ab(Xpp)*F0^-4*L6r * ( - 16*R(Xpp,Xqq)*X12*X33 ) + Ab(Xpp)*F0^-4*L7r * ( + 16/3*RD(Xpp)*Xp3 + 32/3*RD(Xpp)*X12 ) + Ab(Xpp)*F0^-4*L8r * ( - 8*Xpp*X12 - 16/3*R(Xpp,Xqq)*X11*X22 - 32/3*R(Xpp,Xqq)*X12^2 - 4/3*RD(Xpp)^2 ) + Ab(Xpp)^2*F0^-4 * ( + 5/32*X12 + 1/8*R(Xpp,Xqq)^2*X12 - 1/24*R(Xqq,Xpp)*Xpp ) + Ab(Xpp)*Ab(Xp3)*F0^-4 * ( + 1/24*Xpp - 1/8*Xqq + 1/24*R(Xpp,Xqq)*Xpp + 19/72*R(Xpp,Xqq)*Xqq ) + Ab(Xpp)*Ab(Xq3)*F0^-4 * ( + 1/4*X12 + 1/6*R(Xpp,Xqq)*Xqq - 1/24*R(Xqq,Xpp)*Xpp + 1/72*R(Xqq,Xpp)*Xqq ) + Ab(Xpp)*Ab(X12)*F0^-4 * ( + 1/18*Xpp - 1/36*X12 ) + Ab(Xpp)*Ab(X33)*F0^-4 * ( - 1/8*X33 ) + Ab(Xpp)*Bb(Xpp,Xpp,0)*F0^-4 * ( + 11/24*R(Xpp,Xqq)*Xpp*X12 - 1/12*R(Xpp,Xqq)*Xpp^2 - 1/8*R(Xpp,Xqq)*X12^2 + 1/24*R(Xpp,Xqq)*RD(Xpp)*Xpp ) + Ab(Xpp)*Bb(Xqq,Xqq,0)*F0^-4 * ( - 1/24*R(Xpp,Xqq)*RD(Xqq)*Xqq - 1/16*RD(Xqq)*X12 ) + Ab(Xpp)*Bb(X11,X22,0)*F0^-4 * ( + 1/6*R(Xqq,Xpp)*Xpp*X12 ) + Ab(Xpp)*Bb(X11,X22,0,kk)*F0^-4 * ( + 1/12*R(Xqq,Xpp)*Xpp ) + Ab(Xpp,eps)*F0^-4*pi16 * ( + 1/4*Xpp*X12 - 1/4*R(Xpp,Xqq)*X12*X33 ) + Ab(Xp3)*F0^-4*pi16 * ( - 1/3*Xpp*X12 + 2/3*X12*X33 + 1/3*X12^2 ) + Ab(Xp3)*F0^-4*L0r * ( + 8*Xp3*X12 ) + Ab(Xp3)*F0^-4*L3r * ( + 20*Xp3*X12 ) + Ab(Xp3)*F0^-4*L5r * ( - 16*Xp3*X12 ) + Ab(Xp3)*F0^-4*L8r * ( + 32*Xp3*X12 ) + Ab(Xp3)*Bb(Xqq,Xqq,0)*F0^-4 * ( + 1/4*RD(Xqq)*X12 ) + Ab(Xp3)*Bb(X11,X22,0)*F0^-4 * ( - 4/9*Xp3*X12 - 1/9*X11*X22 - 1/9*R(Xqq,Xpp)*Xpp^2 ) + Ab(Xp3)*Bb(X11,X22,0,kk)*F0^-4 * ( - 2/9*Xp3 - 2/9*X12 + 1/9*R(Xqq,Xpp)*Xqq ) + Ab(Xp3,eps)*F0^-4*pi16 * ( - X12*X33 ) + Ab(X11)*Ab(X22)*F0^-4 * ( - 1/16*X12 - 1/24*X33 + 1/4*R(X11,X22)*R(X22,X11)*X12 ) + Ab(X12)*F0^-4*L1r * ( + 8*X12^2 ) + Ab(X12)*F0^-4*L2r * ( + 20*X12^2 ) + Ab(X12)*F0^-4*L6r * ( + 32*X12^2 ) + Ab(X12)^2*F0^-4 * ( - 1/4*X12 ) + Ab(X12)*Bb(X11,X22,0)*F0^-4 * ( + 1/9*X11*X22 + 4/9*X12^2 ) + Ab(X12)*Bb(X11,X22,0,kk)*F0^-4 * ( + 4/9*X12 ) + Ab(X12,eps)*F0^-4*pi16 * ( - 2*X12^2 ) + Ab(X13)*Ab(X23)*F0^-4 * ( - X12 ) + Ab(X33)*F0^-4*L1r * ( + 48*X12*X33 ) + Ab(X33)*F0^-4*L2r * ( + 12*X12*X33 ) + Ab(X33)*F0^-4*L4r * ( - 48*X12*X33 ) + Ab(X33)*F0^-4*L6r * ( + 48*X12*X33 ) + Ab(X33)*Bb(X11,X22,0)*F0^-4 * ( + 1/2*X12*X33 ) + Ab(X33)*Bb(X11,X22,0,kk)*F0^-4 * ( + 1/4*X33 ) + Ab(X33,eps)*F0^-4*pi16 * ( - 3/4*X12*X33 ) + Bb(Xpp,Xpp,0)*F0^-4*pi16 * ( - 1/24*RD(Xpp)*Xqq*X12 - 1/8*RD(Xpp)*X12*X33 ) + Bb(Xpp,Xpp,0)*F0^-4*L0r * ( - 2*RD(Xpp)*Xpp*X12 ) + Bb(Xpp,Xpp,0)*F0^-4*L3r * ( - 5*RD(Xpp)*Xpp*X12 ) + Bb(Xpp,Xpp,0)*F0^-4*L4r * ( + 8*R(Xpp,Xqq)*Xpp*X12*X33 ) + Bb(Xpp,Xpp,0)*F0^-4*L5r * ( + 4*R(Xpp,Xqq)*Xpp^3 + 2*RD(Xpp)*X11*X22 ) + Bb(Xpp,Xpp,0)*F0^-4*L6r * ( - 16*R(Xpp,Xqq)*Xpp*X12*X33 ) + Bb(Xpp,Xpp,0)*F0^-4*L8r * ( - 8*R(Xpp,Xqq)*Xpp^3 - 4*RD(Xpp)*X11*X22 ) + Bb(Xpp,Xpp,0)^2*F0^-4 * ( + 9/32*R(Xpp,Xqq)*RD(Xpp)*Xpp*X12 - 1/32*R(Xpp,Xqq)*RD(Xpp)*Xqq*X12 ) + Bb(Xpp,Xpp,0)*Bb(X11,X22,0)*F0^-4 * ( + 1/6*R(Xqq,Xpp)*RD(Xpp)*Xpp*X12 ) + Bb(Xpp,Xpp,0)*Bb(X11,X22,0,kk)*F0^-4 * ( + 1/12*R(Xqq,Xpp)*RD(Xpp)*Xpp ) + Bb(Xpp,Xpp,0,eps)*F0^-4*pi16 * ( + 1/4*RD(Xpp)*Xp3*X12 ) + Bb(X11,X11,0)*Bb(X22,X22,0)*F0^-4 * ( - 1/16*RD(X11)*RD(X22)*X12 ) + Bb(X11,X22,0)*F0^-4*L7r * ( + 32/3*RD(X11)*RD(X22)*X12 ) + Bb(X11,X22,0)*F0^-4*L8r * ( + 16/3*RD(X11)*RD(X22)*X12 ) + Bb(X11,X22,0,kk)*F0^-4*L7r * ( + 16/3*RD(X11)*RD(X22) ) + Bb(X11,X22,0,kk)*F0^-4*L8r * ( + 8/3*RD(X11)*RD(X22) ) + Hbb(1,Xpp,Xpp,X12,X12)*F0^-4 * ( - 1/4*Xpp*X12 - 15/32*X12^2 + 3/8*R(Xpp,Xqq)*X12^2 - 1/8*R(Xpp,Xqq)^2*X12^2 ) + Hbb(1,Xpp,X13,X23,X12)*F0^-4 * ( + 1/4*X12^2 + 3/4*R(Xqq,Xpp)*Xpp*X12 + 1/4*R(Xqq,Xpp)*Xqq*X12 - 1/4*R(Xqq,Xpp)*X12*X33 ) + Hbb(1,X11,X12,X22,X12)*F0^-4 * ( - 1/16*X12^2 + 3/4*R(X11,X22)*R(X22,X11)*X12^2 ) + Hbb(1,X12,X12,X12,X12)*F0^-4 * ( + 1/4*X12^2 ) + Hbb(1,X13,X23,X33,X12)*F0^-4 * ( + 3/4*X12*X33 ) + Hbb(2,Xpp,Xpp,X12,X12)*F0^-4 * ( - 1/8*R(Xpp,Xqq)*RD(Xpp)*X12^2 + 5/16*RD(Xpp)*X12^2 ) + Hbb(2,Xpp,X12,Xqq,X12)*F0^-4 * ( - 1/8*R(Xqq,Xpp)*RD(Xpp)*X12^2 + 1/16*RD(Xpp)*X12^2 ) + Hbb(2,Xpp,X13,X23,X12)*F0^-4 * ( - 1/4*RD(Xpp)*Xp3*X12 ) + Hbb(5,Xpp,Xpp,X12,X12)*F0^-4 * ( + 5/32*RD(Xpp)^2*X12^2 ) + Hbb(5,X11,X22,X12,X12)*F0^-4 * ( + 1/16*RD(X11)*RD(X22)*X12^2 ) + H1bb(1,Xpp,Xpp,X12,X12)*F0^-4 * ( + 5/2*X12^2 - R(Xpp,Xqq)*R(Xqq,Xpp)*X12^2 ) + H1bb(1,Xpp,X13,X23,X12)*F0^-4 * ( - 2*R(Xqq,Xpp)*X12^2 ) + H1bb(1,Xp3,Xq3,Xpp,X12)*F0^-4 * ( - 2*X12^2 ) + H1bb(1,X12,X11,X22,X12)*F0^-4 * ( + 1/2*X12^2 - R(X11,X22)*R(X22,X11)*X12^2 ) + H1bb(3,X12,Xpp,Xpp,X12)*F0^-4 * ( - 1/2*R(Xqq,Xpp)*RD(Xpp)*X12^2 ) + H1bb(3,X12,Xpp,Xqq,X12)*F0^-4 * ( + 1/2*R(Xqq,Xpp)*RD(Xpp)*X12^2 ) + H1bb(7,X12,Xpp,Xpp,X12)*F0^-4 * ( - 1/4*RD(Xpp)^2*X12^2 ) + H21bb(1,Xpp,Xpp,X12,X12)*F0^-4 * ( - 3/4*X12^2 ) + H21bb(1,Xpp,X13,X23,X12)*F0^-4 * ( + 3/4*R(Xqq,Xpp)*X12^2 ) + H21bb(1,Xp3,Xq3,Xpp,X12)*F0^-4 * ( + 3/4*R(Xpp,Xqq)*X12^2 ) + H21bb(1,Xp3,Xq3,Xqq,X12)*F0^-4 * ( - 3/4*R(Xpp,Xqq)*X12^2 ) + H21bb(1,X12,Xpp,Xpp,X12)*F0^-4 * ( + 15/32*X12^2 - 3/8*R(Xpp,Xqq)*R(Xqq,Xpp)*X12^2 ) + H21bb(1,X12,X11,X22,X12)*F0^-4 * ( - 3/16*X12^2 + 3/4*R(X11,X22)*R(X22,X11)*X12^2 ) + H21bb(1,X12,X12,X12,X12)*F0^-4 * ( + 3/4*X12^2 ) + H21bb(1,X33,X13,X23,X12)*F0^-4 * ( + 9/4*X12^2 ) + H21bb(3,Xp3,Xpp,Xq3,X12)*F0^-4 * ( - 3/4*RD(Xpp)*X12^2 ) + H21bb(3,X12,Xpp,Xpp,X12)*F0^-4 * ( - 3/8*R(Xpp,Xqq)*RD(Xpp)*X12^2 + 3/16*RD(Xpp)*X12^2 ) + H21bb(3,X12,Xpp,Xqq,X12)*F0^-4 * ( - 3/8*R(Xqq,Xpp)*RD(Xpp)*X12^2 + 3/16*RD(Xpp)*X12^2 ) + H21bb(7,X12,Xpp,Xpp,X12)*F0^-4 * ( + 3/32*RD(Xpp)^2*X12^2 ) + H21bb(7,X12,X11,X22,X12)*F0^-4 * ( + 3/16*RD(X11)*RD(X22)*X12^2 );