MODULE XC2SG2E CONTAINS * * ..File: xc2sg2e.f F2_G,PS * * * ..The one-loop and two-loop MS(bar) singlet coefficient functions * for the structure function F_2 in e.m. DIS at mu_r = mu_f = Q. * The expansion parameter is alpha_s/(4 pi). * * ..The code uses the package of Gehrmann and Remiddi for the harmonic * polylogarithms published in hep-ph/0107173 = CPC 141 (2001) 296. * * ===================================================================== * * * ..The one-loop gluonic coefficient function * FUNCTION X2G1A (X, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF * lx = log (x) l1x = log (1.d0 - x) * X2G1A = & + nf * ( -2.D0 + 16.D0*x - 16.D0*x**2 + 2.D0*l1x - 4.D0*l1x*x & + 4.D0*l1x*x**2 - 2.D0*lx + 4.D0*lnx*x - 4.D0*lx*x**2 ) * RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..The two-loop pure-singlet coefficient function * FUNCTION X2S2A (X, NF) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4, HC5 INTEGER NF, NF2, N1, N2, NW PARAMETER ( N1 = -1, N2 = 1, NW = 3 ) DIMENSION HC1(N1:N2),HC2(N1:N2,N1:N2),HC3(N1:N2,N1:N2,N1:N2), , HC4(N1:N2,N1:N2,N1:N2,N1:N2) DIMENSION HR1(N1:N2),HR2(N1:N2,N1:N2),HR3(N1:N2,N1:N2,N1:N2), , HR4(N1:N2,N1:N2,N1:N2,N1:N2) DIMENSION HI1(N1:N2),HI2(N1:N2,N1:N2),HI3(N1:N2,N1:N2,N1:N2), , HI4(N1:N2,N1:N2,N1:N2,N1:N2) PARAMETER ( Z2 = 1.6449 34066 84822 64365 D0, , Z3 = 1.2020 56903 15959 42854 D0 ) * * ...Colour factors and abbreviations * CF = 4./3.D0 CA = 3.D0 * DX = 1.D0/X * * ...Harmonic polylogs (HPLs) up to weight NW=3 by Gehrmann and Remiddi * CALL HPLOG (X, NW, HC1,HC2,HC3,HC4, HR1,HR2,HR3,HR4, , HI1,HI2,HI3,HI4, N1, N2) * * ...The coefficient function in terms of the HPLs * c2qps2 = & + nf*cf * ( 158.D0/9.D0 - 422.D0/9.D0*x + 448.D0/27.D0*x**2 + & 344.D0/27.D0*dx - 8.D0*z3 - 8.D0*z3*x - 16.D0*z2*x + 16.D0*z2 & *x**2 - 16.D0/3.D0*z2*dx + 56.D0*Hr1(0) - 88.D0/3.D0*Hr1(0)*x & - 128.D0/9.D0*Hr1(0)*x**2 - 16.D0*Hr1(0)*z2 - 16.D0*Hr1(0)* & z2*x + 104.D0/3.D0*Hr1(1) - 80.D0/3.D0*Hr1(1)*x + 32.D0/9.D0* & Hr1(1)*x**2 - 104.D0/9.D0*Hr1(1)*dx - 16.D0*Hr2(-1,0) - 16.D0 & *Hr2(-1,0)*x - 16.D0/3.D0*Hr2(-1,0)*x**2 - 16.D0/3.D0*Hr2(-1, & 0)*dx - 2.D0*Hr2(0,0) + 30.D0*Hr2(0,0)*x - 64.D0/3.D0*Hr2(0,0 & )*x**2 - 16.D0*Hr2(0,1)*x**2 + 4.D0*Hr2(1,0) - 4.D0*Hr2(1,0)* & x - 16.D0/3.D0*Hr2(1,0)*x**2 + 16.D0/3.D0*Hr2(1,0)*dx + 4.D0* & Hr2(1,1) - 4.D0*Hr2(1,1)*x - 16.D0/3.D0*Hr2(1,1)*x**2 + 16.D0/ & 3.D0*Hr2(1,1)*dx + 20.D0*Hr3(0,0,0) + 20.D0*Hr3(0,0,0)*x + 16. & D0*Hr3(0,0,1) + 16.D0*Hr3(0,0,1)*x + 8.D0*Hr3(0,1,0) + 8.D0* & Hr3(0,1,0)*x + 8.D0*Hr3(0,1,1) + 8.D0*Hr3(0,1,1)*x ) * X2S2A = C2QPS2 * RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..The two-loop gluonic coefficient function * FUNCTION X2G2A (X, NF) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4, HC5 INTEGER NF, NF2, N1, N2, NW PARAMETER ( N1 = -1, N2 = 1, NW = 3 ) DIMENSION HC1(N1:N2),HC2(N1:N2,N1:N2),HC3(N1:N2,N1:N2,N1:N2), , HC4(N1:N2,N1:N2,N1:N2,N1:N2) DIMENSION HR1(N1:N2),HR2(N1:N2,N1:N2),HR3(N1:N2,N1:N2,N1:N2), , HR4(N1:N2,N1:N2,N1:N2,N1:N2) DIMENSION HI1(N1:N2),HI2(N1:N2,N1:N2),HI3(N1:N2,N1:N2,N1:N2), , HI4(N1:N2,N1:N2,N1:N2,N1:N2) PARAMETER ( Z2 = 1.6449 34066 84822 64365 D0, , Z3 = 1.2020 56903 15959 42854 D0 ) * * ...Colour factors and abbreviations * CF = 4./3.D0 CA = 3.D0 * DX = 1.D0/X * * ...Harmonic polylogs (HPLs) up to weight NW=3 by Gehrmann and Remiddi * CALL HPLOG (X, NW, HC1,HC2,HC3,HC4, HR1,HR2,HR3,HR4, , HI1,HI2,HI3,HI4, N1, N2) * * ...The coefficient function in terms of the HPLs * c2gg2 = & + nf*ca * ( 239.D0/9.D0 + 1072.D0/9.D0*x - 4493.D0/27.D0*x**2 & + 344.D0/27.D0*dx + 4.D0*z3 - 48.D0*z3*x + 24.D0*z3*x**2 + 8. & D0*z2 - 144.D0*z2*x + 148.D0*z2*x**2 - 16.D0/3.D0*z2*dx - 4.D0 & *Hr1(-1)*z2 - 8.D0*Hr1(-1)*z2*x - 16.D0*Hr1(-1)*z2*x**2 + 58.D & 0*Hr1(0) + 584.D0/3.D0*Hr1(0)*x - 2090.D0/9.D0*Hr1(0)*x**2 - & 8.D0*Hr1(0)*z2 - 64.D0*Hr1(0)*z2*x + 16.D0*Hr1(0)*z2*x**2 + & 62.D0/3.D0*Hr1(1) + 454.D0/3.D0*Hr1(1)*x - 1570.D0/9.D0*Hr1(1 & )*x**2 - 104.D0/9.D0*Hr1(1)*dx + 8.D0*Hr1(1)*z2 - 16.D0*Hr1(1 & )*z2*x + 8.D0*Hr1(1)*z2*x**2 - 24.D0*Hr2(-1,0) + 80.D0/3.D0* & Hr2(-1,0)*x**2 - 16.D0/3.D0*Hr2(-1,0)*dx - 2.D0*Hr2(0,0) + & 176.D0*Hr2(0,0)*x - 388.D0/3.D0*Hr2(0,0)*x**2 - 8.D0*Hr2(0,1) & + 144.D0*Hr2(0,1)*x - 148.D0*Hr2(0,1)*x**2 - 4.D0*Hr2(1,0) & + 80.D0*Hr2(1,0)*x - 268.D0/3.D0*Hr2(1,0)*x**2 + 16.D0/3.D0* & Hr2(1,0)*dx - 4.D0*Hr2(1,1) + 72.D0*Hr2(1,1)*x - 244.D0/3.D0* & Hr2(1,1)*x**2 + 16.D0/3.D0*Hr2(1,1)*dx + 8.D0*Hr3(-1,-1,0) + & 16.D0*Hr3(-1,-1,0)*x ) c2gg2 = c2gg2 + nf*ca * ( 8.D0*Hr3(-1,0,0) + 16.D0*Hr3(-1,0,0)*x & + 24.D0*Hr3(-1,0,0)*x**2 + 8.D0*Hr3(-1,0,1) + 16.D0*Hr3(-1,0 & ,1)*x + 16.D0*Hr3(-1,0,1)*x**2 + 16.D0*Hr3(0,-1,0)*x**2 + 20.D & 0*Hr3(0,0,0) + 56.D0*Hr3(0,0,0)*x + 8.D0*Hr3(0,0,1) + 64.D0* & Hr3(0,0,1)*x - 16.D0*Hr3(0,0,1)*x**2 + 48.D0*Hr3(0,1,0)*x - & 16.D0*Hr3(0,1,0)*x**2 + 48.D0*Hr3(0,1,1)*x - 16.D0*Hr3(0,1,1) & *x**2 - 12.D0*Hr3(1,0,0) + 24.D0*Hr3(1,0,0)*x - 16.D0*Hr3(1,0 & ,0)*x**2 - 4.D0*Hr3(1,0,1) + 8.D0*Hr3(1,0,1)*x - 8.D0*Hr3(1,0 & ,1)*x**2 - 12.D0*Hr3(1,1,0) + 24.D0*Hr3(1,1,0)*x - 24.D0*Hr3( & 1,1,0)*x**2 - 4.D0*Hr3(1,1,1) + 8.D0*Hr3(1,1,1)*x - 8.D0*Hr3( & 1,1,1)*x**2 ) c2gg2 = c2gg2 + nf*cf * ( - 647.D0/15.D0 + 239.D0/5.D0*x - 36.D0/ & 5.D0*x**2 + 8.D0/15.D0*dx + 32.D0*z3 + 72.D0*z3*x**2 + 16.D0* & z2 - 104.D0/3.D0*z2*x + 72.D0*z2*x**2 + 96.D0/5.D0*z2*x**3 - & 16.D0*Hr1(-1)*z2 - 32.D0*Hr1(-1)*z2*x - 16.D0*Hr1(-1)*z2*x**2 & - 236.D0/15.D0*Hr1(0) + 113.D0/5.D0*Hr1(0)*x - 216.D0/5.D0* & Hr1(0)*x**2 - 8.D0/15.D0*Hr1(0)*dx + 16.D0*Hr1(0)*z2 - 32.D0* & Hr1(0)*z2*x + 48.D0*Hr1(0)*z2*x**2 - 14.D0*Hr1(1) + 40.D0* & Hr1(1)*x - 24.D0*Hr1(1)*x**2 + 8.D0*Hr1(1)*z2 - 16.D0*Hr1(1)* & z2*x + 32.D0*Hr1(1)*z2*x**2 + 48.D0*Hr2(-1,0) + 64.D0/3.D0* & Hr2(-1,0)*x + 96.D0/5.D0*Hr2(-1,0)*x**3 + 8.D0/15.D0*Hr2(-1,0 & )*dx**2 - 3.D0*Hr2(0,0) + 44.D0/3.D0*Hr2(0,0)*x - 72.D0*Hr2(0 & ,0)*x**2 - 96.D0/5.D0*Hr2(0,0)*x**3 - 16.D0*Hr2(0,1) + 56.D0* & Hr2(0,1)*x - 72.D0*Hr2(0,1)*x**2 - 26.D0*Hr2(1,0) + 80.D0* & Hr2(1,0)*x - 72.D0*Hr2(1,0)*x**2 - 26.D0*Hr2(1,1) + 80.D0* & Hr2(1,1)*x - 72.D0*Hr2(1,1)*x**2 - 32.D0*Hr3(-1,-1,0) - 64.D0 & *Hr3(-1,-1,0)*x ) c2gg2 = c2gg2 + nf*cf * ( - 32.D0*Hr3(-1,-1,0)*x**2 + 16.D0*Hr3( & -1,0,0) + 32.D0*Hr3(-1,0,0)*x + 16.D0*Hr3(-1,0,0)*x**2 + 32.D0 & *Hr3(0,-1,0) + 32.D0*Hr3(0,-1,0)*x**2 - 10.D0*Hr3(0,0,0) + 20. & D0*Hr3(0,0,0)*x - 40.D0*Hr3(0,0,0)*x**2 - 16.D0*Hr3(0,0,1) + & 32.D0*Hr3(0,0,1)*x - 48.D0*Hr3(0,0,1)*x**2 - 12.D0*Hr3(0,1,0) & + 24.D0*Hr3(0,1,0)*x - 32.D0*Hr3(0,1,0)*x**2 - 16.D0*Hr3(0,1 & ,1) + 32.D0*Hr3(0,1,1)*x - 40.D0*Hr3(0,1,1)*x**2 - 4.D0*Hr3(1 & ,0,0) + 8.D0*Hr3(1,0,0)*x - 24.D0*Hr3(1,0,0)*x**2 - 24.D0* & Hr3(1,0,1) + 48.D0*Hr3(1,0,1)*x - 48.D0*Hr3(1,0,1)*x**2 - 16.D & 0*Hr3(1,1,0) + 32.D0*Hr3(1,1,0)*x - 32.D0*Hr3(1,1,0)*x**2 - & 20.D0*Hr3(1,1,1) + 40.D0*Hr3(1,1,1)*x - 40.D0*Hr3(1,1,1)*x**2 & ) * X2G2A = C2GG2 * RETURN END FUNCTION * * =================================================================av== END MODULE XC2SG2E