*FORM by J.Vermaseren,version 3.1(Oct 17 2002) Run at: Fri Jan 20 22:34:32 2006 * * 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 "5" * #define type "1" * * #define pout "1" * #define nsim "0" * * #- * Sigma2 loaded * Sigma4 loaded * Sigma6 loaded * *Time = 0.56 sec Generated terms = 1 * M0p2 Terms in output = 1 * Bytes used = 24 * *Time = 0.56 sec Generated terms = 7 * M0p4 Terms in output = 7 * Bytes used = 304 * *Time = 0.56 sec Generated terms = 172 * M0p6 Terms in output = 172 * Bytes used = 8680 L M0p2timo13 = + X11 ; L M0p4timo13 = + 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(Xn1)*F0^-2 * ( - 1/3*R(Xn1,Xn2,X11,X11)*X11 ) + Ab(X11)*F0^-2 * ( - 1/3*RC(X11)*X11 ) + Bb(X11,X11,0)*F0^-2 * ( - 1/3*RD(X11)*X11 ); L M0p6timo13 = + F0^-4*pi16*L0r * ( - 8/9*Xp0*Xe0*X11 - 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*Xp0*Xe0*X11 + 2*X11^3 + 26/3*Xb(2)*X11 ) + F0^-4*pi16*L3r * ( - 8/9*Xp0*Xe0*X11 - 5/2*X11^3 + 17/3*Xb(1)*X11^2 + 43/18*Xb(2)*X11 ) + F0^-4*pi16^2 * ( + 15/32*Xp0*Xe0*X11 - 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(Xn1)*F0^-4*L0r * ( - 8*R(Xn1,Xn2,X11,X11)*Xn1*X11 ) + Ab(Xn1)*F0^-4*L1r * ( + 16*Xn1*X11 ) + Ab(Xn1)*F0^-4*L2r * ( + 4*Xn1*X11 ) + Ab(Xn1)*F0^-4*L3r * ( - 8*R(Xn1,Xn2,X11,X11)*Xn1*X11 ) + Ab(Xn1)*F0^-4*L4r * ( - 16*Xn1*X11 + 16*Xb(1)*R(Xn1,Xn2,X11,X11)*X11 ) + Ab(Xn1)*F0^-4*L5r * ( + 16/3*R(Xn1,Xn2,X11,X11)*Xn1*X11 + 16/3*R(Xn1,Xn2,X11,X11)*X11^2 ) + Ab(Xn1)*F0^-4*L6r * ( + 16*Xn1*X11 - 16*Xb(1)*R(Xn1,Xn2,X11,X11)*X11 ) + Ab(Xn1)*F0^-4*L7r * ( + 32*RD(Xn1,X44,X55,X66,Xn2,X11)*X11 ) + Ab(Xn1)*F0^-4*L8r * ( - 64/3*R(Xn1,Xn2,X11,X11)*X11^2 ) + Ab(Xn1)^2*F0^-4 * ( + 1/18*R(Xn1,Xn2,X11,X11)^2*X11 ) + Ab(Xn1)*Ab(X11)*F0^-4 * ( + 1/9*R(Xn1,Xn2,X11,X11)*RC(X11)*X11 ) + Ab(Xn1)*Ab(X1s)*F0^-4 * ( - 4/9*R(Xn1,Xn2,X11,Xss)*RS(X11,Xss,Xn1)*X11 ) + Ab(Xn1)*Ab(Xst)*F0^-4 * ( + 1/27*R(Xn1,Xn2,X11,X11)*RV(Xn1,Xn2,Xss,Xtt)*X11 + 2/27*R(Xn1,Xn2,X11,Xss)*R(Xn2,Xn1,X11,Xss)*RS(Xtt,Xss,Xss,Xn1,Xn2) *X11 ) + Ab(Xn1)*Bb(Xn1,Xn1,0)*F0^-4 * ( - 1/27*R(Xn1,Xn2,X11,Xss)^2*R(Xn1,Xn2,Xss,Xss)*X11*Xss ) + Ab(Xn1)*Bb(Xn1,Xn2,0)*F0^-4 * ( - 2/27*R(Xn1,Xn2,X11,Xss)*R(Xn1,Xn2,Xss,Xss)*R(Xn2,Xn1,X11,Xss)*X11* Xss ) + Ab(Xn1)*Bb(Xn1,X11,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)^2*X11^2 - 2/27*R(Xn1,Xn2,X11,Xss)*R(Xn1,Xn2,Xss,Xss)*R(X11,Xss,Xn1,Xn2)*X11* Xss ) + Ab(Xn1)*Bb(Xn2,Xn2,0)*F0^-4 * ( - 1/27*R(Xn1,Xn2,Xss,Xss)*R(Xn2,Xn1,X11,Xss)^2*X11*Xss ) + Ab(Xn1)*Bb(Xn2,X11,0)*F0^-4 * ( - 2/27*R(Xn1,Xn2,Xss,Xss)*R(Xn2,Xn1,X11,Xss)*R(X11,Xss,Xn1,Xn2)*X11* Xss + 2/9*R(Xp0,Xe0,X11,X11)*R(Xe0,Xp0,X11,X11)*X11^2 ) + Ab(Xn1)*Bb(X11,X11,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)*RC(X11)*X11^2 + 1/9*R(Xn1,Xn2,X11,X11)*RD(X11)*X11 - 1/27*R(Xn1,Xn2,Xss,Xss)*R(X11,Xss,Xn1,Xn2)^2*X11*Xss ) + Ab(Xn1)*Cb(X11,X11,X11,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)*RD(X11)*X11^2 ) + Ab(Xn1,eps)*F0^-4*pi16 * ( - 1/4*Xn1*X11 + 1/4*R(Xn1,Xn2,X11,X11)*Xn1*X11 + 5/9*R(Xn1,Xn2,X11,X11)*X11^2 ) + Ab(Xp0)*Ab(Xe0)*F0^-4 * ( + 1/9*R(Xp0,Xe0,X11,X11)*R(Xe0,Xp0,X11,X11)*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(X1s)*F0^-4 * ( + 4/9*R(Xn1,Xn2,X11,Xss)*RS(X11,Xss,Xn1)*X11 ) + Ab(X11)*Ab(Xst)*F0^-4 * ( - 1/27*R(X11,Xss,Xp0,Xe0)^2*RS(Xtt,Xss,Xss,X11,X11)*X11 ) + Ab(X11)*Bb(Xn1,X11,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,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(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)^2*F0^-4 * ( - 1/4*X11 ) + Ab(X1s)*Ab(X1t)*F0^-4 * ( - 1/2*X11 ) + Ab(X1s)*Bb(Xn1,X11,0)*F0^-4 * ( - 4/9*R(Xn1,Xn2,X11,Xss)*X11*X1s - 2/9*R(Xn1,Xn2,X11,Xss)*X11^2 ) + Ab(X1s)*Bb(X11,X11,0)*F0^-4 * ( - 2/3*R(X11,Xss,Xp0,Xe0)*X11*Xss ) + Ab(X1s,eps)*F0^-4*pi16 * ( - 3/4*X11*Xss - 5/6*X11^2 - 3/4*Xb(1)*X11 ) + Ab(Xst)*F0^-4*L1r * ( + 32*X11*Xst ) + Ab(Xst)*F0^-4*L2r * ( + 8*X11*Xst ) + Ab(Xst)*F0^-4*L4r * ( - 32*X11*Xst ) + Ab(Xst)*F0^-4*L6r * ( + 32*X11*Xst ) + Ab(Xst)*Bb(Xn1,Xn1,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)*R(Xn1,Xn2,Xss,Xtt)*X11*Xst ) + Ab(Xst)*Bb(Xn1,X11,0)*F0^-4 * ( - 2/27*RU(X11,Xn1,Xn2,X11,Xss,Xtt)*X11^2 + 2/27*RW(X11,Xn1,Xn2,X11,Xss,Xtt)*X11 ) + Ab(Xst)*Bb(Xp0,Xe0,0)*F0^-4 * ( + 2/27*RW(Xp0,Xe0,X11,Xe0,Xp0,X11,Xss,Xtt)*X11 ) + Ab(Xst)*Bb(Xp0,Xe0,0,kk)*F0^-4 * ( - 2/27*R(Xp0,Xe0,X11,Xss)*R(Xe0,Xp0,X11,Xss)*RS(Xtt,Xss,Xss,Xp0,Xe0) *X11 ) + Ab(Xst)*Bb(X11,X11,0)*F0^-4 * ( + 2/9*R(X11,Xss,Xe0,Xe0)*R(X11,Xtt,Xp0,Xp0)*X11*Xst ) + Ab(Xst,eps)*F0^-4*pi16 * ( - 1/2*X11*Xst ) + Bb(Xn1,Xn1,0)*F0^-4*L4r * ( + 8*Xb(1)*R(Xn1,Xn2,X11,X11)*Xn1*X11 ) + Bb(Xn1,Xn1,0)*F0^-4*L5r * ( + 8/3*R(Xn1,Xn2,X11,X11)*Xn1^2*X11 ) + Bb(Xn1,Xn1,0)*F0^-4*L6r * ( - 16*Xb(1)*R(Xn1,Xn2,X11,X11)*Xn1*X11 ) + Bb(Xn1,Xn1,0)*F0^-4*L7r * ( + 16*RD(Xn1,X44,X55,X66,Xn2,X11)^2*X11 ) + Bb(Xn1,Xn1,0)*F0^-4*L8r * ( - 16/3*R(Xn1,Xn2,X11,X11)*Xn1^2*X11 + 16/3*RD(Xn1,X44,X55,X66,Xn2,X11)^2*X11 ) + Bb(Xn1,X11,0)*F0^-4*L7r * ( + 32*RD(Xn1,X44,X55,X66,Xn2,X11)*RD(X11)*X11 ) + Bb(Xn1,X11,0)*F0^-4*L8r * ( + 32/3*RD(Xn1,X44,X55,X66,Xn2,X11)*RD(X11)*X11 ) + Bb(Xn1,X11,0)*Bb(X11,X11,0)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)*RD(X11)*X11^2 ) + Bb(Xp0,Xe0,0)*F0^-4*L7r * ( + 32*RD(Xp0,X44,X55,X66,Xe0,X11)*RD(Xe0,X44,X55,X66,Xp0,X11)*X11 ) + Bb(Xp0,Xe0,0)*F0^-4*L8r * ( + 32/3*RD(Xp0,X44,X55,X66,Xe0,X11)*RD(Xe0,X44,X55,X66,Xp0,X11)*X11 ) + 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,Xn1,Xn1,X11,X11)*F0^-4 * ( + 2/9*R(Xn1,Xn2,X11,X11)^2*X11^2 ) + Hbb(1,Xn1,X11,X11,X11)*F0^-4 * ( + 4/9*R(Xn1,Xn2,X11,X11)*RC(X11)*X11^2 ) + Hbb(1,Xn1,X1s,X1s,X11)*F0^-4 * ( - 1/3*R(Xn1,Xn2,X11,X11)*X11^2 - 1/12*RV(Xn1,Xn2,X11,Xss)*Xn1*X11 ) + Hbb(1,Xp0,Xe0,X11,X11)*F0^-4 * ( + 4/9*R(Xp0,Xe0,X11,X11)*R(Xe0,Xp0,X11,X11)*X11^2 ) + 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,Xp0,Xe0)*X11^2 + 1/4*RC(X11)*X11^2 - 1/12*RD(X11)*X11 ) + Hbb(1,X1s,X1t,Xst,X11)*F0^-4 * ( + 1/2*X11*Xst ) + Hbb(2,X11,Xn1,X11,X11)*F0^-4 * ( + 4/9*R(Xn1,Xn2,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,Xn1,X1s,X1s,X11)*F0^-4 * ( - 2/3*R(Xn1,Xn2,X11,Xss)*RS(X11,Xss,Xn1)*X11^2 ) + H1bb(1,X1s,X1s,X11,X11)*F0^-4 * ( - 4/3*R(Xn1,Xn2,X11,Xss)*RS(X11,Xss,Xn1)*X11^2 ) + H1bb(3,X1s,X11,X1s,X11)*F0^-4 * ( - 4/3*RD(X11)*X11^2 ) + H21bb(1,Xn1,X1s,X1s,X11)*F0^-4 * ( - 1/4*RV(Xn1,Xn2,X11,Xss)*X11^2 ) + H21bb(1,X11,X1s,X1s,X11)*F0^-4 * ( + 1/2*R(X11,Xss,Xp0,Xe0)*X11^2 - 1/4*RC(X11)*X11^2 ) + H21bb(1,Xst,X1s,X1t,X11)*F0^-4 * ( + 3/2*X11^2 ) + H21bb(2,X11,X1s,X1s,X11)*F0^-4 * ( - 1/4*RD(X11)*X11^2 );