MODULE XC3NS2E CONTAINS * * ..File: xc3ns2e.f F3 (NS, odd-N) * * * ..The exact 2-loop MS(bar) non-singlet coefficient functions for the * (W^+ + W^-) structure function F_3 in DIS at mu_r = mu_f = Q. * Expansion parameter: alpha_s/(4 pi). * * ..The distributions (in the mathematical sense) are given as in eq. * (B.26) of Floratos, Kounnas, Lacaze: Nucl. Phys. B192 (1981) 417. * The name-endings A, B, and C of the functions below correspond to * the kernel superscripts [2], [3], and [1] in that equation. * * ..The code uses the package of Gehrmann and Remiddi for the harmonic * polylogarithms published in hep-ph/0107173 = CPC 141 (2001) 296. * * * ===================================================================== * SUBROUTINE SET_C3SOFT(NF) IMPLICIT REAL*8 (A - Z) INTEGER NF COMMON / C3SOFT / A0, A1, A2, A3 PARAMETER ( Z2 = 1.6449 34066 84822 64365 D0, , Z3 = 1.2020 56903 15959 42854 D0 ) * * ...Colour factors * CF = 4./3.D0 CA = 3.D0 * * ...The soft (`+'-distribution) part of the coefficient function * A3 = & + 8.D0*cf**2 A2 = & - 22.D0/3.D0*ca*cf & - 18.D0*cf**2 & + 4.D0/3.D0*cf*nf A1 = & - 8.D0*z2*ca*cf & - 32.D0*z2*cf**2 & + 367.D0/9.D0*ca*cf & - 27.D0*cf**2 & - 58.D0/9.D0*cf*nf A0 = & + 44.D0/3.D0*z2*ca*cf & + 36.D0*z2*cf**2 & + 40.D0*z3*ca*cf & - 8.D0*z3*cf**2 & - 3155.D0/54.D0*ca*cf & + 51.D0/2.D0*cf**2 & + 247.D0/27.D0*cf*nf & - 8.D0/3.D0*z2*cf*nf END SUBROUTINE * * ..This is the regular piece. * FUNCTION X3NM2A (X, NF) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4 INTEGER NF, NF2, N1, N2, NW, I1, I2, I3, N 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 ) * * ..The soft coefficients for use in X2NP2B and X2NP2C * COMMON / C3SOFT / A0, A1, A2, A3 * * ...Colour factors * CF = 4./3.D0 CA = 3.D0 * * ...Some abbreviations * DX = 1.D0/X DM = 1.D0/(1.D0-X) DP = 1.D0/(1.D0+X) DL1 = LOG (1.D0-X) * * ...The harmonic polylogs up to weight 4 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 harmonic polylogs * (without the delta(1-x) part, but with the soft contribution) * c3qq2 = & + cf*ca * ( 1130.D0/27.D0 + 1415.D0/27.D0*x - 3155.D0/54.D0*dm & - 24.D0*z3 + 12.D0*z3*x + 28.D0*z3*dp + 4.D0*z3*dm - 8.D0/3.D & 0*z2 - 20.D0/3.D0*z2*x + 8.D0*z2*x**2 + 88.D0/3.D0*z2*dm + 20. & D0*Hr1(-1)*z2 - 12.D0*Hr1(-1)*z2*x - 32.D0*Hr1(-1)*z2*dp + 39. & D0*Hr1(0) + 81.D0*Hr1(0)*x - 8.D0*Hr1(0)*dp - 239.D0/3.D0* & Hr1(0)*dm - 8.D0*Hr1(0)*z2 + 8.D0*Hr1(0)*z2*dp + 8.D0*Hr1(0)* & z2*dm + 62.D0/9.D0*Hr1(1) + 386.D0/9.D0*Hr1(1)*x - 367.D0/9.D0 & *Hr1(1)*dm - 16.D0*Hr1(1)*z2 - 8.D0*Hr1(1)*z2*x + 24.D0*Hr1(1 & )*z2*dm + 4.D0*Hr2(-1,0) + 4.D0*Hr2(-1,0)*x + 8.D0*Hr2(-1,0)* & x**2 + 8.D0*Hr2(-1,0)*dx + 7.D0/3.D0*Hr2(0,0) + 19.D0/3.D0* & Hr2(0,0)*x - 8.D0*Hr2(0,0)*x**2 - 110.D0/3.D0*Hr2(0,0)*dm + & 20.D0/3.D0*Hr2(0,1) + 20.D0/3.D0*Hr2(0,1)*x - 88.D0/3.D0*Hr2( & 0,1)*dm + 22.D0/3.D0*Hr2(1,0) + 22.D0/3.D0*Hr2(1,0)*x - 44.D0/ & 3.D0*Hr2(1,0)*dm + 22.D0/3.D0*Hr2(1,1) + 22.D0/3.D0*Hr2(1,1)* & x - 44.D0/3.D0*Hr2(1,1)*dm + 24.D0*Hr3(-1,-1,0) - 8.D0*Hr3(-1 & ,-1,0)*x ) c3qq2 = c3qq2 + cf*ca * ( - 32.D0*Hr3(-1,-1,0)*dp - 24.D0*Hr3(-1 & ,0,0) + 16.D0*Hr3(-1,0,0)*x + 40.D0*Hr3(-1,0,0)*dp - 8.D0* & Hr3(-1,0,1) + 8.D0*Hr3(-1,0,1)*x + 16.D0*Hr3(-1,0,1)*dp + 16.D & 0*Hr3(0,-1,0)*x + 24.D0*Hr3(0,-1,0)*dp - 24.D0*Hr3(0,-1,0)*dm & + 12.D0*Hr3(0,0,0) - 12.D0*Hr3(0,0,0)*dp - 12.D0*Hr3(0,0,0)* & dm + 8.D0*Hr3(0,0,1) - 8.D0*Hr3(0,0,1)*dp - 8.D0*Hr3(0,0,1)* & dm + 12.D0*Hr3(1,0,0) + 4.D0*Hr3(1,0,0)*x - 16.D0*Hr3(1,0,0)* & dm + 4.D0*Hr3(1,0,1) + 4.D0*Hr3(1,0,1)*x - 8.D0*Hr3(1,0,1)*dm & - 4.D0*Hr3(1,1,0) - 4.D0*Hr3(1,1,0)*x + 8.D0*Hr3(1,1,0)*dm ) c3qq2 = c3qq2 + cf**2 * ( - 71.D0 + 20.D0*x + 51.D0/2.D0*dm + 8.D & 0*z3 - 64.D0*z3*x - 56.D0*z3*dp + 64.D0*z3*dm - 44.D0*z2 - 52. & D0*z2*x - 16.D0*z2*x**2 + 24.D0*z2*dm - 40.D0*Hr1(-1)*z2 + 24. & D0*Hr1(-1)*z2*x + 64.D0*Hr1(-1)*z2*dp - 40.D0*Hr1(0) - 62.D0* & Hr1(0)*x + 16.D0*Hr1(0)*dp + 61.D0*Hr1(0)*dm - 24.D0*Hr1(0)* & z2 - 40.D0*Hr1(0)*z2*x - 16.D0*Hr1(0)*z2*dp + 48.D0*Hr1(0)*z2 & *dm + 6.D0*Hr1(1) - 22.D0*Hr1(1)*x + 27.D0*Hr1(1)*dm - 16.D0* & Hr1(1)*z2*x + 16.D0*Hr1(1)*z2*dm - 8.D0*Hr2(-1,0) - 8.D0*Hr2( & -1,0)*x - 16.D0*Hr2(-1,0)*x**2 - 16.D0*Hr2(-1,0)*dx + 48.D0* & Hr2(0,0) + 52.D0*Hr2(0,0)*x + 16.D0*Hr2(0,0)*x**2 - 6.D0*Hr2( & 0,0)*dm + 36.D0*Hr2(0,1) + 52.D0*Hr2(0,1)*x - 24.D0*Hr2(0,1)* & dm + 24.D0*Hr2(1,0) + 24.D0*Hr2(1,0)*x - 36.D0*Hr2(1,0)*dm + & 20.D0*Hr2(1,1) + 28.D0*Hr2(1,1)*x - 36.D0*Hr2(1,1)*dm - 48.D0 & *Hr3(-1,-1,0) + 16.D0*Hr3(-1,-1,0)*x + 64.D0*Hr3(-1,-1,0)*dp & + 48.D0*Hr3(-1,0,0) - 32.D0*Hr3(-1,0,0)*x - 80.D0*Hr3(-1,0,0 & )*dp ) c3qq2 = c3qq2 + cf**2 * ( 16.D0*Hr3(-1,0,1) - 16.D0*Hr3(-1,0,1)*x & - 32.D0*Hr3(-1,0,1)*dp - 32.D0*Hr3(0,-1,0)*x - 48.D0*Hr3(0, & -1,0)*dp + 48.D0*Hr3(0,-1,0)*dm + 6.D0*Hr3(0,0,0) + 30.D0* & Hr3(0,0,0)*x + 24.D0*Hr3(0,0,0)*dp - 16.D0*Hr3(0,0,0)*dm + 24. & D0*Hr3(0,0,1) + 40.D0*Hr3(0,0,1)*x + 16.D0*Hr3(0,0,1)*dp - 48. & D0*Hr3(0,0,1)*dm + 28.D0*Hr3(0,1,0) + 28.D0*Hr3(0,1,0)*x - 48. & D0*Hr3(0,1,0)*dm + 32.D0*Hr3(0,1,1) + 32.D0*Hr3(0,1,1)*x - 56. & D0*Hr3(0,1,1)*dm + 4.D0*Hr3(1,0,0) + 20.D0*Hr3(1,0,0)*x - 24.D & 0*Hr3(1,0,0)*dm + 24.D0*Hr3(1,0,1) + 24.D0*Hr3(1,0,1)*x - 48.D & 0*Hr3(1,0,1)*dm + 32.D0*Hr3(1,1,0) + 32.D0*Hr3(1,1,0)*x - 64.D & 0*Hr3(1,1,0)*dm + 24.D0*Hr3(1,1,1) + 24.D0*Hr3(1,1,1)*x - 48.D & 0*Hr3(1,1,1)*dm ) c3qq2 = c3qq2 + nf*cf * ( - 116.D0/27.D0 - 302.D0/27.D0*x + 247.D c c3qq2 = nf*cf * ( - 116.D0/27.D0 - 302.D0/27.D0*x + 247.D & 0/27.D0*dm + 8.D0/3.D0*z2 + 8.D0/3.D0*z2*x - 16.D0/3.D0*z2*dm & - 6.D0*Hr1(0) - 10.D0*Hr1(0)*x + 38.D0/3.D0*Hr1(0)*dm - 20.D0 & /9.D0*Hr1(1) - 56.D0/9.D0*Hr1(1)*x + 58.D0/9.D0*Hr1(1)*dm - & 10.D0/3.D0*Hr2(0,0) - 10.D0/3.D0*Hr2(0,0)*x + 20.D0/3.D0*Hr2( & 0,0)*dm - 8.D0/3.D0*Hr2(0,1) - 8.D0/3.D0*Hr2(0,1)*x + 16.D0/3. & D0*Hr2(0,1)*dm - 4.D0/3.D0*Hr2(1,0) - 4.D0/3.D0*Hr2(1,0)*x + & 8.D0/3.D0*Hr2(1,0)*dm - 4.D0/3.D0*Hr2(1,1) - 4.D0/3.D0*Hr2(1, & 1)*x + 8.D0/3.D0*Hr2(1,1)*dm ) * C3QQ2L = DM * ( DL1**3 * A3 + DL1**2 * A2 + DL1 * A1 + A0) * * ...The regular piece of the coefficient function * X3NM2A = C3QQ2 - C3QQ2L * RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..This is the singular (soft) piece. * FUNCTION X3NS2B (Y, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF * COMMON / C3SOFT / A0, A1, A2, A3 * DL1 = LOG (1.D0-Y) DM = 1.D0/(1.D0-Y) * X3NS2B = DM * ( DL1**3 * A3 + DL1**2 * A2 + DL1 * A1 + A0) * RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..This is the 'local' piece. * FUNCTION X3NS2C (Y, NF) * IMPLICIT REAL*8 (A - Z) INTEGER NF, NF2 PARAMETER ( Z2 = 1.6449 34066 84822 64365 D0, , Z3 = 1.2020 56903 15959 42854 D0 ) * COMMON / C3SOFT / A0, A1, A2, A3 * * ...Colour factors * CF = 4./3.D0 CA = 3.D0 * * ...The coefficient of delta(1-x) * C3DELT = & - 251.D0/3.D0*z2*ca*cf & + 38.D0/3.D0*z2*cf*nf & + 69.D0*z2*cf**2 & + 71.D0/5.D0*z2**2*ca*cf & + 6.D0*z2**2*cf**2 & + 140.D0/3.D0*z3*ca*cf & + 4.D0/3.D0*z3*cf*nf & - 78.D0*z3*cf**2 & - 5465.D0/72.D0*ca*cf & + 457.D0/36.D0*cf*nf & + 331.D0/8.D0*cf**2 * DL1 = LOG (1.D0-Y) * X3NS2C = DL1**4 * A3/4.D0 + DL1**3 * A2/3.D0 , + DL1**2 * A1/2.D0 + DL1 * A0 + C3DELT * RETURN END FUNCTION * * =================================================================av== END MODULE XC3NS2E