*FORM by J.Vermaseren,version 3.1(Oct 17 2002) Run at: Wed Mar 16 17:13:54 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 "3" * * * 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 "2" * #define type "2" * * #define pout "0" * #define nsim "0" * * #- * Sigma2 loaded * Sigma4 loaded * Sigma6 loaded * *Time = 0.39 sec Generated terms = 1 * M0p2 Terms in output = 1 * Bytes used = 24 * *Time = 0.39 sec Generated terms = 5 * M0p4 Terms in output = 5 * Bytes used = 182 * *Time = 0.39 sec Generated terms = 185 * M0p6 Terms in output = 185 * Bytes used = 7098 L M0p2timo21 = + X13 ; L M0p4timo21 = + F0^-2*L4r * ( - 24*X13*X44 ) + F0^-2*L5r * ( - 8*X13^2 ) + F0^-2*L6r * ( + 48*X13*X44 ) + F0^-2*L8r * ( + 16*X13^2 ) + Ab(Xpp)*F0^-2 * ( - 1/3*R(Xpp,Xqq)*X13 ); L M0p6timo21 = + F0^-4*pi16*L0r * ( + X11*X13*X33 + 3*X13*X44^2 + 26/3*X13^2*X44 - 2*X13^3 ) + F0^-4*pi16*L1r * ( + 4*X13^3 ) + F0^-4*pi16*L2r * ( + 16*X13*X44^2 + 2*X13^3 ) + F0^-4*pi16*L3r * ( + 7/6*X11*X13*X33 + 3/2*X13*X44^2 + 17/3*X13^2*X44 - 11/3*X13^3 ) + F0^-4*pi16^2 * ( + 59/192*X11*X13*X33 + 73/64*X13*X44^2 + 15/32*X13^2*X44 - 77/192*X13^3 ) + F0^-4*L4r*L5r * ( + 384*X13^2*X44 ) + F0^-4*L4r*L6r * ( - 1152*X13*X44^2 ) + F0^-4*L4r*L8r * ( - 384*X13^2*X44 ) + F0^-4*L4r^2 * ( + 576*X13*X44^2 ) + F0^-4*L5r*L6r * ( - 384*X13^2*X44 ) + F0^-4*L5r*L8r * ( - 128*X13^3 ) + F0^-4*L5r^2 * ( + 64*X13^3 ) + F0^-4*K17r * ( - 32*X13^3 ) + F0^-4*K18r * ( - 96*X13^2*X44 ) + F0^-4*K19r * ( - 8*Xpp^2*X13 ) + F0^-4*K20r * ( - 48*X13^2*X44 ) + F0^-4*K21r * ( - 48*X13*X44^2 ) + F0^-4*K22r * ( - 144*X13*X44^2 ) + F0^-4*K23r * ( - 16*X11*X13*X33 ) + F0^-4*K25r * ( + 24*Xpp^2*X13 ) + F0^-4*K26r * ( + 48*X13*X44^2 + 96*X13^2*X44 ) + F0^-4*K27r * ( + 432*X13*X44^2 ) + F0^-4*K39r * ( + 32*X13^3 ) + F0^-4*K40r * ( + 96*X13^2*X44 ) + Ab(Xpp)*F0^-4*pi16 * ( - 1/24*Xqq*X13 - 1/8*X13*X44 + 1/4*R(Xpp,Xqq)*X13*X44 + 1/12*R(Xpp,Xqq)*X13^2 ) + Ab(Xpp)*F0^-4*L0r * ( - 4/3*Xpp*X13 - 16/3*R(Xpp,Xqq)*Xpp*X13 - 4/3*RD(Xpp)*X13 ) + Ab(Xpp)*F0^-4*L3r * ( - 10/3*Xpp*X13 - 4/3*R(Xpp,Xqq)*Xpp*X13 - 10/3*RD(Xpp)*X13 ) + Ab(Xpp)*F0^-4*L4r * ( + 16*R(Xpp,Xqq)*X13*X44 ) + Ab(Xpp)*F0^-4*L5r * ( + 8/3*Xpp*X13 + 16/3*R(Xpp,Xqq)*Xpp*X13 ) + Ab(Xpp)*F0^-4*L6r * ( - 16*R(Xpp,Xqq)*X13*X44 ) + Ab(Xpp)*F0^-4*L7r * ( + 16/3*RD(Xpp)*Xp4 + 32/3*RD(Xpp)*X13 ) + Ab(Xpp)*F0^-4*L8r * ( - 16/3*Xpp*X13 - 32/9*R(Xpp,Xqq)*X11*X33 - 64/9*R(Xpp,Xqq)*X13^2 - 8/9*RD(Xpp)^2 ) + Ab(Xpp)^2*F0^-4 * ( + 5/36*X13 + 1/18*R(Xpp,Xqq)^2*X13 - 1/54*R(Xqq,Xpp)*Xpp ) + Ab(Xpp)*Ab(Xp4)*F0^-4 * ( + 1/24*Xpp - 1/8*Xqq + 1/24*R(Xpp,Xqq)*Xpp + 19/72*R(Xpp,Xqq)*Xqq ) + Ab(Xpp)*Ab(Xq4)*F0^-4 * ( + 1/4*X13 + 1/6*R(Xpp,Xqq)*Xqq - 1/24*R(Xqq,Xpp)*Xpp + 1/72*R(Xqq,Xpp)*Xqq ) + Ab(Xpp)*Ab(X13)*F0^-4 * ( + 1/18*Xpp - 1/36*X13 ) + Ab(Xpp)*Ab(X44)*F0^-4 * ( - 4/27*X44 ) + Ab(Xpp)*Bb(Xpp,Xpp,0)*F0^-4 * ( + 11/54*R(Xpp,Xqq)*Xpp*X13 - 1/27*R(Xpp,Xqq)*Xpp^2 - 1/18*R(Xpp,Xqq)*X13^2 + 1/54*R(Xpp,Xqq)*RD(Xpp)*Xpp ) + Ab(Xpp)*Bb(Xqq,Xqq,0)*F0^-4 * ( - 1/54*R(Xpp,Xqq)*RD(Xqq)*Xqq - 1/36*RD(Xqq)*X13 ) + Ab(Xpp)*Bb(X11,X33,0)*F0^-4 * ( + 2/27*R(Xqq,Xpp)*Xpp*X13 ) + Ab(Xpp)*Bb(X11,X33,0,kk)*F0^-4 * ( + 1/27*R(Xqq,Xpp)*Xpp ) + Ab(Xpp,eps)*F0^-4*pi16 * ( + 13/72*Xpp*X13 + 5/72*Xqq*X13 + 5/36*X13*X44 + 5/18*R(Xpp,Xqq)*Xpp*X13 - 1/4*R(Xpp,Xqq)*X13*X44 ) + Ab(Xp4)*F0^-4*pi16 * ( - 3/4*Xpp*X13 + 3/2*X13*X44 + 3/4*X13^2 ) + Ab(Xp4)*F0^-4*L0r * ( + 12*Xp4*X13 ) + Ab(Xp4)*F0^-4*L3r * ( + 30*Xp4*X13 ) + Ab(Xp4)*F0^-4*L5r * ( - 24*Xp4*X13 ) + Ab(Xp4)*F0^-4*L8r * ( + 48*Xp4*X13 ) + Ab(Xp4)*Bb(Xqq,Xqq,0)*F0^-4 * ( + 1/4*RD(Xqq)*X13 ) + Ab(Xp4)*Bb(X11,X33,0)*F0^-4 * ( - 4/9*Xpp*X13 - 2/9*X13*X44 + 1/9*R(Xpp,Xqq)*Xpp^2 ) + Ab(Xp4)*Bb(X11,X33,0,kk)*F0^-4 * ( - 2/9*Xp4 - 2/9*X13 + 1/9*R(Xqq,Xpp)*Xqq ) + Ab(Xp4,eps)*F0^-4*pi16 * ( - 9/4*X13*X44 - 5/4*X13^2 ) + Ab(X11)*Ab(X33)*F0^-4 * ( - 1/36*X13 - 1/54*X44 + 1/9*R(X11,X33)*R(X33,X11)*X13 ) + Ab(X13)*F0^-4*L1r * ( + 8*X13^2 ) + Ab(X13)*F0^-4*L2r * ( + 20*X13^2 ) + Ab(X13)*F0^-4*L6r * ( + 32*X13^2 ) + Ab(X13)^2*F0^-4 * ( - 1/4*X13 ) + Ab(X13)*Bb(X11,X33,0)*F0^-4 * ( + 1/9*X11*X33 + 4/9*X13^2 ) + Ab(X13)*Bb(X11,X33,0,kk)*F0^-4 * ( + 4/9*X13 ) + Ab(X13,eps)*F0^-4*pi16 * ( - 31/18*X13^2 ) + Ab(X14)*Ab(X34)*F0^-4 * ( - 9/4*X13 ) + Ab(X44)*F0^-4*L1r * ( + 128*X13*X44 ) + Ab(X44)*F0^-4*L2r * ( + 32*X13*X44 ) + Ab(X44)*F0^-4*L4r * ( - 128*X13*X44 ) + Ab(X44)*F0^-4*L6r * ( + 128*X13*X44 ) + Ab(X44)*Bb(X11,X33,0)*F0^-4 * ( + 16/27*X13*X44 ) + Ab(X44)*Bb(X11,X33,0,kk)*F0^-4 * ( + 8/27*X44 ) + Ab(X44,eps)*F0^-4*pi16 * ( - 2*X13*X44 ) + Bb(Xpp,Xpp,0)*F0^-4*pi16 * ( - 1/24*RD(Xpp)*Xqq*X13 - 1/8*RD(Xpp)*X13*X44 ) + Bb(Xpp,Xpp,0)*F0^-4*L0r * ( - 4/3*RD(Xpp)*Xpp*X13 ) + Bb(Xpp,Xpp,0)*F0^-4*L3r * ( - 10/3*RD(Xpp)*Xpp*X13 ) + Bb(Xpp,Xpp,0)*F0^-4*L4r * ( + 8*R(Xpp,Xqq)*Xpp*X13*X44 ) + Bb(Xpp,Xpp,0)*F0^-4*L5r * ( + 8/3*R(Xpp,Xqq)*Xpp^3 + 4/3*RD(Xpp)*X11*X33 ) + Bb(Xpp,Xpp,0)*F0^-4*L6r * ( - 16*R(Xpp,Xqq)*Xpp*X13*X44 ) + Bb(Xpp,Xpp,0)*F0^-4*L8r * ( - 16/3*R(Xpp,Xqq)*Xpp^3 - 8/3*RD(Xpp)*X11*X33 ) + Bb(Xpp,Xpp,0)^2*F0^-4 * ( + 1/8*R(Xpp,Xqq)*RD(Xpp)*Xpp*X13 - 1/72*R(Xpp,Xqq)*RD(Xpp)*Xqq*X13 ) + Bb(Xpp,Xpp,0)*Bb(X11,X33,0)*F0^-4 * ( + 2/27*R(Xqq,Xpp)*RD(Xpp)*Xpp*X13 ) + Bb(Xpp,Xpp,0)*Bb(X11,X33,0,kk)*F0^-4 * ( + 1/27*R(Xqq,Xpp)*RD(Xpp)*Xpp ) + Bb(Xpp,Xpp,0,eps)*F0^-4*pi16 * ( + 1/4*RD(Xpp)*Xp4*X13 + 5/36*RD(Xpp)*X13^2 ) + Bb(X11,X11,0)*Bb(X33,X33,0)*F0^-4 * ( - 1/36*RD(X11)*RD(X33)*X13 ) + Bb(X11,X33,0)*F0^-4*L7r * ( + 32/3*RD(X11)*RD(X33)*X13 ) + Bb(X11,X33,0)*F0^-4*L8r * ( + 32/9*RD(X11)*RD(X33)*X13 ) + Bb(X11,X33,0,kk)*F0^-4*L7r * ( + 16/3*RD(X11)*RD(X33) ) + Bb(X11,X33,0,kk)*F0^-4*L8r * ( + 16/9*RD(X11)*RD(X33) ) + Hbb(1,Xpp,Xpp,X13,X13)*F0^-4 * ( - 1/4*Xpp*X13 - 5/12*X13^2 + 1/6*R(Xpp,Xqq)*X13^2 - 1/18*R(Xpp,Xqq)^2*X13^2 ) + Hbb(1,Xpp,X14,X34,X13)*F0^-4 * ( + 1/4*X13^2 + 3/4*R(Xqq,Xpp)*Xpp*X13 + 1/4*R(Xqq,Xpp)*Xqq*X13 - 1/4*R(Xqq,Xpp)*X13*X44 ) + Hbb(1,X11,X13,X33,X13)*F0^-4 * ( - 1/36*X13^2 + 1/3*R(X11,X33)*R(X33,X11)*X13^2 ) + Hbb(1,X13,X13,X13,X13)*F0^-4 * ( + 1/4*X13^2 ) + Hbb(1,X14,X34,X44,X13)*F0^-4 * ( + 2*X13*X44 ) + Hbb(2,Xpp,Xpp,X13,X13)*F0^-4 * ( - 1/18*R(Xpp,Xqq)*RD(Xpp)*X13^2 + 5/36*RD(Xpp)*X13^2 ) + Hbb(2,Xpp,X13,Xqq,X13)*F0^-4 * ( - 1/18*R(Xqq,Xpp)*RD(Xpp)*X13^2 + 1/36*RD(Xpp)*X13^2 ) + Hbb(2,Xpp,X14,X34,X13)*F0^-4 * ( - 1/4*RD(Xpp)*Xp4*X13 ) + Hbb(5,Xpp,Xpp,X13,X13)*F0^-4 * ( + 5/72*RD(Xpp)^2*X13^2 ) + Hbb(5,X11,X33,X13,X13)*F0^-4 * ( + 1/36*RD(X11)*RD(X33)*X13^2 ) + H1bb(1,Xpp,Xpp,X13,X13)*F0^-4 * ( + 20/9*X13^2 - 4/9*R(Xpp,Xqq)*R(Xqq,Xpp)*X13^2 ) + H1bb(1,Xpp,X14,X34,X13)*F0^-4 * ( - 2*R(Xqq,Xpp)*X13^2 ) + H1bb(1,Xp4,Xq4,Xpp,X13)*F0^-4 * ( - 2*X13^2 ) + H1bb(1,X13,X11,X33,X13)*F0^-4 * ( + 2/9*X13^2 - 4/9*R(X11,X33)*R(X33,X11)*X13^2 ) + H1bb(3,X13,Xpp,Xpp,X13)*F0^-4 * ( + 2/9*R(Xpp,Xqq)*RD(Xpp)*X13^2 - 2/9*RD(Xpp)*X13^2 ) + H1bb(3,X13,Xpp,Xqq,X13)*F0^-4 * ( + 2/9*R(Xqq,Xpp)*RD(Xpp)*X13^2 ) + H1bb(7,X13,Xpp,Xpp,X13)*F0^-4 * ( - 1/9*RD(Xpp)^2*X13^2 ) + H21bb(1,Xpp,Xpp,X13,X13)*F0^-4 * ( - 3/4*X13^2 ) + H21bb(1,Xpp,X14,X34,X13)*F0^-4 * ( + 3/4*R(Xqq,Xpp)*X13^2 ) + H21bb(1,Xp4,Xq4,Xpp,X13)*F0^-4 * ( + 3/4*R(Xpp,Xqq)*X13^2 ) + H21bb(1,Xp4,Xq4,Xqq,X13)*F0^-4 * ( - 3/4*X13^2 + 3/4*R(Xqq,Xpp)*X13^2 ) + H21bb(1,X13,Xpp,Xpp,X13)*F0^-4 * ( + 5/12*X13^2 - 1/6*R(Xpp,Xqq)*R(Xqq,Xpp)*X13^2 ) + H21bb(1,X13,X11,X33,X13)*F0^-4 * ( - 1/12*X13^2 + 1/3*R(X11,X33)*R(X33,X11)*X13^2 ) + H21bb(1,X13,X13,X13,X13)*F0^-4 * ( + 3/4*X13^2 ) + H21bb(1,X44,X14,X34,X13)*F0^-4 * ( + 6*X13^2 ) + H21bb(3,Xp4,Xpp,Xq4,X13)*F0^-4 * ( - 3/4*RD(Xpp)*X13^2 ) + H21bb(3,X13,Xpp,Xpp,X13)*F0^-4 * ( - 1/6*R(Xpp,Xqq)*RD(Xpp)*X13^2 + 1/12*RD(Xpp)*X13^2 ) + H21bb(3,X13,Xpp,Xqq,X13)*F0^-4 * ( - 1/6*R(Xqq,Xpp)*RD(Xpp)*X13^2 + 1/12*RD(Xpp)*X13^2 ) + H21bb(7,X13,Xpp,Xpp,X13)*F0^-4 * ( + 1/24*RD(Xpp)^2*X13^2 ) + H21bb(7,X13,X11,X33,X13)*F0^-4 * ( + 1/12*RD(X11)*RD(X33)*X13^2 );