* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * G R S - P I O N - P A R A M E T R I Z A T I O N S * * * * 1999 * * * * For a detailed explanation see * * M. Glueck, E. Reya, I. Schienbein : * * hep-ph/9903288 = DO-TH 99/01 * * (Eur. Phys. J. C 10, 313 (1999)) * * * * The parametrizations are fitted to the parton distributions * * for * * 0.5 GeV**2 =< Q**2 =< 1.E-5 GeV**2 * * and * * 1.E-5 =< x =< 1. * * * * Regions, where the distribution under consideration is neg- * * ligible, were excluded from the fit. * * * * * * INPUT: X = Bjorken-x (between 1.E-5 and 1 ) * * Q2 = Scale in GeV**2 (between 0.5 and 1.E5) * * * * OUTPUT: VAP = VALENCE : VAP = U_VAL(PI+) = DBAR_VAL(PI+) = ... * * N O T THE SUM, I.E., TOTAL VALENCE DENSITY * * QBP = SU(2) SYMMETRIC LIGHT SEA : * * QBP = UBAR(PI+) = D(PI+) = ... * * SBP = STRANGE SEA : SBP = S = SBAR * * GLP = GLUON * * * * Always x times the distribution is returned * * * * ALPHAS: * * At Q^2 = MZ^2, alpha_s reads 0.114 (0.125) in NLO (LO); the * * heavy quark thresholds, Qh^2 = mh^2, in the beta function are * * mc = 1.4 GeV, mb = 4.5 GeV. * * Note that the NLO alpha_s running is different from GRV(94). * * * * Questions, comments etc to: schien@hal1.physik.uni-dortmund.de * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C C X U(Pi^0) = X UBAR(Pi^0) = (VAP + 2 QBP)/2 C X D(Pi^0) = X DBAR(Pi^0) = (VAP + 2 QBP)/2 C X S = X SBAR = SBP C X G = GLP C SUBROUTINE GRSPILO (X, Q2, VAP, GLP, QBP, SBP) IMPLICIT DOUBLE PRECISION (A - Z) MU2 = 0.26 LAM2 = 0.204 * 0.204 S = LOG (LOG(Q2/LAM2) / LOG(MU2/LAM2)) DS = SQRT (S) S2 = S * S C...X * VALENCE : NV = 0.606 + 0.249 * S + 0.005 * S2 AKV = 0.517 - 0.020 * S AGV = -0.037 - 0.578 * S BGV = 0.241 + 0.251 * S DV = 0.383 + 0.624 * S VAP = FVP (X, NV, AKV, AGV, BGV, DV) C...X * GLUON : ALG = 0.504 BEG = 0.226 AKG = 2.251 - 1.339 * DS BKG = 0.0 AGG = 2.668 - 1.265 * S + 0.156 * S2 BGG = -1.839 + 0.386 * S CG = -1.014 + 0.920 * S - 0.101 * S2 DG = -0.077 + 1.466 * S EG = 1.245 + 1.833 * S ESG = 0.510 + 3.844 * S GLP = FGP (X, S, ALG, BEG, AKG, BKG, AGG, BGG, CG, DG, EG, ESG) C...X * QBAR (LIGHT SEA) : ALS = 1.147 BES = 1.241 AKS = 0.309 - 0.134 * DS BKS = 0.893 - 0.264 * DS AGS = 0.219 - 0.054 * S BGS = -0.593 + 0.240 * S CS = 1.100 - 0.452 * S DS = 3.526 + 0.491 * S ES = 4.521 + 1.583 * S ESS = 3.102 QBP = FGP (X, S, ALS, BES, AKS, BKS, AGS, BGS, CS, DS, ES, ESS) C...X * SBAR = X * S : ALSTR = 0.823 BESTR = 0.650 AKSTR = 1.036 - 0.709 * S AGSTR = -1.245 + 0.713 * S BGSTR = 5.580 - 1.281 * S DSTR = 2.746 - 0.191 * S ESTR = 5.101 + 1.294 * S ESSTR = 4.854 - 0.437 * S SBP = FSP (X, S, ALSTR, BESTR, AKSTR, AGSTR, BGSTR # , DSTR, ESTR, ESSTR) RETURN END C C SUBROUTINE GRSPIHO (X, Q2, VAP, GLP, QBP, SBP) IMPLICIT double precision (A - Z) MU2 = 0.4 LAM2 = 0.299 * 0.299 S = LOG (LOG(Q2/LAM2) / LOG(MU2/LAM2)) DS = SQRT (S) S2 = S * S C...X * VALENCE : NV = 0.750 + 0.263 * S - 0.025 * S2 AKV = 0.560 - 0.034 * S AGV = -0.357 - 0.458 * S BGV = 0.427 + 0.220 * S DV = 0.475 + 0.550 * S VAP = FVP (X, NV, AKV, AGV, BGV, DV) C...X * GLUON : ALG = 0.793 BEG = 1.722 AKG = 1.418 - 0.215 * DS BKG = 0.0 AGG = 5.392 + 0.553 * S - 0.385 * S2 BGG = -11.928 + 1.844 * S CG = 11.548 - 4.316 * S + 0.382 * S2 DG = 1.347 + 1.135 * S EG = 0.104 + 1.980 * S ESG = 2.375 - 0.188 * S GLP = FGP (X, S, ALG, BEG, AKG, BKG, AGG, BGG, CG, DG, EG, ESG) C...X * QBAR (LIGHT SEA) : ALS = 1.118 BES = 0.457 AKS = 0.111 - 0.326 * DS BKS = -0.978 - 0.488 * DS AGS = 1.035 - 0.295 * S BGS = -3.008 + 1.165 * S CS = 4.111 - 1.575 * S DS = 6.192 + 0.705 * S ES = 5.035 + 0.997 * S ESS = 1.486 + 1.288 * S QBP = FGP (X, S, ALS, BES, AKS, BKS, AGS, BGS, CS, DS, ES, ESS) C...X * SBAR = X * S : ALSTR = 0.908 BESTR = 0.812 AKSTR = -0.567 - 0.466 * S AGSTR = -2.348 + 1.433 * S BGSTR = 4.403 DSTR = 2.061 ESTR = 3.796 + 1.618 * S ESSTR = 0.309 + 0.355 * S SBP = FSP (X, S, ALSTR, BESTR, AKSTR, AGSTR, BGSTR # , DSTR, ESTR, ESSTR) RETURN END C C PION C c... AK = a; AG = A c... BK = b; BG = B c... AL = alpha; BE = beta c... E' = ES; N = N; C = C; D = D; E = E c valence FUNCTION FVP (X, N, AK, AG, BG, D) IMPLICIT double precision (A - Z) DX = SQRT (X) FVP = N * X**AK * (1.+ AG*DX + BG*X) * (1.- X)**D RETURN END C gluon and light sea FUNCTION FGP (X, S, AL, BE, AK, BK, AG, BG, C, D, E, ES) IMPLICIT double precision (A - Z) DX = SQRT (X) LX = LOG (1./X) FGP = (X**AK * (AG + BG*DX + C*X) * LX**BK + S**AL 1 * EXP (-E + SQRT (ES * S**BE * LX))) * (1.- X)**D RETURN END C strange sea FUNCTION FSP (X, S, AL, BE, AK, AG, BG, D, E, ES) IMPLICIT double precision (A - Z) DX = SQRT (X) LX = LOG (1./X) FSP = (1. + AG*DX + BG*X) / LX**AK * S**AL 1 * EXP (-E + SQRT (ES * S**BE * LX)) * (1.- X)**D RETURN END