*FORM by J.Vermaseren,version 3.1(Oct 17 2002) Run at: Mon Mar 14 20:06:28 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 "2" * #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 = 0.25 sec Generated terms = 1 * F0p2 Terms in output = 1 * Bytes used = 24 * *Time = 0.25 sec Generated terms = 6 * F0p4 Terms in output = 6 * Bytes used = 196 * *Time = 0.25 sec Generated terms = 179 * F0p6 Terms in output = 179 * Bytes used = 6954 L F0p2timo21 = + F0 * ( + 1 ); L F0p4timo21 = + F0^-1*L4r * ( + 8*X33 ) + F0^-1*L5r * ( + 4*X12 ) + Ab(Xpp)*F0^-1 * ( - 1/8 + 1/4*R(Xpp,Xqq) ) + Ab(Xp3)*F0^-1 * ( + 1/2 ) + Bb(Xpp,Xpp,0)*F0^-1 * ( - 1/8*RD(Xpp) ); L F0p6timo21 = + F0^-3*pi16*L0r * ( - 2*X11*X22 - 4*X12*X33 + 4*X12^2 - X33^2 ) + F0^-3*pi16*L1r * ( - 2*X12^2 ) + F0^-3*pi16*L2r * ( - X12^2 - 3*X33^2 ) + F0^-3*pi16*L3r * ( - 3/2*X11*X22 - 3*X12*X33 + 4*X12^2 - 1/2*X33^2 ) + F0^-3*pi16^2 * ( - 17/192*X11*X22 - 23/96*X12*X33 + 5/48*X12^2 - 47/192*X33^2 ) + F0^-3*L4r*L5r * ( - 32*X12*X33 ) + F0^-3*L4r^2 * ( - 32*X33^2 ) + F0^-3*L5r^2 * ( - 8*X12^2 ) + F0^-3*L11r^2 * ( + 8*X12^2 ) + F0^-3*K19r * ( + 4*Xpp^2 ) + F0^-3*K20r * ( + 16*X12*X33 ) + F0^-3*K21r * ( + 16*X33^2 ) + F0^-3*K22r * ( + 32*X33^2 ) + F0^-3*K23r * ( + 8*X11*X22 ) + Ab(Xpp)*F0^-3*pi16 * ( + 1/48*Xqq + 1/48*X12 + 1/16*X33 - 1/12*R(Xpp,Xqq)*X12 - 1/8*R(Xpp,Xqq)*X33 ) + Ab(Xpp)*F0^-3*L0r * ( + Xpp + 4*R(Xpp,Xqq)*Xpp + RD(Xpp) ) + Ab(Xpp)*F0^-3*L3r * ( + 5/2*Xpp + R(Xpp,Xqq)*Xpp + 5/2*RD(Xpp) ) + Ab(Xpp)*F0^-3*L4r * ( + X33 - 2*R(Xpp,Xqq)*X33 ) + Ab(Xpp)*F0^-3*L5r * ( - 1/2*X12 - R(Xpp,Xqq)*X12 ) + Ab(Xpp)^2*F0^-3 * ( + 9/128 - 1/32*R(Xpp,Xqq)*R(Xqq,Xpp) ) + Ab(Xpp)*Ab(Xp3)*F0^-3 * ( - 1/16 - 1/12*R(Xpp,Xqq) ) + Ab(Xpp)*Ab(Xq3)*F0^-3 * ( - 3/16 - 1/12*R(Xpp,Xqq) ) + Ab(Xpp)*Ab(X12)*F0^-3 * ( + 1/8 ) + Ab(Xpp)*Bb(Xpp,Xpp,0)*F0^-3 * ( + 3/8*Xpp - 1/8*R(Xpp,Xqq)*Xpp - 1/32*R(Xpp,Xqq)*RD(Xpp) + 1/64*RD(Xpp) ) + Ab(Xpp)*Bb(Xqq,Xqq,0)*F0^-3 * ( - 1/32*R(Xpp,Xqq)*RD(Xqq) + 1/64*RD(Xqq) ) + Ab(Xpp)*Bb(Xp3,Xp3,0)*F0^-3 * ( - 1/4*Xp3 ) + Ab(Xpp)*Bb(X11,X22,0)*F0^-3 * ( - 1/8*R(Xqq,Xpp)*Xpp ) + Ab(Xpp)*Cb(Xpp,Xpp,Xpp,0)*F0^-3 * ( + 1/8*RD(Xpp)*Xpp ) + Ab(Xpp,eps)*F0^-3*pi16 * ( - 1/8*Xpp + 1/8*R(Xpp,Xqq)*X33 ) + Ab(Xp3)*F0^-3*pi16 * ( + 1/12*Xp3 - 1/4*Xq3 - 1/4*X33 ) + Ab(Xp3)*F0^-3*L0r * ( - 4*Xp3 ) + Ab(Xp3)*F0^-3*L3r * ( - 10*Xp3 ) + Ab(Xp3)*F0^-3*L4r * ( - 4*X33 ) + Ab(Xp3)*F0^-3*L5r * ( + 2*X12 ) + Ab(Xp3)^2*F0^-3 * ( - 1/8 ) + Ab(Xp3)*Bb(Xpp,Xpp,0)*F0^-3 * ( + 1/8*Xpp - 5/8*Xp3 ) + Ab(Xp3)*Bb(Xqq,Xqq,0)*F0^-3 * ( - 1/16*RD(Xqq) ) + Ab(Xp3)*Bb(X11,X22,0)*F0^-3 * ( + 1/6*X33 ) + Ab(Xp3)*Bb(X11,X22,0,kk)*F0^-3 * ( + 1/3 ) + Ab(Xp3,eps)*F0^-3*pi16 * ( + 1/2*X33 ) + Ab(X11)*Ab(X22)*F0^-3 * ( - 1/64 + 1/16*R(X11,X22)*R(X22,X11) ) + Ab(X12)*F0^-3*L1r * ( - 4*X12 ) + Ab(X12)*F0^-3*L2r * ( - 10*X12 ) + Ab(X12)^2*F0^-3 * ( + 1/8 ) + Ab(X12)*Bb(X11,X22,0,kk)*F0^-3 * ( - 1/2 ) + Ab(X12,eps)*F0^-3*pi16 * ( + 1/4*X12 ) + Ab(X13)*Ab(X23)*F0^-3 * ( + 1/4 ) + Ab(X33)*F0^-3*L1r * ( - 24*X33 ) + Ab(X33)*F0^-3*L2r * ( - 6*X33 ) + Ab(X33)*F0^-3*L4r * ( + 12*X33 ) + Ab(X33)*Bb(Xpp,Xpp,0)*F0^-3 * ( + 3/16*X33 ) + Ab(X33)*Bb(X11,X22,0)*F0^-3 * ( - 3/8*X33 ) + Ab(X33,eps)*F0^-3*pi16 * ( + 3/8*X33 ) + Bb(Xpp,Xpp,0)*F0^-3*pi16 * ( + 1/96*RD(Xpp)*Xpp + 1/32*RD(Xpp)*Xqq + 1/16*RD(Xpp)*X33 ) + Bb(Xpp,Xpp,0)*F0^-3*L0r * ( + RD(Xpp)*Xpp ) + Bb(Xpp,Xpp,0)*F0^-3*L3r * ( + 5/2*RD(Xpp)*Xpp ) + Bb(Xpp,Xpp,0)*F0^-3*L4r * ( + 2*Xpp*X33 - 4*R(Xpp,Xqq)*Xpp*X33 + 3*RD(Xpp)*X33 ) + Bb(Xpp,Xpp,0)*F0^-3*L5r * ( + Xpp^2 - 2*R(Xpp,Xqq)*X11*X22 - 1/2*RD(Xpp)*X12 ) + Bb(Xpp,Xpp,0)*F0^-3*L6r * ( + 4*X33^2 - 8*R(Xqq,Xpp)*Xpp*X33 ) + Bb(Xpp,Xpp,0)*F0^-3*L7r * ( + 4*RD(Xpp)^2 ) + Bb(Xpp,Xpp,0)*F0^-3*L8r * ( + 2*X33^2 - 4*R(Xqq,Xpp)*Xpp^2 ) + Bb(Xpp,Xpp,0)^2*F0^-3 * ( + 1/8*R(Xqq,Xpp)*RD(Xpp)*Xpp + 1/128*RD(Xpp)^2 ) + Bb(Xpp,Xpp,0)*Bb(X11,X22,0)*F0^-3 * ( - 1/8*R(Xqq,Xpp)*RD(Xpp)*Xpp ) + Bb(Xpp,Xpp,0)*Cb(Xpp,Xpp,Xpp,0)*F0^-3 * ( + 1/8*RD(Xpp)^2*Xpp ) + Bb(Xpp,Xpp,0,eps)*F0^-3*pi16 * ( - 1/8*RD(Xpp)*Xp3 ) + Bb(Xp3,Xp3,0)*F0^-3*L4r * ( - 8*Xp3*X33 ) + Bb(Xp3,Xp3,0)*F0^-3*L5r * ( - 4*Xp3^2 ) + Bb(Xp3,Xp3,0)*F0^-3*L6r * ( + 16*Xp3*X33 ) + Bb(Xp3,Xp3,0)*F0^-3*L8r * ( + 8*Xp3^2 ) + Bb(X11,X11,0)*Bb(X22,X22,0)*F0^-3 * ( + 1/64*RD(X11)*RD(X22) ) + Bb(X11,X22,0)*F0^-3*L7r * ( - 8*RD(X11)*RD(X22) ) + Bb(X11,X22,0)*F0^-3*L8r * ( - 4*RD(X11)*RD(X22) ) + Cb(Xpp,Xpp,Xpp,0)*F0^-3*L4r * ( + 4*RD(Xpp)*Xpp*X33 ) + Cb(Xpp,Xpp,Xpp,0)*F0^-3*L5r * ( + 2*RD(Xpp)*Xpp^2 ) + Cb(Xpp,Xpp,Xpp,0)*F0^-3*L6r * ( - 8*RD(Xpp)*Xpp*X33 ) + Cb(Xpp,Xpp,Xpp,0)*F0^-3*L8r * ( - 4*RD(Xpp)*Xpp^2 ) + Hbb(1,Xpp,Xpp,X12,X12)*F0^-3 * ( + 1/8*Xpp - 5/64*X12 + 1/16*R(Xpp,Xqq)*R(Xqq,Xpp)*X12 ) + Hbb(1,Xpp,X13,X23,X12)*F0^-3 * ( - 1/16*Xpp + 1/16*Xqq - 1/8*R(Xpp,Xqq)*X33 ) + Hbb(1,X11,X12,X22,X12)*F0^-3 * ( + 1/32*X12 - 1/8*R(X11,X22)*R(X22,X11)*X12 ) + Hbb(1,X12,X12,X12,X12)*F0^-3 * ( - 1/8*X12 ) + Hbb(1,X13,X23,X33,X12)*F0^-3 * ( - 3/8*X33 ) + Hbb(2,Xpp,Xpp,X12,X12)*F0^-3 * ( + 1/16*R(Xpp,Xqq)*RD(Xpp)*X12 - 1/32*RD(Xpp)*X12 ) + Hbb(2,Xpp,X12,Xqq,X12)*F0^-3 * ( + 1/16*R(Xqq,Xpp)*RD(Xpp)*X12 - 1/32*RD(Xpp)*X12 ) + Hbb(2,Xpp,X13,X23,X12)*F0^-3 * ( + 1/8*RD(Xpp)*Xp3 ) + Hbb(5,Xpp,Xpp,X12,X12)*F0^-3 * ( - 1/64*RD(Xpp)^2*X12 ) + Hbb(5,X11,X22,X12,X12)*F0^-3 * ( - 1/32*RD(X11)*RD(X22)*X12 ) + dHbb(1,Xpp,Xpp,X12,X12)*F0^-3 * ( - 1/8*Xpp*X12 - 15/64*X12^2 + 3/16*R(Xpp,Xqq)*X12^2 - 1/16*R(Xpp,Xqq)^2*X12^2 ) + dHbb(1,Xpp,X13,X23,X12)*F0^-3 * ( + 1/8*X12^2 + 3/8*R(Xqq,Xpp)*Xpp*X12 + 1/8*R(Xqq,Xpp)*Xqq*X12 - 1/8*R(Xqq,Xpp)*X12*X33 ) + dHbb(1,X11,X12,X22,X12)*F0^-3 * ( - 1/32*X12^2 + 3/8*R(X11,X22)*R(X22,X11)*X12^2 ) + dHbb(1,X12,X12,X12,X12)*F0^-3 * ( + 1/8*X12^2 ) + dHbb(1,X13,X23,X33,X12)*F0^-3 * ( + 3/8*X12*X33 ) + dHbb(2,Xpp,Xpp,X12,X12)*F0^-3 * ( - 1/16*R(Xpp,Xqq)*RD(Xpp)*X12^2 + 5/32*RD(Xpp)*X12^2 ) + dHbb(2,Xpp,X12,Xqq,X12)*F0^-3 * ( - 1/16*R(Xqq,Xpp)*RD(Xpp)*X12^2 + 1/32*RD(Xpp)*X12^2 ) + dHbb(2,Xpp,X13,X23,X12)*F0^-3 * ( - 1/8*RD(Xpp)*Xp3*X12 ) + dHbb(5,Xpp,Xpp,X12,X12)*F0^-3 * ( + 5/64*RD(Xpp)^2*X12^2 ) + dHbb(5,X11,X22,X12,X12)*F0^-3 * ( + 1/32*RD(X11)*RD(X22)*X12^2 ) + dH1bb(1,Xpp,Xpp,X12,X12)*F0^-3 * ( + 5/4*X12^2 - 1/2*R(Xpp,Xqq)*R(Xqq,Xpp)*X12^2 ) + dH1bb(1,Xpp,X13,X23,X12)*F0^-3 * ( - R(Xqq,Xpp)*X12^2 ) + dH1bb(1,Xp3,Xq3,Xpp,X12)*F0^-3 * ( - X12^2 ) + dH1bb(1,X12,X11,X22,X12)*F0^-3 * ( + 1/4*X12^2 - 1/2*R(X11,X22)*R(X22,X11)*X12^2 ) + dH1bb(3,X12,Xpp,Xpp,X12)*F0^-3 * ( - 1/4*R(Xqq,Xpp)*RD(Xpp)*X12^2 ) + dH1bb(3,X12,Xpp,Xqq,X12)*F0^-3 * ( + 1/4*R(Xqq,Xpp)*RD(Xpp)*X12^2 ) + dH1bb(7,X12,Xpp,Xpp,X12)*F0^-3 * ( - 1/8*RD(Xpp)^2*X12^2 ) + dH21bb(1,Xpp,Xpp,X12,X12)*F0^-3 * ( - 3/8*X12^2 ) + dH21bb(1,Xpp,X13,X23,X12)*F0^-3 * ( + 3/8*R(Xqq,Xpp)*X12^2 ) + dH21bb(1,Xp3,Xq3,Xpp,X12)*F0^-3 * ( + 3/8*R(Xpp,Xqq)*X12^2 ) + dH21bb(1,Xp3,Xq3,Xqq,X12)*F0^-3 * ( - 3/8*R(Xpp,Xqq)*X12^2 ) + dH21bb(1,X12,Xpp,Xpp,X12)*F0^-3 * ( + 15/64*X12^2 - 3/16*R(Xpp,Xqq)*R(Xqq,Xpp)*X12^2 ) + dH21bb(1,X12,X11,X22,X12)*F0^-3 * ( - 3/32*X12^2 + 3/8*R(X11,X22)*R(X22,X11)*X12^2 ) + dH21bb(1,X12,X12,X12,X12)*F0^-3 * ( + 3/8*X12^2 ) + dH21bb(1,X33,X13,X23,X12)*F0^-3 * ( + 9/8*X12^2 ) + dH21bb(3,Xp3,Xpp,Xq3,X12)*F0^-3 * ( - 3/8*RD(Xpp)*X12^2 ) + dH21bb(3,X12,Xpp,Xpp,X12)*F0^-3 * ( - 3/16*R(Xpp,Xqq)*RD(Xpp)*X12^2 + 3/32*RD(Xpp)*X12^2 ) + dH21bb(3,X12,Xpp,Xqq,X12)*F0^-3 * ( - 3/16*R(Xqq,Xpp)*RD(Xpp)*X12^2 + 3/32*RD(Xpp)*X12^2 ) + dH21bb(7,X12,Xpp,Xpp,X12)*F0^-3 * ( + 3/64*RD(Xpp)^2*X12^2 ) + dH21bb(7,X12,X11,X22,X12)*F0^-3 * ( + 3/32*RD(X11)*RD(X22)*X12^2 );