MODULE XCDIFF2E CONTAINS * * ..File: xcdiff2e.f Fi_NS, i = 2,3,L (even-N - odd-N) * * * ..The exact 2-loop MS(bar) even-odd differences of the NS coefficient * functions F2, F3 and FL in charged-current DIS at mu_r = mu_f = Q. * The expansion parameter is normalized as a_s = 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. * * ..Equivalent expressions for F2 and F3 were first published in * E.B. Zijlstra and W.L van Neerven, Phys. Lett. B272 (1991) 127, * Phys. Lett. B297 (1992) 377. * The FL results were also calculated by them, but not published. * * ..Reference: M. Rogal, S. Moch and A. Vogt, * arXiv:0807.3731 = Nucl.Phys. B790 (2008) 317-335 * * ===================================================================== * * ..F2 * FUNCTION XC2DFF2 (X) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4 INTEGER 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 ) * * ...Colour factors and abbreviations * CF = 4./3.D0 CA = 3.D0 CAM2CF = CA - 2.* CF * DX = 1.D0/X DP = 1.D0/(1.D0+X) * * ...The harmonic polylogs up to weight 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 harmonic polylogs * c2qq2d = & + cf*cam2cf * ( 162.D0/5.D0 - 82.D0/5.D0*x - 72.D0/5.D0*x**2 & - 8.D0/5.D0*dx + 20.D0*z3 - 68.D0*z3*x - 56.D0*z3*dp - 4.D0* & z2 - 28.D0*z2*x - 48.D0*z2*x**2 + 72.D0/5.D0*z2*x**3 - 24.D0* & Hr1(-1)*z2 + 72.D0*Hr1(-1)*z2*x + 64.D0*Hr1(-1)*z2*dp - 14.D0/ & 5.D0*Hr1(0) + 146.D0/5.D0*Hr1(0)*x - 72.D0/5.D0*Hr1(0)*x**2 & + 8.D0/5.D0*Hr1(0)*dx + 16.D0*Hr1(0)*dp + 8.D0*Hr1(0)*z2 - 8. & D0*Hr1(0)*z2*x - 16.D0*Hr1(0)*z2*dp + 16.D0*Hr1(1) - 16.D0* & Hr1(1)*x - 32.D0*Hr2(-1,0) - 32.D0*Hr2(-1,0)*x - 48.D0*Hr2(-1 & ,0)*x**2 + 72.D0/5.D0*Hr2(-1,0)*x**3 - 8.D0/5.D0*Hr2(-1,0)* & dx**2 + 8.D0*Hr2(0,0) + 32.D0*Hr2(0,0)*x + 48.D0*Hr2(0,0)* & x**2 - 72.D0/5.D0*Hr2(0,0)*x**3 + 8.D0*Hr2(0,1) + 8.D0*Hr2(0, & 1)*x - 16.D0*Hr3(-1,-1,0) + 112.D0*Hr3(-1,-1,0)*x + 64.D0* & Hr3(-1,-1,0)*dp + 32.D0*Hr3(-1,0,0) - 80.D0*Hr3(-1,0,0)*x - & 80.D0*Hr3(-1,0,0)*dp + 16.D0*Hr3(-1,0,1) - 16.D0*Hr3(-1,0,1)* & x - 32.D0*Hr3(-1,0,1)*dp + 16.D0*Hr3(0,-1,0) - 64.D0*Hr3(0,-1 & ,0)*x ) c2qq2d = c2qq2d + cf*cam2cf * ( - 48.D0*Hr3(0,-1,0)*dp - 12.D0 & *Hr3(0,0,0) + 12.D0*Hr3(0,0,0)*x + 24.D0*Hr3(0,0,0)*dp - 8.D0 & *Hr3(0,0,1) + 8.D0*Hr3(0,0,1)*x + 16.D0*Hr3(0,0,1)*dp ) * XC2DFF2 = C2QQ2D * RETURN END FUNCTION * * --------------------------------------------------------------------- * * ..FL * FUNCTION XCLDFF2 (X) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4 INTEGER 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 ) * * ...Colour factors and abbreviations * CF = 4./3.D0 CA = 3.D0 CAM2CF = CA - 2.* CF * DX = 1.D0/X DP = 1.D0/(1.D0+X) * * ...The harmonic polylogs up to weight 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 harmonic polylogs * cLqq2d = & + cf*cam2cf * ( 208.D0/5.D0 - 128.D0/5.D0*x - 48.D0/5.D0*x**2 & - 32.D0/5.D0*dx - 32.D0*z3*x - 16.D0*z2*x - 32.D0*z2*x**2 + & 48.D0/5.D0*z2*x**3 + 32.D0*Hr1(-1)*z2*x - 16.D0/5.D0*Hr1(0) & + 224.D0/5.D0*Hr1(0)*x - 48.D0/5.D0*Hr1(0)*x**2 + 32.D0/5.D0 & *Hr1(0)*dx - 32.D0*Hr2(-1,0) - 32.D0*Hr2(-1,0)*x - 32.D0*Hr2( & -1,0)*x**2 + 48.D0/5.D0*Hr2(-1,0)*x**3 + 16.D0*Hr2(-1,0)*dx & - 32.D0/5.D0*Hr2(-1,0)*dx**2 + 16.D0*Hr2(0,0)*x + 32.D0*Hr2( & 0,0)*x**2 - 48.D0/5.D0*Hr2(0,0)*x**3 + 64.D0*Hr3(-1,-1,0)*x & - 32.D0*Hr3(-1,0,0)*x - 32.D0*Hr3(0,-1,0)*x ) * XCLDFF2 = CLQQ2D * RETURN END FUNCTION * * --------------------------------------------------------------------- * * ..F3 * FUNCTION XC3DFF2 (X) * IMPLICIT REAL*8 (A - Z) COMPLEX*16 HC1, HC2, HC3, HC4 INTEGER 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 ) * * ...Colour factors and abbreviations * CF = 4./3.D0 CA = 3.D0 CAM2CF = CA - 2.* CF * DX = 1.D0/X DP = 1.D0/(1.D0+X) * * ...The harmonic polylogs up to weight 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 harmonic polylogs * c3qq2d = & + cf*cam2cf * ( - 30.D0 + 30.D0*x + 36.D0*z3 - 20.D0*z3*x - & 56.D0*z3*dp - 12.D0*z2 - 4.D0*z2*x - 8.D0*z2*x**2 - 40.D0* & Hr1(-1)*z2 + 24.D0*Hr1(-1)*z2*x + 64.D0*Hr1(-1)*z2*dp - 14.D0 & *Hr1(0) - 30.D0*Hr1(0)*x + 16.D0*Hr1(0)*dp + 8.D0*Hr1(0)*z2 & - 8.D0*Hr1(0)*z2*x - 16.D0*Hr1(0)*z2*dp + 16.D0*Hr1(1) - 16.D & 0*Hr1(1)*x - 8.D0*Hr2(-1,0)*x**2 - 8.D0*Hr2(-1,0)*dx + 16.D0* & Hr2(0,0) + 8.D0*Hr2(0,0)*x + 8.D0*Hr2(0,0)*x**2 + 8.D0*Hr2(0, & 1) + 8.D0*Hr2(0,1)*x - 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 + 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) - 16. & D0*Hr3(0,-1,0)*x - 48.D0*Hr3(0,-1,0)*dp - 12.D0*Hr3(0,0,0) + & 12.D0*Hr3(0,0,0)*x + 24.D0*Hr3(0,0,0)*dp - 8.D0*Hr3(0,0,1) + & 8.D0*Hr3(0,0,1)*x + 16.D0*Hr3(0,0,1)*dp ) * XC3DFF2 = C3QQ2D * RETURN END FUNCTION * * =================================================================av== END MODULE XCDIFF2E