C*********************************************************************** C* This file contains the 'asymptotic' DO, 'full' DG and VMD parametri-* C* zations of the parton content of the photon, as well as the Weiz- * C* saecker-Williams photon density within the electron. Note that DO is* C* only good for Nf=4 flavors, but for all lambda's. DG is for lambda= * C* 400 MeV; it is valid for 1200 FOR Nf=5 (all values in GeV**2). Note that INIT has to be * C* called before the DG-functions can be used. Also, all quark and * C* gluon densities (but not the photon density inside the electron) * C* have to be multiplied with alpha-em. * C*********************************************************************** C **** General form for quark-distributions within the photon *** FUNCTION QU(X,A,B,C,D,E,FAK) IMPLICIT REAL*8 (A-H,M,O-Z) X1=1.D0-X QU=FAK*(X*X+X1*X1)/(A-B*DLOG(X1))+C*X**(D-1.D0)*X1**E RETURN END C **** General form for gluon-distribution within the photon *** FUNCTION GL(X,A,B,C) IMPLICIT REAL*8 (A-H,M,O-Z) GL=A*X**(B-1.D0)*(1.D0-X)**C RETURN END C **** General form of parameters for parametrization **** FUNCTION PAR(T,Z1,Z2,Z3,Z4) IMPLICIT REAL*8 (A-H,M,O-Z) PAR=Z1*T**Z2+Z3*T**(-Z4) RETURN END C **** Contains numerical values of parameters *** SUBROUTINE INIT IMPLICIT REAL*8 (A-H,M,O-Z) DIMENSION AG(4,3),BG(4,3),CG(4,3),AN(4,3),BN(4,3),CN(4,3),DN(4,3), & EN(4,3),AS(4,3),BS(4,3),CS(4,3),DS(4,3),ES(4,3) COMMON /GLU/ AG,BG,CG COMMON /QUA/ AN,BN,CN,DN,EN,AS,BS,CS,DS,ES AG(1,1)=-.207D0 AG(2,1)=.6158D0 AG(3,1)=1.074D0 AG(4,1)=0.D0 BG(1,1)=-.1987D0 BG(2,1)=.6257D0 BG(3,1)=8.352D0 BG(4,1)=5.024D0 CG(1,1)=5.119D0 CG(2,1)=-.2752D0 CG(3,1)=-6.993D0 CG(4,1)=2.298D0 AG(1,2)=.8926D-2 AG(2,2)=.6594D0 AG(3,2)=.4766D0 AG(4,2)=.1975D-1 BG(1,2)=.5085D-1 BG(2,2)=.2774D0 BG(3,2)=-.3906D0 BG(4,2)=-.3212D0 CG(1,2)=-.2313D0 CG(2,2)=.1382D0 CG(3,2)=6.542D0 CG(4,2)=.5162D0 AG(1,3)=.03197D0 AG(2,3)=1.018D0 AG(3,3)=.2461D0 AG(4,3)=.2707D-1 BG(1,3)=-.618D-2 BG(2,3)=.9476D0 BG(3,3)=-.6094D0 BG(4,3)=-.1067D-1 CG(1,3)=-.1216D0 CG(2,3)=.9047D0 CG(3,3)=2.653D0 CG(4,3)=.2003D-2 AN(1,1)=2.285D0 AN(2,1)=-.1526D-1 AN(3,1)=1330.D0 AN(4,1)=4.219D0 BN(1,1)=6.073D0 BN(2,1)=-.8132D0 BN(3,1)=-41.31D0 BN(4,1)=3.165D0 CN(1,1)=-.4202D0 CN(2,1)=.1778D-1 CN(3,1)=.9216D0 CN(4,1)=.18D0 DN(1,1)=-.8083D-1 DN(2,1)=.6346D0 DN(3,1)=1.208D0 DN(4,1)=.203D0 EN(1,1)=.5526D-1 EN(2,1)=1.136D0 EN(3,1)=.9512D0 EN(4,1)=.1163D-1 AN(1,2)=-.3711D0 AN(2,2)=1.061D0 AN(3,2)=4.758D0 AN(4,2)=-.1503D-1 BN(1,2)=-.1717D0 BN(2,2)=.7815D0 BN(3,2)=1.535D0 BN(4,2)=.7067D-2 CN(1,2)=.8766D-1 CN(2,2)=.2197D-1 CN(3,2)=.1096D0 CN(4,2)=.204D0 DN(1,2)=-.8915D0 DN(2,2)=.2857D0 DN(3,2)=2.973D0 DN(4,2)=.1185D0 EN(1,2)=-.1816D0 EN(2,2)=.5866D0 EN(3,2)=2.421D0 EN(4,2)=.4059D0 AN(1,3)=15.8D0 AN(2,3)=-.9464D0 AN(3,3)=-.5D0 AN(4,3)=-.2118D0 BN(1,3)=2.742D0 BN(2,3)=-.7332D0 BN(3,3)=.7148D0 BN(4,3)=3.287D0 CN(1,3)=.2917D-1 CN(2,3)=.4657D-1 CN(3,3)=.1785D0 CN(4,3)=.4811D-1 DN(1,3)=-.342D-1 DN(2,3)=.7196D0 DN(3,3)=.7338D0 DN(4,3)=.8139D-1 EN(1,3)=-.2302D-1 EN(2,3)=.9229D0 EN(3,3)=.5873D0 EN(4,3)=-.79D-4 AS(1,1)=16.69D0 AS(2,1)=-.7916D0 AS(3,1)=1099.D0 AS(4,1)=4.428D0 BS(1,1)=.176D0 BS(2,1)=.4794D-1 BS(3,1)=1.047D0 BS(4,1)=.25D-1 CS(1,1)=-.208D-1 CS(2,1)=.3386D-2 CS(3,1)=4.853D0 CS(4,1)=.8404D0 DS(1,1)=-.1685D-1 DS(2,1)=1.353D0 DS(3,1)=1.426D0 DS(4,1)=1.239D0 ES(1,1)=-.1986D0 ES(2,1)=1.1D0 ES(3,1)=1.136D0 ES(4,1)=-.2779D0 AS(1,2)=-.1207D0 AS(2,2)=1.071D0 AS(3,2)=1.977D0 AS(4,2)=-.8625D-2 BS(1,2)=25.D0 BS(2,2)=-1.648D0 BS(3,2)=-.1563D-1 BS(4,2)=6.438D0 CS(1,2)=-.123D-1 CS(2,2)=1.162D0 CS(3,2)=.4824D0 CS(4,2)=-.11D-1 DS(1,2)=-.9194D-1 DS(2,2)=.7912D0 DS(3,2)=.6397D0 DS(4,2)=2.327D0 ES(1,2)=.2015D-1 ES(2,2)=.9869D0 ES(3,2)=-.7036D-1 ES(4,2)=.1694D-1 AS(1,3)=6.734D0 AS(2,3)=-1.008D0 AS(3,3)=-.8594D-1 AS(4,3)=.7625D-1 BS(1,3)=59.88D0 BS(2,3)=-2.983D0 BS(3,3)=4.48D0 BS(4,3)=.9686D0 CS(1,3)=-.3226D-2 CS(2,3)=.8432D0 CS(3,3)=.3616D0 CS(4,3)=.1383D-2 DS(1,3)=-.3321D-1 DS(2,3)=.9475D0 DS(3,3)=-.3198D0 DS(4,3)=.2132D-1 ES(1,3)=.1059D0 ES(2,3)=.6954D0 ES(3,3)=-.6663D0 ES(4,3)=.3683D0 WRITE(*,1) 1 FORMAT(' Warning: Photonic parton distributions have to be', &' multiplied with alpha(E-M)!') RETURN END CC CC C **** Gluon-distribution within the photon *** FUNCTION GPH(NF,X,T) IMPLICIT REAL*8 (A-H,M,O-Z) DIMENSION AG(4,3),BG(4,3),CG(4,3) COMMON /GLU/ AG,BG,CG JF=NF-2 A=PAR(T,AG(1,JF),AG(2,JF),AG(3,JF),AG(4,JF)) B=PAR(T,BG(1,JF),BG(2,JF),BG(3,JF),BG(4,JF)) C=PAR(T,CG(1,JF),CG(2,JF),CG(3,JF),CG(4,JF)) GPH=GL(X,A,B,C) RETURN END CC CC C **** Quark-distributions within the photon *** FUNCTION QPH(NF,IFLAG,X,T) C **** IFLAG=1: up-quarks; C IFLAG=2: down-quarks C T=ln(Q**2/lambda**2) IMPLICIT REAL*8 (A-H,M,O-Z) DIMENSION AN(4,3),BN(4,3),CN(4,3),DN(4,3),EN(4,3),AS(4,3),BS(4,3), & CS(4,3),DS(4,3),ES(4,3) COMMON /QUA/ AN,BN,CN,DN,EN,AS,BS,CS,DS,ES JF=NF-2 A1=PAR(T,AN(1,JF),AN(2,JF),AN(3,JF),AN(4,JF)) B1=PAR(T,BN(1,JF),BN(2,JF),BN(3,JF),BN(4,JF)) C1=PAR(T,CN(1,JF),CN(2,JF),CN(3,JF),CN(4,JF)) D1=PAR(T,DN(1,JF),DN(2,JF),DN(3,JF),DN(4,JF)) E1=PAR(T,EN(1,JF),EN(2,JF),EN(3,JF),EN(4,JF)) A2=PAR(T,AS(1,JF),AS(2,JF),AS(3,JF),AS(4,JF)) B2=PAR(T,BS(1,JF),BS(2,JF),BS(3,JF),BS(4,JF)) C2=PAR(T,CS(1,JF),CS(2,JF),CS(3,JF),CS(4,JF)) D2=PAR(T,DS(1,JF),DS(2,JF),DS(3,JF),DS(4,JF)) E2=PAR(T,ES(1,JF),ES(2,JF),ES(3,JF),ES(4,JF)) QNS=QU(X,A1,B1,C1,D1,E1,1.D0) IF(NF.EQ.3)FAK=9.D0 IF(NF.EQ.4)FAK=1.D1 IF(NF.EQ.5)FAK=55.D0/6.D0 QS=QU(X,A2,B2,C2,D2,E2,FAK) IF(IFLAG.EQ.1)THEN IF(NF.EQ.3)QPH=(QS+9.D0*QNS)/6.D0 IF(NF.EQ.4)QPH=(QS+6.D0*QNS)/8.D0 IF(NF.EQ.5)QPH=(QS+7.5D0*QNS)*.1D0 ELSE IF(NF.EQ.3)QPH=(QS-4.5D0*QNS)/6.D0 IF(NF.EQ.4)QPH=(QS-6.D0*QNS)/8.D0 IF(NF.EQ.5)QPH=(QS-5.D0*QNS)*.1D0 END IF RETURN END CCC CCC FUNCTION PHOT(E2,Z) C *** Computes photon-density within electron in Weizsaecker- *** C *** Williams-approximation; E2 is a typical squared energy scale. *** IMPLICIT REAL*8 (A-H,M,O-Z) Z1=1.D0-Z PHOT=1.162D-3*(1.D0+Z1*Z1)*DLOG(E2/2.61D-7)/Z RETURN END CCC CCC FUNCTION GASYM(X) C *** Computes x-dependence of asymptotic gluon-distribution within *** C *** the photon; has to be multiplied with *** C *** alpha(EM)*ln(Q**2/lambda**2) *** IMPLICIT REAL*8 (A-H,M,O-Z) H=.194D0*(1.D0-X)**1.03D0/X**1.97D0 GASYM=H/6.283D0 RETURN END CCC CCC FUNCTION QASYM(X,E) C *** Computes x-dependence of asymptotic quark-distribution within *** C *** the photon; has to be multiplied with *** C *** alpha(EM)*ln(Q**2/lambda**2); E is the charge of the quark, *** C ** not the energy! *** IMPLICIT REAL*8 (A-H,M,O-Z) X1=1.D0-X H=E*E*(1.81D0-1.67D0*X+2.16D0*X*X)/X**.3D0/(1.D0-.4D0*DLOG(X1)) & +.38D-2*X1**1.82D0/X**2.18D0 QASYM=H/6.283D0 RETURN END CCC CCC FUNCTION QVMD(X) C********************************************************************** C* A parametrization of the quark density inside the photon inspired * C* by VMD-type ideas: q-gamma = alpha-em*q-pion, assuming u=d=s. The * C* pion distribution functions have been taken from Glueck et al. Re- * C* call that alpha-em is factored out. * C********************************************************************** IMPLICIT REAL*8 (A-H,M,O-Z) X1=1.D0-X QVMD=5.D0*X1/(16.D0*DSQRT(X))+.1D0*(X1**5)/X RETURN END CCC CCC FUNCTION GVMD(X) C *** As QVMD, but for the gluon. *** IMPLICIT REAL*8 (A-H,M,O-Z) GVMD=2.D0*(1.D0-X)**3.D0/X RETURN END FUNCTION PHOTNEW(E,Z) C*********************************************************************** C* This function computes the WW-function a la Brodsky et al; E is the * C* electron energy, and Z=Egamma/E. * C*********************************************************************** IMPLICIT REAL*8 (A-H,M,O-Z) Z1=1.D0-Z H=2.32D-3*( (1.D0+Z1*Z1)*(DLOG(E*Z1/(.511D-3*(1.D0-0.5D0*Z)))) + & 0.5D0*Z*Z*DLOG((1.D0-Z)/Z) -Z1) PHOTNEW=H/Z RETURN END