! $Id: xpns2p.f90,v 1.1 2004/06/01 09:30:31 salam Exp $ ! Automatically generated from f77 file, with addition of "d0" ! and the placement inside a module. module xpns2p character(len=*), parameter :: name_xpns2 = "xpns2p" contains ! ! ..File: xpns2p.f ! ! __ ! ..The parametrized 3-loop MS non-singlet splitting functions P^(2) ! for the evolution of unpolarized partons densities, mu_r = mu_f. ! The expansion parameter is 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) 417.0d0 ! The name-endings A, B, and C of the functions below correspond to ! the kernel superscripts [2], [3], and [1] in that equation. ! ! ..The relative accuracy of these parametrizations, as well as of ! the convolution results, is better than one part in thousand. ! ! ..References: S. Moch, J. Vermaseren and A. Vogt, ! hep-ph/0209100 = Nucl. Phys. B646 (2002) 181, ! hep-ph/0403192 (submitted to Nucl. Phys. B) ! ! ===================================================================== ! ! ! ..This is the regular piece of P2_NS+. The rational coefficients are ! exact, the rest has been fitted for x between 10^-6 and 1 - 10^-6.0d0 ! The N_f^2 part is exact and was first determined in N-space by ! J.A. Gracey in Phys. Lett. B322 (1994) 141.0d0 ! FUNCTION P2NSPA (Y, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF ! DL = LOG (Y) DL1 = LOG (1.0d0-Y) D81 = 1.0d0/81.0d0 ! P2NSPA = 1641.1d0 - 3135.0d0* Y + 243.6d0 * Y**2 - 522.1d0 * Y**3 & & + 128.0d0*D81 * DL**4 + 2400.0d0*D81 * DL**3 & & + 294.9d0 * DL**2 + 1258.0d0* DL & & + 714.1d0 * DL1 + DL*DL1 * (563.9d0 + 256.8d0 * DL) & & + NF * ( -197.0d0 + 381.1d0 * Y + 72.94d0 * Y**2 + 44.79d0 * Y**3 & & - 192.0d0*D81 * DL**3 - 2608.0d0*D81 * DL**2 - 152.6d0 * DL & & - 5120.0d0*D81 * DL1 - 56.66d0 * DL*DL1 - 1.497d0 * Y*DL**3 )& & + NF**2 * ( 32.0d0* Y*DL/(1.0d0-Y) * (3.0d0* DL + 10.0d0) + 64.0d0 & & + (48.0d0* DL**2 + 352.0d0* DL + 384.0d0) * (1.0d0-Y) ) * D81 ! RETURN END FUNCTION ! ! --------------------------------------------------------------------- ! ! ! ..This is the regular piece of P2_NS-. The rational coefficients are ! exact, the rest has been fitted for x between 10^-6 and 1 - 10^-6.0d0 ! The N_f^2 part is exact (and identical to that of P2_NS+). ! FUNCTION P2NSMA (Y, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF ! DL = LOG (Y) DL1 = LOG (1.0d0-Y) D81 = 1.0d0/81.0d0 ! P2NSMA = 1860.2d0 - 3505.0d0* Y + 297.0d0 * Y**2 - 433.2d0 * Y**3 & & + 116.0d0*D81 * DL**4 + 2880.0d0*D81 * DL**3 & & + 399.2d0 * DL**2 + 1465.2d0 * DL & & + 714.1d0 * DL1 + DL*DL1 * (684.0d0 + 251.2d0 * DL) & & + NF * ( -216.62d0 + 406.5d0 * Y + 77.89d0 * Y**2 + 34.76d0 * Y**3& & - 256.0d0*D81 * DL**3 - 3216.0d0*D81 * DL**2 - 172.69d0 * DL & & - 5120.0d0*D81 * DL1 - 65.43d0 * DL*DL1 - 1.136d0 * Y*DL**3 )& & + NF**2 * ( 32.0d0* Y*DL/(1.0d0-Y) * (3.0d0* DL + 10.0d0) + 64.0d0 & & + (48.0d0* DL**2 + 352.0d0* DL + 384.0d0) * (1.0d0-Y) ) * D81 ! RETURN END FUNCTION ! ! --------------------------------------------------------------------- ! ! ! ..This is the singular piece of both P2_NS+ and P2_NS-. It is exact ! up to the truncation of the irrational coefficients. ! FUNCTION P2NSB (Y, NF) IMPLICIT REAL*8 (A-Z) INTEGER NF ! P2NSB = ( 1174.898d0 - NF * 183.187d0 - NF**2 * 64.0d0/81.0d0 ) / (1.0d0-Y) ! RETURN END FUNCTION ! ! --------------------------------------------------------------------- ! ! ! ..This is the 'local' piece of P2_NS+. The coefficients of delta(1-x) ! have been partly shifted relative to the exact (truncated) values. ! FUNCTION P2NSPC (Y, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF ! DL1 = LOG (1.0d0-Y) ! P2NSPC = 1174.898d0 * DL1 + 1295.624d0 - 0.24d0 & & - NF * ( 183.187d0 * DL1 + 173.938d0 - 0.011d0 ) & & + NF**2 * ( - 64.0d0/81.0d0 * DL1 + 1.13067d0 ) ! RETURN END FUNCTION ! ! ! --------------------------------------------------------------------- ! ! ! ..This is the 'local' piece of P2_NS-. The coefficients of delta(1-x) ! have been partly shifted relative to the exact (truncated) values. ! FUNCTION P2NSMC (Y, NF) IMPLICIT REAL*8 (A - Z) INTEGER NF ! DL1 = LOG (1.0d0-Y) ! P2NSMC = 1174.898d0 * DL1 + 1295.624d0 - 0.154d0 & & - NF * ( 183.187d0 * DL1 + 173.938d0 - 0.005d0 ) & & + NF**2 * ( - 64.0d0/81.0d0 * DL1 + 1.13067d0 ) ! RETURN END FUNCTION ! ! --------------------------------------------------------------------- ! ! ! ..This is P2_NSS, the difference of P2_NSV and P2_NS-. ! FUNCTION P2NSSA (Y, NF) ! IMPLICIT REAL*8 (A-Z) INTEGER NF ! D27 = 1.0d0/27.0d0 DL = LOG (Y) Y1 = 1.0d0- Y DL1 = LOG (Y1) ! P2NSSA = Y1* ( 151.49d0 + 44.51d0 * Y - 43.12d0 * Y**2 + 4.820d0 * Y**3 )& & + 40.0d0*D27 * DL**4 - 80.0d0*D27 * DL**3 + 6.892d0 * DL**2 & & + 178.04d0 * DL + DL*DL1 * ( - 173.1d0 + 46.18d0 * DL ) & & + Y1*DL1 * ( - 163.9d0 / Y - 7.208d0 * Y ) ! P2NSSA = NF * P2NSSA ! RETURN END FUNCTION end module xpns2p