MODULE XC2NS3P CONTAINS * * ..File: xc2ns3p.f F2_NS * * * ..Parametrization of the 3-loop MS(bar) non-singlet coefficient * functions for the structure function F_2 in electromagnetic DIS. * at mu_r = mu_f = Q. 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. * 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 one part in thousand or better. * * ..References: S. Moch, J. Vermaseren and A. Vogt, hep-ph/0209100 * J. Vermaseren, A. Vogt and S. Moch, hep-ph/0504242 * * * ===================================================================== * * * ..The regular piece. The rational end-point coefficients are exact, * the rest has been fitted for x between 10^-6 and 1 - 10^-6. * FUNCTION C2NP3A (Y, DL, NF, CC) IMPLICIT REAL*8 (A - Z) INTEGER NF INTEGER CC ! charged current DIMENSION FL(6) DATA FL / -1.d0, 0.5d0, 0.d0, 0.5d0, 0.2d0, 0.5d0 / * FL11 = FL(NF) * Y1 = Y1VAL(Y, DL) DL1 = DL1VAL(Y, DL) D27 = 1./27.D0 D243 = 1./243.D0 * C2NP3A = 0.D0 IF (CC.EQ.1) THEN C2NP3A = , - 4926. + 7725.* Y + 57256.* Y**2 + 12898.* Y**3 , - 32.*D27 * DL**5 - 8796.*D243 * DL**4 - 309.1 * DL**3 , - 899.6 * DL**2 - 775.8 * DL + 4.719 * Y*DL**5 , - 512.*D27 * DL1**5 + 6336.*D27 * DL1**4 , - 3368.* DL1**3 - 2978.* DL1**2 + 18832.* DL1 , - 56000.* (1.-Y)*DL1**2 - DL*DL1 * (6158. + 1836.*DL) , + NF * ( 831.6 - 6752.* Y - 2778.* Y**2 , + 728.* D243 * DL**4 + 12224.* D243 * DL**3 , + 187.3 * DL**2 + 275.6 * DL + 4.102 * Y*DL**4 , - 1920.* D243 * DL1**4 + 153.5 * DL1**3 , - 828.7 * DL1**2 - 501.1 * DL1 + 171.0 * (1.-Y)*DL1**4 , + DL*DL1 * (4365. + 716.2 * DL - 5983.* DL1) ) , + NF**2 * ( 129.2 * Y + 102.5 * Y**2 - 368.* D243 * DL**3 , - 1984.* D243 * DL**2 - 8.042 * DL , - 192.* D243 * DL1**3 + 18.21 * DL1**2 - 19.09 * DL1 , + DL*DL1 * ( - 96.07 - 12.46 * DL + 85.88 * DL1) ) , + FL11*NF * ( ( 126.42 - 50.29 * Y - 50.15 * Y**2) * Y1 , - 26.717 - 960.*D243 * DL**2 * (DL+5.D0) + 59.59 * DL , - Y*DL**2 * (101.8 + 34.79 * DL + 3.070 * DL**2) , - 9.075 * Y*Y1*DL1 ) * Y ELSE C2NP3A = FL11*NF * ( ( 126.42 - 50.29 * Y - 50.15 * Y**2) * Y1 , - 26.717 - 960.*D243 * DL**2 * (DL+5.D0) + 59.59 * DL , - Y*DL**2 * (101.8 + 34.79 * DL + 3.070 * DL**2) , - 9.075 * Y*Y1*DL1 ) * Y * ENDIF RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..The exact singular piece (irrational coefficients truncated) * FUNCTION C2NS3B (Y, DL, NF) IMPLICIT REAL*8 (A-Z) INTEGER NF * DL1 = DL1VAL(Y, DL) DM = DMVAL(Y, DL) D81 = 1./81.D0 * C2NS3B = , + 1536.*D81 * DL1**5 - 16320.* D81 * DL1**4 , + 5.01099E+2 * DL1**3 + 1.17154E+3 * DL1**2 , - 7.32845E+3 * DL1 + 4.44276E+3 , + NF * ( 640.* D81 * DL1**4 - 6592.* D81 * DL1**3 , + 220.573 * DL1**2 + 294.906 * DL1 - 729.359 ) , + NF**2 * ( 64.* D81 * DL1**3 - 464.* D81 * DL1**2 , + 7.67505 * DL1 + 1.00830 ) * C2NS3B = DM * C2NS3B * RETURN END FUNCTION * * --------------------------------------------------------------------- * * * ..The 'local' piece. The coefficients of delta(1-x) have been * slightly shifted with respect to their (truncated) exact values. * FUNCTION C2NP3C (Y, NF, CC) IMPLICIT REAL*8 (A - Z) INTEGER NF INTEGER CC ! charged current DIMENSION FL(6) DATA FL / -1.d0, 0.5d0, 0.d0, 0.5d0, 0.2d0, 0.5d0 / * FL11 = FL(NF) DL1 = LOG (1.D0-Y) D81 = 1./81.D0 D3 = 1./3.D0 * C2NP3C = 0.D0 IF (CC.EQ.1) THEN C2NP3C = , + 256.*D81 * DL1**6 - 3264.*D81 * DL1**5 , + 1.252745E+2 * DL1**4 + 3.905133E+2 * DL1**3 , - 3.664225E+3 * DL1**2 + 4.44276E+3 * DL1 , - 9195.48 + 25.10 , + NF * ( 128.* D81 * DL1**5 - 1648.* D81 * DL1**4 , + 220.573 * D3 * DL1**3 + 147.453 * DL1**2 , - 729.359 * DL1 + 2575.074 - 0.387 ) , + NF**2 * ( 16.* D81 * DL1**4 - 464.* D81*D3 * DL1**3 , + 7.67505 * 5.D-1 * DL1**2 + 1.0083 * DL1 - 103.2521 , + 0.0155 ) ELSE C2NP3C = - FL11*NF * 11.8880 ENDIF * RETURN END FUNCTION * ..For Y values close to 1, use the series expansion close * to Y1=0 instead of full value, for numerical convergence * FUNCTION Y1VAL (Y, DL) IMPLICIT REAL*8 (A - Z) IF (ABS(DL).LT.1D-4) THEN Y1VAL = - DL - DL**2/2.0D0 - DL**3/6.0D0 - DL**4/24.0D0 , - DL**5/120.0D0 ELSE Y1VAL = 1.0D0 - Y ENDIF RETURN END FUNCTION * ..For Y values close to 1, use the series expansion close * to Y1=0 instead of full value, for numerical convergence * FUNCTION DL1VAL (Y, DL) IMPLICIT REAL*8 (A - Z) IF (ABS(DL).LT.1D-4) THEN DL1VAL = LOG(-DL) + DL/2.0D0 + DL**2/24.0D0 - DL**4/2880.0D0 ELSE DL1VAL = LOG(1.0D0 - Y) ENDIF RETURN END FUNCTION * ..For Y values close to 1, use the series expansion close * to Y1=0 instead of full value, for numerical convergence * FUNCTION DMVAL (Y, DL) IMPLICIT REAL*8 (A - Z) IF (ABS(DL).LT.1D-3) THEN DMVAL = 0.5D0 - 1.0D0/DL - DL/12.0D0 + DL**3/720.0D0 , - DL**5/30240.0D0 ELSE DMVAL = 1.0D0/(1.0D0-Y) ENDIF RETURN END FUNCTION * =================================================================av== END MODULE XC2NS3P