*FORM by J.Vermaseren,version 3.1(Oct 17 2002) Run at: Mon Sep 19 16:04:22 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 "4" * #define type "1" * * #define pout "0" * #define nsim "0" * * #- * Sigma2 loaded * Sigma4 loaded * Sigma6 loaded * *Time = 0.26 sec Generated terms = 1 * M0p2 Terms in output = 1 * Bytes used = 24 * *Time = 0.26 sec Generated terms = 7 * M0p4 Terms in output = 7 * Bytes used = 300 * *Time = 0.26 sec Generated terms = 172 * M0p6 Terms in output = 172 * Bytes used = 7830 L M0p2timo12 = + X11 ; L M0p4timo12 = + F0^-2*L4r * ( - 24*Xb(1)*X11 ) + F0^-2*L5r * ( - 8*X11^2 ) + F0^-2*L6r * ( + 48*Xb(1)*X11 ) + F0^-2*L8r * ( + 16*X11^2 ) + Ab(Xe0)*F0^-2 * ( - 1/3*R(Xe0,X11,X11)*X11 ) + Ab(X11)*F0^-2 * ( - 1/3*RC(X11)*X11 ) + Bb(X11,X11,0)*F0^-2 * ( - 1/3*RD(X11)*X11 ); L M0p6timo12 = + F0^-4*pi16*L0r * ( - 8/9*Xe0*X11*X44 - X11^3 + 26/3*Xb(1)*X11^2 + 35/9*Xb(2)*X11 ) + F0^-4*pi16*L1r * ( + 4*X11^3 ) + F0^-4*pi16*L2r * ( + 22/3*Xe0*X11*X44 + 2*X11^3 + 26/3*Xb(2)*X11 ) + F0^-4*pi16*L3r * ( - 8/9*Xe0*X11*X44 - 5/2*X11^3 + 17/3*Xb(1)*X11^2 + 43/18*Xb(2)*X11 ) + F0^-4*pi16^2 * ( + 15/32*Xe0*X11*X44 - 3/32*X11^3 + 15/32*Xb(1)*X11^2 + 43/64*Xb(2)*X11 ) + F0^-4*L4r*L5r * ( + 384*Xb(1)*X11^2 ) + F0^-4*L4r*L6r * ( - 1152*Xb(1)^2*X11 ) + F0^-4*L4r*L8r * ( - 384*Xb(1)*X11^2 ) + F0^-4*L4r^2 * ( + 576*Xb(1)^2*X11 ) + F0^-4*L5r*L6r * ( - 384*Xb(1)*X11^2 ) + F0^-4*L5r*L8r * ( - 128*X11^3 ) + F0^-4*L5r^2 * ( + 64*X11^3 ) + F0^-4*K17r * ( - 32*X11^3 ) + F0^-4*K18r * ( - 96*Xb(1)*X11^2 ) + F0^-4*K19r * ( - 16*X11^3 ) + F0^-4*K20r * ( - 48*Xb(1)*X11^2 ) + F0^-4*K21r * ( - 48*Xb(2)*X11 ) + F0^-4*K22r * ( - 144*Xb(1)^2*X11 ) + F0^-4*K23r * ( - 16*X11^3 ) + F0^-4*K25r * ( + 48*X11^3 ) + F0^-4*K26r * ( + 96*Xb(1)*X11^2 + 48*Xb(2)*X11 ) + F0^-4*K27r * ( + 432*Xb(1)^2*X11 ) + F0^-4*K39r * ( + 32*X11^3 ) + F0^-4*K40r * ( + 96*Xb(1)*X11^2 ) + Ab(Xe0)*F0^-4*L0r * ( - 8*R(Xe0,X11,X11)*Xe0*X11 ) + Ab(Xe0)*F0^-4*L1r * ( + 16*Xe0*X11 ) + Ab(Xe0)*F0^-4*L2r * ( + 4*Xe0*X11 ) + Ab(Xe0)*F0^-4*L3r * ( - 8*R(Xe0,X11,X11)*Xe0*X11 ) + Ab(Xe0)*F0^-4*L4r * ( - 16*Xe0*X11 + 16*Xb(1)*R(Xe0,X11,X11)*X11 ) + Ab(Xe0)*F0^-4*L5r * ( + 16/3*R(Xe0,X11,X11)*Xe0*X11 + 16/3*R(Xe0,X11,X11)*X11^2 ) + Ab(Xe0)*F0^-4*L6r * ( + 16*Xe0*X11 - 16*Xb(1)*R(Xe0,X11,X11)*X11 ) + Ab(Xe0)*F0^-4*L7r * ( + 32*RD(Xe0,X44,X66,X11)*X11 ) + Ab(Xe0)*F0^-4*L8r * ( - 64/3*R(Xe0,X11,X11)*X11^2 ) + Ab(Xe0)^2*F0^-4 * ( + 1/18*R(Xe0,X11,X11)^2*X11 ) + Ab(Xe0)*Ab(X11)*F0^-4 * ( + 1/9*R(Xe0,X11,X11)*RC(X11)*X11 ) + Ab(Xe0)*Ab(X46)*F0^-4 * ( - 1/3*R(Xe0,X11,X11)*X11 ) + Ab(Xe0)*Ab(X1s)*F0^-4 * ( - 4/9*R(Xe0,X11,Xss)*RS(X11,Xss,Xe0)*X11 ) + Ab(Xe0)*Bb(Xe0,Xe0,0)*F0^-4 * ( + 1/9*Xb(1)*R(Xe0,X11,X11)*X11 - 5/18*R(Xe0,X11,X11)*Xe0*X11 ) + Ab(Xe0)*Bb(X11,Xe0,0)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)*R(X11,Xe0,Xe0)*X11^2 - 2/9*R(Xe0,X11,X44)*R(X11,Xe0,Xe0)*Xe0*X11 ) + Ab(Xe0)*Bb(X11,X11,0)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)*RC(X11)*X11^2 + 1/9*R(Xe0,X11,X11)*RD(X11)*X11 - 1/27*R(Xe0,Xss,Xss)*R(X11,Xss,Xe0)^2*X11*Xss ) + Ab(Xe0)*Cb(X11,X11,X11,0)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)*RD(X11)*X11^2 ) + Ab(Xe0,eps)*F0^-4*pi16 * ( + 5/9*R(Xe0,X11,X11)*X11^2 - 1/4*RC(X11)*Xe0*X11 ) + Ab(X11)*F0^-4*L0r * ( - 8*RC(X11)*X11^2 - 8*RD(X11)*X11 ) + Ab(X11)*F0^-4*L1r * ( + 8*X11^2 ) + Ab(X11)*F0^-4*L2r * ( + 20*X11^2 ) + Ab(X11)*F0^-4*L3r * ( - 8*RC(X11)*X11^2 - 8*RD(X11)*X11 ) + Ab(X11)*F0^-4*L4r * ( + 16*Xb(1)*RC(X11)*X11 ) + Ab(X11)*F0^-4*L5r * ( + 32/3*RC(X11)*X11^2 + 16/3*RD(X11)*X11 ) + Ab(X11)*F0^-4*L6r * ( + 32*X11^2 - 16*Xb(1)*RC(X11)*X11 ) + Ab(X11)*F0^-4*L7r * ( + 32*RD(X11)*X11 ) + Ab(X11)*F0^-4*L8r * ( - 64/3*RC(X11)*X11^2 ) + Ab(X11)^2*F0^-4 * ( + 1/2*X11 + 1/18*RC(X11)^2*X11 ) + Ab(X11)*Ab(X46)*F0^-4 * ( + 1/3*R(Xe0,X11,X11)*X11 ) + Ab(X11)*Ab(X1s)*F0^-4 * ( + 4/9*R(Xe0,X11,Xss)*RS(X11,Xss,Xe0)*X11 ) + Ab(X11)*Bb(X11,Xe0,0)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)*RC(X11)*X11^2 ) + Ab(X11)*Bb(X11,X11,0)*F0^-4 * ( + X11^2 + 2/9*RC(X11)^2*X11^2 + 1/9*RC(X11)*RD(X11)*X11 ) + Ab(X11)*Cb(X11,X11,X11,0)*F0^-4 * ( + 2/9*RC(X11)*RD(X11)*X11^2 ) + Ab(X11,eps)*F0^-4*pi16 * ( - 31/18*X11^2 + 29/36*RC(X11)*X11^2 + 1/4*RD(X11)*X11 ) + Ab(X14)^2*F0^-4 * ( - X11 ) + Ab(X14)*Ab(X16)*F0^-4 * ( - X11 ) + Ab(X16)^2*F0^-4 * ( - 1/4*X11 ) + Ab(X44)*F0^-4*L1r * ( + 48*X11*X44 ) + Ab(X44)*F0^-4*L2r * ( + 12*X11*X44 ) + Ab(X44)*F0^-4*L4r * ( - 48*X11*X44 ) + Ab(X44)*F0^-4*L6r * ( + 48*X11*X44 ) + Ab(X44)*Bb(Xe0,Xe0,0)*F0^-4 * ( - 1/6*R(Xe0,X11,X11)*X11*X44 ) + Ab(X44)*Bb(X11,Xe0,0)*F0^-4 * ( + 2/3*R(Xe0,X11,X44)*R(X11,X44,Xe0)*X11*X44 ) + Ab(X44)*Bb(X11,X11,0)*F0^-4 * ( + 1/3*R(X11,X44,Xe0)^2*X11*X44 ) + Ab(X44,eps)*F0^-4*pi16 * ( - 3/4*X11*X44 ) + Ab(X46)*F0^-4*L1r * ( + 64*X11*X46 ) + Ab(X46)*F0^-4*L2r * ( + 16*X11*X46 ) + Ab(X46)*F0^-4*L4r * ( - 64*X11*X46 ) + Ab(X46)*F0^-4*L6r * ( + 64*X11*X46 ) + Ab(X46)*Bb(Xe0,Xe0,0)*F0^-4 * ( + 4/9*R(Xe0,X11,X11)*X11*X46 ) + Ab(X46)*Bb(X11,Xe0,0)*F0^-4 * ( - 4/27*RU(X11,Xe0,X11,X44,X66)*X11^2 + 4/27*RW(X11,Xe0,X11,X44,X66)*X11 ) + Ab(X46)*Bb(X11,X11,0)*F0^-4 * ( + 4/9*R(X11,Xe0,Xe0)*X11*X46 ) + Ab(X46,eps)*F0^-4*pi16 * ( - X11*X46 ) + Ab(X1s)*F0^-4*pi16 * ( + 1/4*X11*Xss + 3/4*Xb(1)*X11 ) + Ab(X1s)*F0^-4*L0r * ( + 8*X11*X1s ) + Ab(X1s)*F0^-4*L3r * ( + 20*X11*X1s ) + Ab(X1s)*F0^-4*L5r * ( - 16*X11*X1s ) + Ab(X1s)*F0^-4*L8r * ( + 32*X11*X1s ) + Ab(X1s)*Bb(X11,Xe0,0)*F0^-4 * ( - 4/9*R(Xe0,X11,Xss)*X11*X1s - 2/9*R(Xe0,X11,Xss)*X11^2 ) + Ab(X1s)*Bb(X11,X11,0)*F0^-4 * ( - 2/3*R(X11,Xss,Xe0)*X11*Xss ) + Ab(X1s,eps)*F0^-4*pi16 * ( - 3/4*X11*Xss - 5/6*X11^2 - 3/4*Xb(1)*X11 ) + Bb(Xe0,Xe0,0)*F0^-4*L4r * ( + 8*Xb(1)*R(Xe0,X11,X11)*Xe0*X11 ) + Bb(Xe0,Xe0,0)*F0^-4*L5r * ( + 8/3*R(Xe0,X11,X11)*Xe0^2*X11 ) + Bb(Xe0,Xe0,0)*F0^-4*L6r * ( - 16*Xb(1)*R(Xe0,X11,X11)*Xe0*X11 ) + Bb(Xe0,Xe0,0)*F0^-4*L7r * ( + 16*RD(Xe0,X44,X66,X11)^2*X11 ) + Bb(Xe0,Xe0,0)*F0^-4*L8r * ( - 16/3*R(Xe0,X11,X11)*Xe0^2*X11 + 16/3*RD(Xe0,X44,X66,X11)^2*X11 ) + Bb(X11,Xe0,0)*F0^-4*L7r * ( + 32*RD(Xe0,X44,X66,X11)*RD(X11)*X11 ) + Bb(X11,Xe0,0)*F0^-4*L8r * ( + 32/3*RD(Xe0,X44,X66,X11)*RD(X11)*X11 ) + Bb(X11,Xe0,0)*Bb(X11,X11,0)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)*RD(X11)*X11^2 ) + Bb(X11,X11,0)*F0^-4*L0r * ( - 8*RD(X11)*X11^2 ) + Bb(X11,X11,0)*F0^-4*L3r * ( - 8*RD(X11)*X11^2 ) + Bb(X11,X11,0)*F0^-4*L4r * ( + 8*Xb(1)*RC(X11)*X11^2 + 24*Xb(1)*RD(X11)*X11 ) + Bb(X11,X11,0)*F0^-4*L5r * ( + 8/3*RC(X11)*X11^3 + 16*RD(X11)*X11^2 ) + Bb(X11,X11,0)*F0^-4*L6r * ( - 16*Xb(1)*RC(X11)*X11^2 - 32*Xb(1)*RD(X11)*X11 ) + Bb(X11,X11,0)*F0^-4*L7r * ( + 16*RD(X11)^2*X11 ) + Bb(X11,X11,0)*F0^-4*L8r * ( - 16/3*RC(X11)*X11^3 - 32*RD(X11)*X11^2 + 16/3*RD(X11)^2*X11 ) + Bb(X11,X11,0)^2*F0^-4 * ( + 2/9*RC(X11)*RD(X11)*X11^2 + 1/18*RD(X11)^2*X11 ) + Bb(X11,X11,0)*Cb(X11,X11,X11,0)*F0^-4 * ( + 2/9*RD(X11)^2*X11^2 ) + Bb(X11,X11,0,eps)*F0^-4*pi16 * ( + 29/36*RD(X11)*X11^2 ) + Cb(X11,X11,X11,0)*F0^-4*L4r * ( + 16*Xb(1)*RD(X11)*X11^2 ) + Cb(X11,X11,X11,0)*F0^-4*L5r * ( + 16/3*RD(X11)*X11^3 ) + Cb(X11,X11,X11,0)*F0^-4*L6r * ( - 32*Xb(1)*RD(X11)*X11^2 ) + Cb(X11,X11,X11,0)*F0^-4*L8r * ( - 32/3*RD(X11)*X11^3 ) + Hbb(1,Xe0,Xe0,X11,X11)*F0^-4 * ( + 2/9*R(Xe0,X11,X11)^2*X11^2 ) + Hbb(1,Xe0,X11,X11,X11)*F0^-4 * ( + 4/9*R(Xe0,X11,X11)*RC(X11)*X11^2 ) + Hbb(1,Xe0,X1s,X1s,X11)*F0^-4 * ( - 1/3*R(Xe0,X11,X11)*X11^2 - 1/12*RV(Xe0,X11,Xss)*Xe0*X11 ) + Hbb(1,X11,X11,X11,X11)*F0^-4 * ( + 1/3*X11^2 + 2/9*RC(X11)^2*X11^2 ) + Hbb(1,X11,X1s,X1s,X11)*F0^-4 * ( - 1/2*R(X11,Xss,Xe0)*X11^2 + 1/4*RC(X11)*X11^2 - 1/12*RD(X11)*X11 ) + Hbb(1,X14,X14,X44,X11)*F0^-4 * ( + 3/4*X11*X44 ) + Hbb(1,X14,X16,X46,X11)*F0^-4 * ( + X11*X46 ) + Hbb(2,X11,Xe0,X11,X11)*F0^-4 * ( + 4/9*R(Xe0,X11,X11)*RD(X11)*X11^2 ) + Hbb(2,X11,X11,X11,X11)*F0^-4 * ( + 4/9*RC(X11)*RD(X11)*X11^2 ) + Hbb(2,X11,X1s,X1s,X11)*F0^-4 * ( + 1/4*RD(X11)*X11^2 ) + Hbb(5,X11,X11,X11,X11)*F0^-4 * ( + 2/9*RD(X11)^2*X11^2 ) + H1bb(1,Xe0,X1s,X1s,X11)*F0^-4 * ( - 2/3*R(Xe0,X11,Xss)*RS(X11,Xss,Xe0)*X11^2 ) + H1bb(1,X1s,X1s,X11,X11)*F0^-4 * ( - 4/3*R(Xe0,X11,Xss)*RS(X11,Xss,Xe0)*X11^2 ) + H1bb(3,X1s,X11,X1s,X11)*F0^-4 * ( - 4/3*RD(X11)*X11^2 ) + H21bb(1,Xe0,X1s,X1s,X11)*F0^-4 * ( - 1/4*RV(Xe0,X11,Xss)*X11^2 ) + H21bb(1,X11,X1s,X1s,X11)*F0^-4 * ( + 1/2*R(X11,Xss,Xe0)*X11^2 - 1/4*RC(X11)*X11^2 ) + H21bb(1,X44,X14,X14,X11)*F0^-4 * ( + 9/4*X11^2 ) + H21bb(1,X46,X14,X16,X11)*F0^-4 * ( + 3*X11^2 ) + H21bb(2,X11,X1s,X1s,X11)*F0^-4 * ( - 1/4*RD(X11)*X11^2 );