// PartonDistributions.cc is a part of the PYTHIA event generator. // Copyright (C) 2017 Torbjorn Sjostrand. // PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. // Please respect the MCnet Guidelines, see GUIDELINES for details. // Function definitions (not found in the header) for the PDF, LHAPDF, // GRV94L, CTEQ5L, MSTWpdf, CTEQ6pdf, GRVpiL, PomFix, PomH1FitAB, // PomH1Jets, Lepton, NNPDF and CJKL classes. #include "Pythia8/PartonDistributions.h" namespace Pythia8 { //========================================================================== // Base class for parton distribution functions. //-------------------------------------------------------------------------- // Resolve valence content for assumed meson. Possibly modified later. void PDF::setValenceContent() { // Subdivide meson by flavour content. if (idBeamAbs < 100 || idBeamAbs > 1000) return; int idTmp1 = idBeamAbs/100; int idTmp2 = (idBeamAbs/10)%10; // Find which is quark and which antiquark. if (idTmp1%2 == 0) { idVal1 = idTmp1; idVal2 = -idTmp2; } else { idVal1 = idTmp2; idVal2 = -idTmp1; } if (idBeam < 0) { idVal1 = -idVal1; idVal2 = -idVal2; } // Special case for Pomeron, to start off. if (idBeamAbs == 990) { idVal1 = 1; idVal2 = -1; } // Photon not fixed until at Process-/PartonLevel. if (idBeamAbs == 22) { idVal1 = 10; idVal2 = -10; } } //-------------------------------------------------------------------------- // Standard parton densities. double PDF::xf(int id, double x, double Q2) { // Need to update if flavour, x or Q2 changed. // Use idSav = 9 to indicate that ALL flavours are up-to-date. // Assume that flavour and antiflavour always updated simultaneously. if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} // Baryon beams: only p and pbar for now. if (idBeamAbs == 2212) { int idNow = (idBeam > 0) ? id : -id; int idAbs = abs(id); if (idNow == 0 || idAbs == 21) return max(0., xg); if (idNow == 1) return max(0., xd); if (idNow == -1) return max(0., xdbar); if (idNow == 2) return max(0., xu); if (idNow == -2) return max(0., xubar); if (idNow == 3) return max(0., xs); if (idNow == -3) return max(0., xsbar); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Baryon beams: n and nbar by isospin conjugation of p and pbar. } else if (idBeamAbs == 2112) { int idNow = (idBeam > 0) ? id : -id; int idAbs = abs(id); if (idNow == 0 || idAbs == 21) return max(0., xg); if (idNow == 1) return max(0., xu); if (idNow == -1) return max(0., xubar); if (idNow == 2) return max(0., xd); if (idNow == -2) return max(0., xdbar); if (idNow == 3) return max(0., xs); if (idNow == -3) return max(0., xsbar); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Nondiagonal meson beams: only pi+ and pi- for now. // Some LHAPDF sets are stored with u d as valence, so use dbar = u. } else if (idBeamAbs == 211) { int idNow = (idBeam > 0) ? id : -id; int idAbs = abs(id); if (idNow == 0 || idAbs == 21) return max(0., xg); if (idNow == 1) return max(0., xubar ); if (idNow == -1) return max(0., xu ); if (idNow == 2) return max(0., xu); if (idNow == -2) return max(0., xubar); if (idNow == 3) return max(0., xs); if (idNow == -3) return max(0., xsbar); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Diagonal meson beams: only pi0, Pomeron for now. } else if (idBeam == 111 || idBeam == 990) { int idAbs = abs(id); if (id == 0 || idAbs == 21) return max(0., xg); if (id == idVal1 || id == idVal2) return max(0., xu); if (idAbs <= 2) return max(0., xubar); if (idAbs == 3) return max(0., xs); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Photon beam. } else if (idBeam == 22) { int idAbs = abs(id); if (id == 0 || idAbs == 21) return max(0., xg); if (id == 1) return max(0., xd); if (id == -1) return max(0., xdbar); if (id == 2) return max(0., xu); if (id == -2) return max(0., xubar); if (id == 3) return max(0., xs); if (id == -3) return max(0., xsbar); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Photon beam inside lepton beam. } else if ( ( idBeamAbs == 11 || idBeamAbs == 13 || idBeamAbs == 15 ) && hasGammaInLepton ) { int idAbs = abs(id); if (idAbs == 0 || idAbs == 21) return max(0., xg); if (idAbs == 1) return max(0., xd); if (idAbs == 2) return max(0., xu); if (idAbs == 3) return max(0., xs); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Lepton beam. } else { if (id == idBeam ) return max(0., xlepton); if (abs(id) == 22) return max(0., xgamma); return 0.; } } //-------------------------------------------------------------------------- // Only valence part of parton densities. double PDF::xfVal(int id, double x, double Q2) { // Need to update if flavour, x or Q2 changed. // Use idSav = 9 to indicate that ALL flavours are up-to-date. // Assume that flavour and antiflavour always updated simultaneously. if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} // Baryon and nondiagonal meson beams: only p, pbar, n, nbar, pi+, pi-. if (idBeamAbs == 2212) { int idNow = (idBeam > 0) ? id : -id; if (idNow == 1) return max(0., xdVal); if (idNow == 2) return max(0., xuVal); return 0.; } else if (idBeamAbs == 2112) { int idNow = (idBeam > 0) ? id : -id; if (idNow == 1) return max(0., xuVal); if (idNow == 2) return max(0., xdVal); return 0.; } else if (idBeamAbs == 211) { int idNow = (idBeam > 0) ? id : -id; if (idNow == 2 || idNow == -1) return max(0., xuVal); return 0.; // Diagonal meson beams: only pi0, Pomeron for now. } else if (idBeam == 111 || idBeam == 990) { if (id == idVal1 || id == idVal2) return max(0., xuVal); return 0.; // Photon beam. } else if (idBeam == 22) { int idAbs = abs(id); if (id == idVal1 || id == idVal2) { if (idAbs == 1) return max(0., xdVal); if (idAbs == 2) return max(0., xuVal); if (idAbs == 3) return max(0., xsVal); if (idAbs == 4) return max(0., xcVal); if (idAbs == 5) return max(0., xbVal); } return 0.; // Lepton beam. } else { if (id == idBeam) return max(0., xlepton); return 0.; } } //-------------------------------------------------------------------------- // Only sea part of parton densities. double PDF::xfSea(int id, double x, double Q2) { // Need to update if flavour, x or Q2 changed. // Use idSav = 9 to indicate that ALL flavours are up-to-date. // Assume that flavour and antiflavour always updated simultaneously. if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} // Hadron beams. if (idBeamAbs > 100) { int idNow = (idBeam > 0) ? id : -id; int idAbs = abs(id); if (idNow == 0 || idAbs == 21) return max(0., xg); if (idBeamAbs == 2212) { if (idNow == 1) return max(0., xdSea); if (idNow == -1) return max(0., xdbar); if (idNow == 2) return max(0., xuSea); if (idNow == -2) return max(0., xubar); } else if (idBeamAbs == 2112) { if (idNow == 1) return max(0., xuSea); if (idNow == -1) return max(0., xubar); if (idNow == 2) return max(0., xdSea); if (idNow == -2) return max(0., xdbar); } else { if (idAbs <= 2) return max(0., xuSea); } if (idNow == 3) return max(0., xs); if (idNow == -3) return max(0., xsbar); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); if (idAbs == 22) return max(0., xgamma); return 0.; // Photon beam. } else if (idBeamAbs == 22) { int idAbs = abs(id); if ( id == 0 || idAbs == 21 ) return max(0., xg); if ( idAbs == 22 ) return max(0., xgamma); // If a valence parton return only the sea part. // Otherwise return the total PDF. if ( id == idVal1 || id == idVal2 ) { if (idAbs == 1) return max(0., xdSea); if (idAbs == 2) return max(0., xuSea); if (idAbs == 3) return max(0., xsSea); if (idAbs == 4) return max(0., xcSea); if (idAbs == 5) return max(0., xbSea); } else { if (idAbs == 1) return max(0., xd); if (idAbs == 2) return max(0., xu); if (idAbs == 3) return max(0., xs); if (idAbs == 4) return max(0., xc); if (idAbs == 5) return max(0., xb); } return 0.; // Lepton beam. } else { if (abs(id) == 22) return max(0., xgamma); return 0.; } } //========================================================================== // Gives the GRV 94 L (leading order) parton distribution function set // in parametrized form. Authors: M. Glueck, E. Reya and A. Vogt. // Ref: M. Glueck, E. Reya and A. Vogt, Z.Phys. C67 (1995) 433. void GRV94L::xfUpdate(int , double x, double Q2) { // Common expressions. Constrain Q2 for which parametrization is valid. double mu2 = 0.23; double lam2 = 0.2322 * 0.2322; double s = (Q2 > mu2) ? log( log(Q2/lam2) / log(mu2/lam2) ) : 0.; double ds = sqrt(s); double s2 = s * s; double s3 = s2 * s; // uv : double nu = 2.284 + 0.802 * s + 0.055 * s2; double aku = 0.590 - 0.024 * s; double bku = 0.131 + 0.063 * s; double au = -0.449 - 0.138 * s - 0.076 * s2; double bu = 0.213 + 2.669 * s - 0.728 * s2; double cu = 8.854 - 9.135 * s + 1.979 * s2; double du = 2.997 + 0.753 * s - 0.076 * s2; double uv = grvv (x, nu, aku, bku, au, bu, cu, du); // dv : double nd = 0.371 + 0.083 * s + 0.039 * s2; double akd = 0.376; double bkd = 0.486 + 0.062 * s; double ad = -0.509 + 3.310 * s - 1.248 * s2; double bd = 12.41 - 10.52 * s + 2.267 * s2; double cd = 6.373 - 6.208 * s + 1.418 * s2; double dd = 3.691 + 0.799 * s - 0.071 * s2; double dv = grvv (x, nd, akd, bkd, ad, bd, cd, dd); // udb : double alx = 1.451; double bex = 0.271; double akx = 0.410 - 0.232 * s; double bkx = 0.534 - 0.457 * s; double agx = 0.890 - 0.140 * s; double bgx = -0.981; double cx = 0.320 + 0.683 * s; double dx = 4.752 + 1.164 * s + 0.286 * s2; double ex = 4.119 + 1.713 * s; double esx = 0.682 + 2.978 * s; double udb = grvw (x, s, alx, bex, akx, bkx, agx, bgx, cx, dx, ex, esx); // del : double ne = 0.082 + 0.014 * s + 0.008 * s2; double ake = 0.409 - 0.005 * s; double bke = 0.799 + 0.071 * s; double ae = -38.07 + 36.13 * s - 0.656 * s2; double be = 90.31 - 74.15 * s + 7.645 * s2; double ce = 0.; double de = 7.486 + 1.217 * s - 0.159 * s2; double del = grvv (x, ne, ake, bke, ae, be, ce, de); // sb : double sts = 0.; double als = 0.914; double bes = 0.577; double aks = 1.798 - 0.596 * s; double as = -5.548 + 3.669 * ds - 0.616 * s; double bs = 18.92 - 16.73 * ds + 5.168 * s; double dst = 6.379 - 0.350 * s + 0.142 * s2; double est = 3.981 + 1.638 * s; double ess = 6.402; double sb = grvs (x, s, sts, als, bes, aks, as, bs, dst, est, ess); // cb : double stc = 0.888; double alc = 1.01; double bec = 0.37; double akc = 0.; double ac = 0.; double bc = 4.24 - 0.804 * s; double dct = 3.46 - 1.076 * s; double ect = 4.61 + 1.49 * s; double esc = 2.555 + 1.961 * s; double chm = grvs (x, s, stc, alc, bec, akc, ac, bc, dct, ect, esc); // bb : double stb = 1.351; double alb = 1.00; double beb = 0.51; double akb = 0.; double ab = 0.; double bb = 1.848; double dbt = 2.929 + 1.396 * s; double ebt = 4.71 + 1.514 * s; double esb = 4.02 + 1.239 * s; double bot = grvs (x, s, stb, alb, beb, akb, ab, bb, dbt, ebt, esb); // gl : double alg = 0.524; double beg = 1.088; double akg = 1.742 - 0.930 * s; double bkg = - 0.399 * s2; double ag = 7.486 - 2.185 * s; double bg = 16.69 - 22.74 * s + 5.779 * s2; double cg = -25.59 + 29.71 * s - 7.296 * s2; double dg = 2.792 + 2.215 * s + 0.422 * s2 - 0.104 * s3; double eg = 0.807 + 2.005 * s; double esg = 3.841 + 0.316 * s; double gl = grvw (x, s, alg, beg, akg, bkg, ag, bg, cg, dg, eg, esg); // Update values xg = gl; xu = uv + 0.5*(udb - del); xd = dv + 0.5*(udb + del); xubar = 0.5*(udb - del); xdbar = 0.5*(udb + del); xs = sb; xsbar = sb; xc = chm; xb = bot; // Subdivision of valence and sea. xuVal = uv; xuSea = xubar; xdVal = dv; xdSea = xdbar; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- double GRV94L::grvv (double x, double n, double ak, double bk, double a, double b, double c, double d) { double dx = sqrt(x); return n * pow(x, ak) * (1. + a * pow(x, bk) + x * (b + c * dx)) * pow(1. - x, d); } //-------------------------------------------------------------------------- double GRV94L::grvw (double x, double s, double al, double be, double ak, double bk, double a, double b, double c, double d, double e, double es) { double lx = log(1./x); return (pow(x, ak) * (a + x * (b + x * c)) * pow(lx, bk) + pow(s, al) * exp(-e + sqrt(es * pow(s, be) * lx))) * pow(1. - x, d); } //-------------------------------------------------------------------------- double GRV94L::grvs (double x, double s, double sth, double al, double be, double ak, double ag, double b, double d, double e, double es) { if(s <= sth) { return 0.; } else { double dx = sqrt(x); double lx = log(1./x); return pow(s - sth, al) / pow(lx, ak) * (1. + ag * dx + b * x) * pow(1. - x, d) * exp(-e + sqrt(es * pow(s, be) * lx)); } } //========================================================================== // Gives the CTEQ 5 L (leading order) parton distribution function set // in parametrized form. Parametrization by J. Pumplin. // Ref: CTEQ Collaboration, H.L. Lai et al., Eur.Phys.J. C12 (2000) 375. // The range of (x, Q) covered by this parametrization of the QCD // evolved parton distributions is 1E-6 < x < 1, 1.1 GeV < Q < 10 TeV. // In the current implementation, densities are frozen at borders. void CTEQ5L::xfUpdate(int , double x, double Q2) { // Constrain x and Q2 to range for which parametrization is valid. double Q = sqrt( max( 1., min( 1e8, Q2) ) ); x = max( 1e-6, min( 1.-1e-10, x) ); // Derived kinematical quantities. double y = - log(x); double u = log( x / 0.00001); double x1 = 1. - x; double x1L = log(1. - x); double sumUbarDbar = 0.; // Parameters of parametrizations. const double Qmin[8] = { 0., 0., 0., 0., 0., 0., 1.3, 4.5}; const double alpha[8] = { 0.2987216, 0.3407552, 0.4491863, 0.2457668, 0.5293999, 0.3713141, 0.03712017, 0.004952010 }; const double ut1[8] = { 4.971265, 2.612618, -0.4656819, 3.862583, 0.1895615, 3.753257, 4.400772, 5.562568 }; const double ut2[8] = { -1.105128, -1.258304e5, -274.2390, -1.265969, -3.069097, -1.113085, -1.356116, -1.801317 }; const double am[8][9][3] = { // d. { { 0.5292616E+01, -0.2751910E+01, -0.2488990E+01 }, { 0.9714424E+00, 0.1011827E-01, -0.1023660E-01 }, { -0.1651006E+02, 0.7959721E+01, 0.8810563E+01 }, { -0.1643394E+02, 0.5892854E+01, 0.9348874E+01 }, { 0.3067422E+02, 0.4235796E+01, -0.5112136E+00 }, { 0.2352526E+02, -0.5305168E+01, -0.1169174E+02 }, { -0.1095451E+02, 0.3006577E+01, 0.5638136E+01 }, { -0.1172251E+02, -0.2183624E+01, 0.4955794E+01 }, { 0.1662533E-01, 0.7622870E-02, -0.4895887E-03 } }, // u. { { 0.9905300E+00, -0.4502235E+00, 0.1624441E+00 }, { 0.8867534E+00, 0.1630829E-01, -0.4049085E-01 }, { 0.8547974E+00, 0.3336301E+00, 0.1371388E+00 }, { 0.2941113E+00, -0.1527905E+01, 0.2331879E+00 }, { 0.3384235E+02, 0.3715315E+01, 0.8276930E+00 }, { 0.6230115E+01, 0.3134639E+01, -0.1729099E+01 }, { -0.1186928E+01, -0.3282460E+00, 0.1052020E+00 }, { -0.8545702E+01, -0.6247947E+01, 0.3692561E+01 }, { 0.1724598E-01, 0.7120465E-02, 0.4003646E-04 } }, // g. { { 0.1193572E+03, -0.3886845E+01, -0.1133965E+01 }, { -0.9421449E+02, 0.3995885E+01, 0.1607363E+01 }, { 0.4206383E+01, 0.2485954E+00, 0.2497468E+00 }, { 0.1210557E+03, -0.3015765E+01, -0.1423651E+01 }, { -0.1013897E+03, -0.7113478E+00, 0.2621865E+00 }, { -0.1312404E+01, -0.9297691E+00, -0.1562531E+00 }, { 0.1627137E+01, 0.4954111E+00, -0.6387009E+00 }, { 0.1537698E+00, -0.2487878E+00, 0.8305947E+00 }, { 0.2496448E-01, 0.2457823E-02, 0.8234276E-03 } }, // ubar + dbar. { { 0.2647441E+02, 0.1059277E+02, -0.9176654E+00 }, { 0.1990636E+01, 0.8558918E-01, 0.4248667E-01 }, { -0.1476095E+02, -0.3276255E+02, 0.1558110E+01 }, { -0.2966889E+01, -0.3649037E+02, 0.1195914E+01 }, { -0.1000519E+03, -0.2464635E+01, 0.1964849E+00 }, { 0.3718331E+02, 0.4700389E+02, -0.2772142E+01 }, { -0.1872722E+02, -0.2291189E+02, 0.1089052E+01 }, { -0.1628146E+02, -0.1823993E+02, 0.2537369E+01 }, { -0.1156300E+01, -0.1280495E+00, 0.5153245E-01 } }, // dbar/ubar. { { -0.6556775E+00, 0.2490190E+00, 0.3966485E-01 }, { 0.1305102E+01, -0.1188925E+00, -0.4600870E-02 }, { -0.2371436E+01, 0.3566814E+00, -0.2834683E+00 }, { -0.6152826E+01, 0.8339877E+00, -0.7233230E+00 }, { -0.8346558E+01, 0.2892168E+01, 0.2137099E+00 }, { 0.1279530E+02, 0.1021114E+00, 0.5787439E+00 }, { 0.5858816E+00, -0.1940375E+01, -0.4029269E+00 }, { -0.2795725E+02, -0.5263392E+00, 0.1290229E+01 }, { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, // sbar. { { 0.1580931E+01, -0.2273826E+01, -0.1822245E+01 }, { 0.2702644E+01, 0.6763243E+00, 0.7231586E-02 }, { -0.1857924E+02, 0.3907500E+01, 0.5850109E+01 }, { -0.3044793E+02, 0.2639332E+01, 0.5566644E+01 }, { -0.4258011E+01, -0.5429244E+01, 0.4418946E+00 }, { 0.3465259E+02, -0.5532604E+01, -0.4904153E+01 }, { -0.1658858E+02, 0.2923275E+01, 0.2266286E+01 }, { -0.1149263E+02, 0.2877475E+01, -0.7999105E+00 }, { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, // cbar. { { -0.8293661E+00, -0.3982375E+01, -0.6494283E-01 }, { 0.2754618E+01, 0.8338636E+00, -0.6885160E-01 }, { -0.1657987E+02, 0.1439143E+02, -0.6887240E+00 }, { -0.2800703E+02, 0.1535966E+02, -0.7377693E+00 }, { -0.6460216E+01, -0.4783019E+01, 0.4913297E+00 }, { 0.3141830E+02, -0.3178031E+02, 0.7136013E+01 }, { -0.1802509E+02, 0.1862163E+02, -0.4632843E+01 }, { -0.1240412E+02, 0.2565386E+02, -0.1066570E+02 }, { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, // bbar. { { -0.6031237E+01, 0.1992727E+01, -0.1076331E+01 }, { 0.2933912E+01, 0.5839674E+00, 0.7509435E-01 }, { -0.8284919E+01, 0.1488593E+01, -0.8251678E+00 }, { -0.1925986E+02, 0.2805753E+01, -0.3015446E+01 }, { -0.9480483E+01, -0.9767837E+00, -0.1165544E+01 }, { 0.2193195E+02, -0.1788518E+02, 0.9460908E+01 }, { -0.1327377E+02, 0.1201754E+02, -0.6277844E+01 }, { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 }, { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } } }; // Loop over 8 different parametrizations. Check if inside allowed region. for (int i = 0; i < 8; ++i) { double answer = 0.; if (Q > max(Qmin[i], alpha[i])) { // Evaluate answer. double tmp = log(Q / alpha[i]); double sb = log(tmp); double sb1 = sb - 1.2; double sb2 = sb1*sb1; double af[9]; for (int j = 0; j < 9; ++j) af[j] = am[i][j][0] + sb1 * am[i][j][1] + sb2 * am[i][j][2]; double part1 = af[1] * pow( y, 1. + 0.01 * af[4]) * (1. + af[8] * u); double part2 = af[0] * x1 + af[3] * x; double part3 = x * x1 * (af[5] + af[6] * x1 + af[7] * x * x1); double part4 = (ut2[i] < -100.) ? ut1[i] * x1L + af[2] * x1L : ut1[i] * x1L + af[2] * log(x1 + exp(ut2[i])); answer = x * exp( part1 + part2 + part3 + part4); answer *= 1. - Qmin[i] / Q; } // Store results. if (i == 0) xd = x * answer; else if (i == 1) xu = x * answer; else if (i == 2) xg = x * answer; else if (i == 3) sumUbarDbar = x * answer; else if (i == 4) { xubar = sumUbarDbar / (1. + answer); xdbar = sumUbarDbar * answer / (1. + answer); } else if (i == 5) {xs = x * answer; xsbar = xs;} else if (i == 6) xc = x * answer; else if (i == 7) xb = x * answer; } // Subdivision of valence and sea. xuVal = xu - xubar; xuSea = xubar; xdVal = xd - xdbar; xdSea = xdbar; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // The MSTWpdf class. // MSTW 2008 PDF's, specifically the LO one. // Original C++ version by Jeppe Andersen. // Modified by Graeme Watt . //-------------------------------------------------------------------------- // Constants: could be changed here if desired, but normally should not. // These are of technical nature, as described for each. // Number of parton flavours, x and Q2 grid points, // bins below c and b thresholds. const int MSTWpdf::np = 12; const int MSTWpdf::nx = 64; const int MSTWpdf::nq = 48; const int MSTWpdf::nqc0 = 4; const int MSTWpdf::nqb0 = 14; // Range of (x, Q2) grid. const double MSTWpdf::xmin = 1e-6; const double MSTWpdf::xmax = 1.0; const double MSTWpdf::qsqmin = 1.0; const double MSTWpdf::qsqmax = 1e9; // Array of x values. const double MSTWpdf::xxInit[65] = {0., 1e-6, 2e-6, 4e-6, 6e-6, 8e-6, 1e-5, 2e-5, 4e-5, 6e-5, 8e-5, 1e-4, 2e-4, 4e-4, 6e-4, 8e-4, 1e-3, 2e-3, 4e-3, 6e-3, 8e-3, 1e-2, 1.4e-2, 2e-2, 3e-2, 4e-2, 6e-2, 8e-2, 0.10, 0.125, 0.15, 0.175, 0.20, 0.225, 0.25, 0.275, 0.30, 0.325, 0.35, 0.375, 0.40, 0.425, 0.45, 0.475, 0.50, 0.525, 0.55, 0.575, 0.60, 0.625, 0.65, 0.675, 0.70, 0.725, 0.75, 0.775, 0.80, 0.825, 0.85, 0.875, 0.90, 0.925, 0.95, 0.975, 1.0 }; // Array of Q values. const double MSTWpdf::qqInit[49] = {0., 1.0, 1.25, 1.5, 0., 0., 2.5, 3.2, 4.0, 5.0, 6.4, 8.0, 10., 12., 0., 0., 26.0, 40.0, 64.0, 1e2, 1.6e2, 2.4e2, 4e2, 6.4e2, 1e3, 1.8e3, 3.2e3, 5.6e3, 1e4, 1.8e4, 3.2e4, 5.6e4, 1e5, 1.8e5, 3.2e5, 5.6e5, 1e6, 1.8e6, 3.2e6, 5.6e6, 1e7, 1.8e7, 3.2e7, 5.6e7, 1e8, 1.8e8, 3.2e8, 5.6e8, 1e9 }; //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void MSTWpdf::init(int iFitIn, string xmlPath, Info* infoPtr) { // Choice of fit among possibilities. iFit = iFitIn; // Select which data file to read for current fit. if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; string fileName = " "; if (iFit == 1) fileName = "mrstlostar.00.dat"; if (iFit == 2) fileName = "mrstlostarstar.00.dat"; if (iFit == 3) fileName = "mstw2008lo.00.dat"; if (iFit == 4) fileName = "mstw2008nlo.00.dat"; // Open data file. ifstream data_file( (xmlPath + fileName).c_str() ); if (!data_file.good()) { printErr("Error in MSTWpdf::init: did not find data file ", infoPtr); isSet = false; return; } // Initialization with a stream. init(data_file, infoPtr); data_file.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void MSTWpdf::init(istream& data_file, Info* infoPtr) { // Check that data stream is available. if (!data_file.good()) { printErr("Error in MSTWpdf::init: cannot read from stream", infoPtr); isSet = false; return; } // Counters and temporary variables. int i,n,m,k,l,j; double dtemp; // Variables used for initialising c_ij array: double f[np+1][nx+1][nq+1]; double f1[np+1][nx+1][nq+1]; // derivative w.r.t. x double f2[np+1][nx+1][nq+1]; // derivative w.r.t. q double f12[np+1][nx+1][nq+1];// cross derivative double f21[np+1][nx+1][nq+1];// cross derivative int wt[16][16]={{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}, {-3,0,0,3,0,0,0,0,-2,0,0,-1,0,0,0,0}, {2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0}, {0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0}, {0,0,0,0,-3,0,0,3,0,0,0,0,-2,0,0,-1}, {0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1}, {-3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0}, {9,-9,9,-9,6,3,-3,-6,6,-6,-3,3,4,2,1,2}, {-6,6,-6,6,-4,-2,2,4,-3,3,3,-3,-2,-1,-1,-2}, {2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0}, {-6,6,-6,6,-3,-3,3,3,-4,4,2,-2,-2,-2,-1,-1}, {4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1}}; double xxd,d1d2,cl[16],x[16],d1,d2,y[5],y1[5],y2[5],y12[5]; double mc2,mb2,eps=1e-6; // q^2 grid points at mc2+eps, mb2+eps // Read distance, tolerance, heavy quark masses // and alphaS values from file. char comma; int nExtraFlavours; data_file.ignore(256,'\n'); data_file.ignore(256,'\n'); data_file.ignore(256,'='); data_file >> distance >> tolerance; data_file.ignore(256,'='); data_file >> mCharm; data_file.ignore(256,'='); data_file >> mBottom; data_file.ignore(256,'='); data_file >> alphaSQ0; data_file.ignore(256,'='); data_file >> alphaSMZ; data_file.ignore(256,'='); data_file >> alphaSorder >> comma >> alphaSnfmax; data_file.ignore(256,'='); data_file >> nExtraFlavours; data_file.ignore(256,'\n'); data_file.ignore(256,'\n'); data_file.ignore(256,'\n'); // Use c and b quark masses for outlay of qq array. for (int iqq = 0; iqq < 49; ++iqq) qq[iqq] = qqInit[iqq]; mc2=mCharm*mCharm; mb2=mBottom*mBottom; qq[4]=mc2; qq[5]=mc2+eps; qq[14]=mb2; qq[15]=mb2+eps; // Check that the heavy quark masses are sensible. if (mc2 < qq[3] || mc2 > qq[6]) { printErr("Error in MSTWpdf::init: invalid mCharm", infoPtr); isSet = false; return; } if (mb2 < qq[13] || mb2 > qq[16]) { printErr("Error in MSTWpdf::init: invalid mBottom", infoPtr); isSet = false; return; } // The nExtraFlavours variable is provided to aid compatibility // with future grids where, for example, a photon distribution // might be provided (cf. the MRST2004QED PDFs). if (nExtraFlavours < 0 || nExtraFlavours > 1) { printErr("Error in MSTWpdf::init: invalid nExtraFlavours", infoPtr); isSet = false; return; } // Now read in the grids from the grid file. for (n=1;n<=nx-1;n++) for (m=1;m<=nq;m++) { for (i=1;i<=9;i++) data_file >> f[i][n][m]; if (alphaSorder==2) { // only at NNLO data_file >> f[10][n][m]; // = chm-cbar data_file >> f[11][n][m]; // = bot-bbar } else { f[10][n][m] = 0.; // = chm-cbar f[11][n][m] = 0.; // = bot-bbar } if (nExtraFlavours>0) data_file >> f[12][n][m]; // = photon else f[12][n][m] = 0.; // photon if (data_file.eof()) { printErr("Error in MSTWpdf::init: could not read data stream", infoPtr); isSet = false; return; } } // Check that ALL the file contents have been read in. data_file >> dtemp; if (!data_file.eof()) { printErr("Error in MSTWpdf::init: could not read data stream", infoPtr); isSet = false; return; } // PDFs are identically zero at x = 1. for (i=1;i<=np;i++) for (m=1;m<=nq;m++) f[i][nx][m]=0.0; // Set up the new array in log10(x) and log10(qsq). for (i=1;i<=nx;i++) xx[i]=log10(xxInit[i]); for (m=1;m<=nq;m++) qq[m]=log10(qq[m]); // Now calculate the derivatives used for bicubic interpolation. for (i=1;i<=np;i++) { // Start by calculating the first x derivatives // along the first x value: for (m=1;m<=nq;m++) { f1[i][1][m]=polderivative1(xx[1],xx[2],xx[3],f[i][1][m],f[i][2][m], f[i][3][m]); // Then along the rest (up to the last): for (k=2;kpow(10.,qq[nqc0]) && qsqpow(10.,qq[nqb0]) && qsqxmax) return 0.; if (qsqqsqmax) { interpolate=0; } if (f==0) ip=1; else if (f>=1 && f<=5) ip=f+1; else if (f<=-1 && f>=-5) ip=-f+1; else if (f>=7 && f<=11) ip=f; else if (f==13) ip=12; else if (abs(f)==6 || f==12) return 0.; else return 0.; // Interpolation in log10(x), log10(qsq): xxx=log10(x); qqq=log10(qsq); if (interpolate==1) { // do usual interpolation parton_pdf=parton_interpolate(ip,xxx,qqq); if (f<=-1 && f>=-5) // antiquark = quark - valence parton_pdf -= parton_interpolate(ip+5,xxx,qqq); } else if (interpolate==-1) { // extrapolate to low Q^2 if (x=-5) { // antiquark = quark - valence parton_pdf -= parton_extrapolate(ip+5,xxx,log10(qsqmin)); parton_pdf1 -= parton_extrapolate(ip+5,xxx,log10(1.01*qsqmin)); } } else { // do usual interpolation parton_pdf = parton_interpolate(ip,xxx,log10(qsqmin)); parton_pdf1 = parton_interpolate(ip,xxx,log10(1.01*qsqmin)); if (f<=-1 && f>=-5) { // antiquark = quark - valence parton_pdf -= parton_interpolate(ip+5,xxx,log10(qsqmin)); parton_pdf1 -= parton_interpolate(ip+5,xxx,log10(1.01*qsqmin)); } } // Calculate the anomalous dimension, dlog(xf)/dlog(qsq), // evaluated at qsqmin. Then extrapolate the PDFs to low // qsq < qsqmin by interpolating the anomalous dimenion between // the value at qsqmin and a value of 1 for qsq << qsqmin. // If value of PDF at qsqmin is very small, just set // anomalous dimension to 1 to prevent rounding errors. if (fabs(parton_pdf) >= 1.e-5) anom = max(-2.5, (parton_pdf1-parton_pdf)/parton_pdf/0.01); else anom = 1.; parton_pdf = parton_pdf*pow(qsq/qsqmin,anom*qsq/qsqmin+1.-qsq/qsqmin); } else { // extrapolate outside PDF grid to low x or high Q^2 parton_pdf = parton_extrapolate(ip,xxx,qqq); if (f<=-1 && f>=-5) // antiquark = quark - valence parton_pdf -= parton_extrapolate(ip+5,xxx,qqq); } return parton_pdf; } //-------------------------------------------------------------------------- // Interpolate PDF value inside data grid. double MSTWpdf::parton_interpolate(int ip, double xxx, double qqq) { double g, t, u; int n, m, l; n=locate(xx,nx,xxx); // 0: below xmin, nx: above xmax m=locate(qq,nq,qqq); // 0: below qsqmin, nq: above qsqmax t=(xxx-xx[n])/(xx[n+1]-xx[n]); u=(qqq-qq[m])/(qq[m+1]-qq[m]); // Assume PDF proportional to (1-x)^p as x -> 1. if (n==nx-1) { double g0=((c[ip][n][m][1][4]*u+c[ip][n][m][1][3])*u +c[ip][n][m][1][2])*u+c[ip][n][m][1][1]; // value at xx[n] double g1=((c[ip][n-1][m][1][4]*u+c[ip][n-1][m][1][3])*u +c[ip][n-1][m][1][2])*u+c[ip][n-1][m][1][1]; // value at xx[n-1] double p = 1.0; if (g0>0.0&&g1>0.0) p = log(g1/g0)/log((xx[n+1]-xx[n-1])/(xx[n+1]-xx[n])); if (p<=1.0) p=1.0; g=g0*pow((xx[n+1]-xxx)/(xx[n+1]-xx[n]),p); } // Usual interpolation. else { g=0.0; for (l=4;l>=1;l--) { g=t*g+((c[ip][n][m][l][4]*u+c[ip][n][m][l][3])*u +c[ip][n][m][l][2])*u+c[ip][n][m][l][1]; } } return g; } //-------------------------------------------------------------------------- // Extrapolate PDF value outside data grid. double MSTWpdf::parton_extrapolate(int ip, double xxx, double qqq) { double parton_pdf=0.; int n,m; n=locate(xx,nx,xxx); // 0: below xmin, nx: above xmax m=locate(qq,nq,qqq); // 0: below qsqmin, nq: above qsqmax if (n==0&&(m>0&&m1e-3 && f1>1e-3 ) { // if values are positive, keep them so f0=log(f0); f1=log(f1); parton_pdf=exp(f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1])); } else // otherwise just extrapolate in the value parton_pdf=f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1]); } if (n>0&&m==nq) { // if extrapolation into large q only double f0,f1; f0=parton_interpolate(ip,xxx,qq[nq]); f1=parton_interpolate(ip,xxx,qq[nq-1]); if ( f0>1e-3 && f1>1e-3 ) { // if values are positive, keep them so f0=log(f0); f1=log(f1); parton_pdf=exp(f0+(f0-f1)/(qq[nq]-qq[nq-1])*(qqq-qq[nq])); } else // otherwise just extrapolate in the value parton_pdf=f0+(f0-f1)/(qq[nq]-qq[nq-1])*(qqq-qq[nq]); } if (n==0&&m==nq) { // if extrapolation into large q AND small x double f0,f1; f0=parton_extrapolate(ip,xx[1],qqq); f1=parton_extrapolate(ip,xx[2],qqq); if ( f0>1e-3 && f1>1e-3 ) { // if values are positive, keep them so f0=log(f0); f1=log(f1); parton_pdf=exp(f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1])); } else // otherwise just extrapolate in the value parton_pdf=f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1]); } return parton_pdf; } //-------------------------------------------------------------------------- // Returns an integer j such that x lies inbetween xloc[j] and xloc[j+1]. // unit offset of increasing ordered array xloc assumed. // n is the length of the array (xloc[n] highest element). int MSTWpdf::locate(double xloc[],int n,double x) { int ju,jm,jl(0),j; ju=n+1; while (ju-jl>1) { jm=(ju+jl)/2; // compute a mid point. if ( x>= xloc[jm]) jl=jm; else ju=jm; } if (x==xloc[1]) j=1; else if (x==xloc[n]) j=n-1; else j=jl; return j; } //-------------------------------------------------------------------------- // Returns the estimate of the derivative at x1 obtained by a polynomial // interpolation using the three points (x_i,y_i). double MSTWpdf::polderivative1(double x1, double x2, double x3, double y1, double y2, double y3) { return (x3*x3*(y1-y2)+2.0*x1*(x3*(-y1+y2)+x2*(y1-y3))+x2*x2*(-y1+y3) +x1*x1*(-y2+y3))/((x1-x2)*(x1-x3)*(x2-x3)); } //-------------------------------------------------------------------------- // Returns the estimate of the derivative at x2 obtained by a polynomial // interpolation using the three points (x_i,y_i). double MSTWpdf::polderivative2(double x1, double x2, double x3, double y1, double y2, double y3) { return (x3*x3*(y1-y2)-2.0*x2*(x3*(y1-y2)+x1*(y2-y3))+x2*x2*(y1-y3) +x1*x1*(y2-y3))/((x1-x2)*(x1-x3)*(x2-x3)); } //-------------------------------------------------------------------------- // Returns the estimate of the derivative at x3 obtained by a polynomial // interpolation using the three points (x_i,y_i). double MSTWpdf::polderivative3(double x1, double x2, double x3, double y1, double y2, double y3) { return (x3*x3*(-y1+y2)+2.0*x2*x3*(y1-y3)+x1*x1*(y2-y3)+x2*x2*(-y1+y3) +2.0*x1*x3*(-y2+y3))/((x1-x2)*(x1-x3)*(x2-x3)); } //========================================================================== // The CTEQ6pdf class. // Code for handling CTEQ6L, CTEQ6L1, CTEQ66.00, CT09MC1, CT09MC2, CT09MCS. // Also handles ACTW Pomeron sets B, D and SG (alpha = 1.14) and D (= 1.19). // Constants: could be changed here if desired, but normally should not. // These are of technical nature, as described for each. // Stay away from xMin, xMax, Qmin, Qmax limits. const double CTEQ6pdf::EPSILON = 1e-6; // Assumed approximate power of small-x behaviour for interpolation. const double CTEQ6pdf::XPOWER = 0.3; //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void CTEQ6pdf::init(int iFitIn, string xmlPath, Info* infoPtr) { // Choice of fit among possibilities. iFit = iFitIn; // Select which data file to read for current fit. if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; string fileName = " "; if (iFit == 1) fileName = "cteq6l.tbl"; if (iFit == 2) fileName = "cteq6l1.tbl"; if (iFit == 3) fileName = "ctq66.00.pds"; if (iFit == 4) fileName = "ct09mc1.pds"; if (iFit == 5) fileName = "ct09mc2.pds"; if (iFit == 6) fileName = "ct09mcs.pds"; // Ditto for current Pomeron fit. if (iFit == 11) fileName = "pomactwb14.pds"; if (iFit == 12) fileName = "pomactwd14.pds"; if (iFit == 13) fileName = "pomactwsg14.pds"; if (iFit == 14) fileName = "pomactwd19.pds"; bool isPdsGrid = (iFit > 2); // Open data file. ifstream pdfgrid( (xmlPath + fileName).c_str() ); if (!pdfgrid.good()) { printErr("Error in CTEQ6pdf::init: did not find data file", infoPtr); isSet = false; return; } // Initialization with a stream. init( pdfgrid, isPdsGrid, infoPtr); pdfgrid.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void CTEQ6pdf::init(istream& pdfgrid, bool isPdsGrid, Info* infoPtr) { // Check that data stream is available. if (!pdfgrid.good()) { printErr("Error in CTEQ6pdf::init: cannot read from stream", infoPtr); isSet = false; return; } // Read in common information. int iDum; double orderTmp, nQTmp, qTmp, rDum; string line; getline( pdfgrid, line); getline( pdfgrid, line); getline( pdfgrid, line); istringstream is1(line); is1 >> orderTmp >> nQTmp >> lambda >> mQ[1] >> mQ[2] >> mQ[3] >> mQ[4] >> mQ[5] >> mQ[6]; order = int(orderTmp + 0.5); nQuark = int(nQTmp + 0.5); getline( pdfgrid, line); // Read in information for the .pds grid format. if (isPdsGrid) { getline( pdfgrid, line); istringstream is2(line); is2 >> iDum >> iDum >> iDum >> nfMx >> mxVal >> iDum; if (mxVal > 4) mxVal = 3; getline( pdfgrid, line); getline( pdfgrid, line); istringstream is3(line); is3 >> nX >> nT >> iDum >> nG >> iDum; for (int i = 0; i < nG + 2; ++i) getline( pdfgrid, line); getline( pdfgrid, line); istringstream is4(line); is4 >> qIni >> qMax; for (int iT = 0; iT <= nT; ++iT) { getline( pdfgrid, line); istringstream is5(line); is5 >> qTmp; tv[iT] = log( log( qTmp/lambda)); } getline( pdfgrid, line); getline( pdfgrid, line); istringstream is6(line); is6 >> xMin >> rDum; int nPackX = 6; xv[0] = 0.; for (int iXrng = 0; iXrng < int( (nX + nPackX - 1) / nPackX); ++iXrng) { getline( pdfgrid, line); istringstream is7(line); for (int iX = nPackX * iXrng + 1; iX <= nPackX * (iXrng + 1); ++iX) if (iX <= nX) is7 >> xv[iX]; } } // Read in information for the .tbl grid format. else { mxVal = 2; getline( pdfgrid, line); istringstream is2(line); is2 >> nX >> nT >> nfMx; getline( pdfgrid, line); getline( pdfgrid, line); istringstream is3(line); is3 >> qIni >> qMax; int nPackT = 6; for (int iTrng = 0; iTrng < int( (nT + nPackT) / nPackT); ++iTrng) { getline( pdfgrid, line); istringstream is4(line); for (int iT = nPackT * iTrng; iT < nPackT * (iTrng + 1); ++iT) if (iT <= nT) { is4 >> qTmp; tv[iT] = log( log( qTmp / lambda) ); } } getline( pdfgrid, line); getline( pdfgrid, line); istringstream is5(line); is5 >> xMin; int nPackX = 6; for (int iXrng = 0; iXrng < int( (nX + nPackX) / nPackX); ++iXrng) { getline( pdfgrid, line); istringstream is6(line); for (int iX = nPackX * iXrng; iX < nPackX * (iXrng + 1); ++iX) if (iX <= nX) is6 >> xv[iX]; } } // Read in the grid proper. getline( pdfgrid, line); int nBlk = (nX + 1) * (nT + 1); int nPts = nBlk * (nfMx + 1 + mxVal); int nPack = (isPdsGrid) ? 6 : 5; for (int iRng = 0; iRng < int( (nPts + nPack - 1) / nPack); ++iRng) { getline( pdfgrid, line); istringstream is8(line); for (int i = nPack * iRng + 1; i <= nPack * (iRng + 1); ++i) if (i <= nPts) is8 >> upd[i]; } // Initialize x grid mapped to x^0.3. xvpow[0] = 0.; for (int iX = 1; iX <= nX; ++iX) xvpow[iX] = pow(xv[iX], XPOWER); // Set x and Q borders with some margin. xMinEps = xMin * (1. + EPSILON); xMaxEps = 1. - EPSILON; qMinEps = qIni * (1. + EPSILON); qMaxEps = qMax * (1. - EPSILON); // Initialize (x, Q) values of previous call. xLast = 0.; qLast = 0.; } //-------------------------------------------------------------------------- // Update PDF values. void CTEQ6pdf::xfUpdate(int , double x, double Q2) { // Update using CTEQ6 routine, within allowed (x, q) range. double xEps = doExtraPol ? x : max( xMinEps, x); double qEps = max( qMinEps, min( qMaxEps, sqrtpos(Q2) ) ); // Gluon: double glu = xEps * parton6( 0, xEps, qEps); // Sea quarks (note wrong order u, d). ACTW has no s, c, b. double bot = (iFit > 10) ? 0. : xEps * parton6( 5, xEps, qEps); double chm = (iFit > 10) ? 0. : xEps * parton6( 4, xEps, qEps); double str = xEps * parton6( 3, xEps, qEps); double usea = xEps * parton6(-1, xEps, qEps); double dsea = xEps * parton6(-2, xEps, qEps); // Valence quarks: double upv = xEps * parton6( 1, xEps, qEps) - usea; double dnv = xEps * parton6( 2, xEps, qEps) - dsea; // Check that rescaling *only* occurs for ACTW Pomeron PDF sets. if (iFit < 10) rescale = 1.; // Transfer to Pythia notation. xg = rescale * glu; xu = rescale * (upv + usea); xd = rescale * (dnv + dsea); xubar = rescale * usea; xdbar = rescale * dsea; xs = rescale * str; xsbar = rescale * str; xc = rescale * chm; xb = rescale * bot; xgamma = 0.; // Subdivision of valence and sea. xuVal = rescale * upv; xuSea = rescale * usea; xdVal = rescale * dnv; xdSea = rescale * dsea; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- // Returns the PDF value for parton of flavour iParton at x, q. double CTEQ6pdf::parton6(int iParton, double x, double q) { // Put zero for large x. Parton table and interpolation variables. if (x > xMaxEps) return 0.; int iP = (iParton > mxVal) ? -iParton : iParton; double ss = pow( x, XPOWER); double tt = log( log(q / lambda) ); // Find location in grid.Skip if same as in latest call. if (x != xLast || q != qLast) { // Binary search in x grid. iGridX = 0; iGridLX = -1; int ju = nX + 1; int jm = 0; while (ju - iGridLX > 1 && jm >= 0) { jm = (ju + iGridLX) / 2; if (x >= xv[jm]) iGridLX = jm; else ju = jm; } // Separate acceptable from unacceptable grid points. if (iGridLX <= -1) return 0.; else if (iGridLX == 0) iGridX = 0; else if (iGridLX <= nX - 2) iGridX = iGridLX - 1; else if (iGridLX == nX - 1) iGridX = iGridLX - 2; else return 0.; // Expressions for interpolation in x Grid. if (iGridLX > 1 && iGridLX < nX - 1) { double svec1 = xvpow[iGridX]; double svec2 = xvpow[iGridX+1]; double svec3 = xvpow[iGridX+2]; double svec4 = xvpow[iGridX+3]; double s12 = svec1 - svec2; double s13 = svec1 - svec3; xConst[8] = svec2 - svec3; double s24 = svec2 - svec4; double s34 = svec3 - svec4; xConst[6] = ss - svec2; xConst[7] = ss - svec3; xConst[0] = s13 / xConst[8]; xConst[1] = s12 / xConst[8]; xConst[2] = s34 / xConst[8]; xConst[3] = s24 / xConst[8]; double s1213 = s12 + s13; double s2434 = s24 + s34; double sdet = s12 * s34 - s1213 * s2434; double tmp = xConst[6] * xConst[7] / sdet; xConst[4] = (s34 * xConst[6] - s2434 * xConst[7]) * tmp / s12; xConst[5] = (s1213 * xConst[6] - s12 * xConst[7]) * tmp / s34; } // Expression for extrapolation in x Grid. dlx = (iGridLX == 0 && doExtraPol) ? log(x / xv[1]) / log(xv[2] / xv[1]) : 1.; // Binary search in Q grid. iGridQ = 0; iGridLQ = -1; ju = nT + 1; jm = 0; while (ju - iGridLQ > 1 && jm >= 0) { jm = (ju + iGridLQ) / 2; if (tt >= tv[jm]) iGridLQ = jm; else ju = jm; } if (iGridLQ == 0) iGridQ = 0; else if (iGridLQ <= nT - 2) iGridQ = iGridLQ - 1; else iGridQ = nT - 3; // Expressions for interpolation in Q Grid. if (iGridLQ > 0 && iGridLQ < nT - 1) { double tvec1 = tv[iGridQ]; double tvec2 = tv[iGridQ+1]; double tvec3 = tv[iGridQ+2]; double tvec4 = tv[iGridQ+3]; double t12 = tvec1 - tvec2; double t13 = tvec1 - tvec3; tConst[8] = tvec2 - tvec3; double t24 = tvec2 - tvec4; double t34 = tvec3 - tvec4; tConst[6] = tt - tvec2; tConst[7] = tt - tvec3; double tmp1 = t12 + t13; double tmp2 = t24 + t34; double tdet = t12 * t34 - tmp1 * tmp2; tConst[0] = t13 / tConst[8]; tConst[1] = t12 / tConst[8]; tConst[2] = t34 / tConst[8]; tConst[3] = t24 / tConst[8]; tConst[4] = (t34 * tConst[6] - tmp2 * tConst[7]) / t12 * tConst[6] * tConst[7] / tdet; tConst[5] = (tmp1 * tConst[6] - t12 * tConst[7]) / t34 * tConst[6] * tConst[7] / tdet; } // Save x and q values so do not have to redo same again. xLast = x; qLast = q; } // Jump to here if x and q are the same as for the last call. int jtmp = ( (iP + nfMx) * (nT + 1) + (iGridQ - 1) ) * (nX + 1) + iGridX + 1; // Interpolate in x space for four different q values. // Also option for extrapolation to small x values. for(int it = 1; it <= 4; ++it) { int j1 = jtmp + it * (nX + 1); if (iGridLX == 0 && doExtraPol) { fVec[it] = upd[j1+1] * pow( upd[j1+2] / upd[j1+1], dlx ); } else if (iGridX == 0) { double fij[5]; fij[1] = 0.; fij[2] = upd[j1+1] * pow2(xv[1]); fij[3] = upd[j1+2] * pow2(xv[2]); fij[4] = upd[j1+3] * pow2(xv[3]); double fX = polint4F( &xvpow[0], &fij[1], ss); fVec[it] = (x > 0.) ? fX / pow2(x) : 0.; } else if (iGridLX==nX-1) { fVec[it] = polint4F( &xvpow[nX-3], &upd[j1], ss); } else { double sf2 = upd[j1+1]; double sf3 = upd[j1+2]; double g1 = sf2 * xConst[0] - sf3 * xConst[1]; double g4 = -sf2 * xConst[2] + sf3 * xConst[3]; fVec[it] = (xConst[4] * (upd[j1] - g1) + xConst[5] * (upd[j1+3] - g4) + sf2 * xConst[7] - sf3 * xConst[6]) / xConst[8]; } } // Interpolate in q space for x-interpolated values found above. double ff; if( iGridLQ <= 0 ) { ff = polint4F( &tv[0], &fVec[1], tt); } else if (iGridLQ >= nT - 1) { ff=polint4F( &tv[nT-3], &fVec[1], tt); } else { double tf2 = fVec[2]; double tf3 = fVec[3]; double g1 = tf2 * tConst[0] - tf3 * tConst[1]; double g4 = -tf2 * tConst[2] + tf3 * tConst[3]; ff = (tConst[4] * (fVec[1] - g1) + tConst[5] * (fVec[4] - g4) + tf2 * tConst[7] - tf3 * tConst[6]) / tConst[8]; } // Done. return ff; } //-------------------------------------------------------------------------- // The POLINT4 routine is based on the POLINT routine from "Numerical Recipes", // but assuming N=4, and ignoring the error estimation. // Suggested by Z. Sullivan. double CTEQ6pdf::polint4F(double xa[],double ya[],double x) { double y, h1, h2, h3, h4, w, den, d1, c1, d2, c2, d3, c3, cd1, cc1, cd2, cc2, dd1, dc1; h1 = xa[0] - x; h2 = xa[1] - x; h3 = xa[2] - x; h4 = xa[3] - x; w = ya[1] - ya[0]; den = w / (h1 - h2); d1 = h2 * den; c1 = h1 * den; w = ya[2] - ya[1]; den = w / (h2 - h3); d2 = h3 * den; c2 = h2 * den; w = ya[3] - ya[2]; den = w / (h3 - h4); d3 = h4 * den; c3 = h3 * den; w = c2 - d1; den = w / (h1 - h3); cd1 = h3 * den; cc1 = h1 * den; w = c3 - d2; den = w / (h2 - h4); cd2 = h4 * den; cc2 = h2 * den; w = cc2 - cd1; den = w / (h1 - h4); dd1 = h4 * den; dc1 = h1 * den; if (h3 + h4 < 0.) y = ya[3] + d3 + cd2 + dd1; else if (h2 + h3 < 0.) y = ya[2] + d2 + cd1 + dc1; else if (h1 + h2 < 0.) y = ya[1] + c2 + cd1 + dc1; else y = ya[0] + c1 + cc1 + dc1; return y; } //========================================================================== // SA Unresolved proton: equivalent photon spectrum from // V.M. Budnev, I.F. Ginzburg, G.V. Meledin and V.G. Serbo, // Phys. Rept. 15 (1974/1975) 181. // Constants: const double ProtonPoint::ALPHAEM = 0.00729735; const double ProtonPoint::Q2MAX = 2.0; const double ProtonPoint::Q20 = 0.71; const double ProtonPoint::A = 7.16; const double ProtonPoint::B = -3.96; const double ProtonPoint::C = 0.028; //-------------------------------------------------------------------------- // Gives a generic Q2-independent equivalent photon spectrum. void ProtonPoint::xfUpdate(int , double x, double /*Q2*/ ) { // Photon spectrum double tmpQ2Min = 0.88 * pow2(x); double phiMax = phiFunc(x, Q2MAX / Q20); double phiMin = phiFunc(x, tmpQ2Min / Q20); double fgm = 0.; if (phiMax < phiMin) { printErr("Error in ProtonPoint::xfUpdate: phiMax - phiMin < 0!", infoPtr); } else { // Corresponds to: x*f(x) fgm = (ALPHAEM / M_PI) * (1 - x) * (phiMax - phiMin); } // Update values xg = 0.; xu = 0.; xd = 0.; xubar = 0.; xdbar = 0.; xs = 0.; xsbar = 0.; xc = 0.; xb = 0.; xgamma = fgm; // Subdivision of valence and sea. xuVal = 0.; xuSea = 0; xdVal = 0.; xdSea = 0; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- // Function related to Q2 integration. double ProtonPoint::phiFunc(double x, double Q) { double tmpV = 1. + Q; double tmpSum1 = 0; double tmpSum2 = 0; for (int k=1; k<4; ++k) { tmpSum1 += 1. / (k * pow(tmpV, k)); tmpSum2 += pow(B, k) / (k * pow(tmpV, k)); } double tmpY = pow2(x) / (1 - x); double funVal = (1 + A * tmpY) * (-1.*log(tmpV / Q) + tmpSum1) + (1 - B) * tmpY / (4 * Q * pow(tmpV, 3)) + C * (1 + tmpY/4.)* (log((tmpV - B)/tmpV) + tmpSum2); return funVal; } //========================================================================== // Gives the GRV 1992 pi+ (leading order) parton distribution function set // in parametrized form. Authors: Glueck, Reya and Vogt. // Ref: M. Glueck, E. Reya and A. Vogt, Z. Phys. C53 (1992) 651. // Allowed variable range: 0.25 GeV^2 < Q^2 < 10^8 GeV^2 and 10^-5 < x < 1. void GRVpiL::xfUpdate(int , double x, double Q2) { // Common expressions. Constrain Q2 for which parametrization is valid. double mu2 = 0.25; double lam2 = 0.232 * 0.232; double s = (Q2 > mu2) ? log( log(Q2/lam2) / log(mu2/lam2) ) : 0.; double s2 = s * s; double x1 = 1. - x; double xL = -log(x); double xS = sqrt(x); // uv, dbarv. double uv = (0.519 + 0.180 * s - 0.011 * s2) * pow(x, 0.499 - 0.027 * s) * (1. + (0.381 - 0.419 * s) * xS) * pow(x1, 0.367 + 0.563 * s); // g. double gl = ( pow(x, 0.482 + 0.341 * sqrt(s)) * ( (0.678 + 0.877 * s - 0.175 * s2) + (0.338 - 1.597 * s) * xS + (-0.233 * s + 0.406 * s2) * x) + pow(s, 0.599) * exp(-(0.618 + 2.070 * s) + sqrt(3.676 * pow(s, 1.263) * xL) ) ) * pow(x1, 0.390 + 1.053 * s); // sea: u, d, s. double ub = pow(s, 0.55) * (1. - 0.748 * xS + (0.313 + 0.935 * s) * x) * pow(x1, 3.359) * exp(-(4.433 + 1.301 * s) + sqrt((9.30 - 0.887 * s) * pow(s, 0.56) * xL) ) / pow(xL, 2.538 - 0.763 * s); // c. double chm = (s < 0.888) ? 0. : pow(s - 0.888, 1.02) * (1. + 1.008 * x) * pow(x1, 1.208 + 0.771 * s) * exp(-(4.40 + 1.493 * s) + sqrt( (2.032 + 1.901 * s) * pow(s, 0.39) * xL) ); // b. double bot = (s < 1.351) ? 0. : pow(s - 1.351, 1.03) * pow(x1, 0.697 + 0.855 * s) * exp(-(4.51 + 1.490 * s) + sqrt( (3.056 + 1.694 * s) * pow(s, 0.39) * xL) ); // Update values. xg = gl; xu = uv + ub; xd = ub; xubar = ub; xdbar = uv + ub; xs = ub; xsbar = ub; xc = chm; xb = bot; // Subdivision of valence and sea. xuVal = uv; xuSea = ub; xdVal = uv; xdSea = ub; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // Pomeron PDF: simple Q2-independent parametrizations N x^a (1 - x)^b. //-------------------------------------------------------------------------- // Calculate normalization factors once and for all. void PomFix::init() { normGluon = GammaReal(PomGluonA + PomGluonB + 2.) / (GammaReal(PomGluonA + 1.) * GammaReal(PomGluonB + 1.)); normQuark = GammaReal(PomQuarkA + PomQuarkB + 2.) / (GammaReal(PomQuarkA + 1.) * GammaReal(PomQuarkB + 1.)); } //-------------------------------------------------------------------------- // Gives a generic Q2-independent Pomeron PDF. void PomFix::xfUpdate(int , double x, double) { // Gluon and quark distributions. double gl = normGluon * pow(x, PomGluonA) * pow( (1. - x), PomGluonB); double qu = normQuark * pow(x, PomQuarkA) * pow( (1. - x), PomQuarkB); // Update values xg = (1. - PomQuarkFrac) * gl; xu = (PomQuarkFrac / (4. + 2. * PomStrangeSupp) ) * qu; xd = xu; xubar = xu; xdbar = xu; xs = PomStrangeSupp * xu; xsbar = xs; xc = 0.; xb = 0.; // Subdivision of valence and sea. xuVal = 0.; xuSea = xu; xdVal = 0.; xdSea = xd; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // Pomeron PDF: the H1 2006 Fit A and Fit B Q2-dependent parametrizations. //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void PomH1FitAB::init( int iFit, string xmlPath, Info* infoPtr) { // Open files from which grids should be read in. if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; string dataFile = "pomH1FitBlo.data"; if (iFit == 1) dataFile = "pomH1FitA.data"; if (iFit == 2) dataFile = "pomH1FitB.data"; ifstream is( (xmlPath + dataFile).c_str() ); if (!is.good()) { printErr("Error in PomH1FitAB::init: did not find data file", infoPtr); isSet = false; return; } // Initialization with a stream. init( is, infoPtr ); is.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void PomH1FitAB::init( istream& is, Info* infoPtr) { // Check that data stream is available. if (!is.good()) { printErr("Error in PomH1FitAB::init: cannot read from stream", infoPtr); isSet = false; return; } // Lower and upper bounds. Bin widths for logarithmic spacing. nx = 100; xlow = 0.001; xupp = 0.99; dx = log(xupp / xlow) / (nx - 1.); nQ2 = 30; Q2low = 1.0; Q2upp = 30000.; dQ2 = log(Q2upp / Q2low) / (nQ2 - 1.); // Read in quark data grid. for (int i = 0; i < nx; ++i) for (int j = 0; j < nQ2; ++j) is >> quarkGrid[i][j]; // Read in gluon data grid. for (int i = 0; i < nx; ++i) for (int j = 0; j < nQ2; ++j) is >> gluonGrid[i][j]; // Check for errors during read-in of file. if (!is) { printErr("Error in PomH1FitAB::init: could not read data stream", infoPtr); isSet = false; return; } // Done. isSet = true; return; } //-------------------------------------------------------------------------- void PomH1FitAB::xfUpdate(int , double x, double Q2) { // Retrict input to validity range. double xt = min( xupp, max( xlow, x) ); double Q2t = min( Q2upp, max( Q2low, Q2) ); // Lower grid point and distance above it. double dlx = log( xt / xlow) / dx; int i = min( nx - 2, int(dlx) ); dlx -= i; double dlQ2 = log( Q2t / Q2low) / dQ2; int j = min( nQ2 - 2, int(dlQ2) ); dlQ2 -= j; // Extrapolate to small x values for quark and gluon PDF. double qu, gl; if (x < xlow && doExtraPol) { dlx = log( x / xlow) / dx; qu = (1. - dlQ2) * quarkGrid[0][j] * pow( quarkGrid[1][j] / quarkGrid[0][j], dlx) + dlQ2 * quarkGrid[0][j + 1] * pow( quarkGrid[1][j + 1] / quarkGrid[0][j + 1], dlx); gl = (1. - dlQ2) * gluonGrid[0][j] * pow( gluonGrid[1][j] / gluonGrid[0][j], dlx) + dlQ2 * gluonGrid[0][j + 1] * pow( gluonGrid[1][j + 1] / gluonGrid[0][j + 1], dlx); } else { // Interpolate to derive quark PDF. qu = (1. - dlx) * (1. - dlQ2) * quarkGrid[i][j] + dlx * (1. - dlQ2) * quarkGrid[i + 1][j] + (1. - dlx) * dlQ2 * quarkGrid[i][j + 1] + dlx * dlQ2 * quarkGrid[i + 1][j + 1]; // Interpolate to derive gluon PDF. gl = (1. - dlx) * (1. - dlQ2) * gluonGrid[i][j] + dlx * (1. - dlQ2) * gluonGrid[i + 1][j] + (1. - dlx) * dlQ2 * gluonGrid[i][j + 1] + dlx * dlQ2 * gluonGrid[i + 1][j + 1]; } // Update values. xg = rescale * gl; xu = rescale * qu; xd = xu; xubar = xu; xdbar = xu; xs = xu; xsbar = xu; xc = 0.; xb = 0.; // Subdivision of valence and sea. xuVal = 0.; xuSea = xu; xdVal = 0.; xdSea = xu; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // Pomeron PDF: the H1 2007 Jets Q2-dependent parametrization. //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void PomH1Jets::init( int , string xmlPath, Info* infoPtr) { // Open files from which grids should be read in. if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; ifstream is( (xmlPath + "pomH1Jets.data").c_str() ); if (!is.good()) { printErr("Error in PomH1Jets::init: did not find data file", infoPtr); isSet = false; return; } // Initialization with a stream. init( is, infoPtr); is.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void PomH1Jets::init( istream& is, Info* infoPtr) { // Check that data stream is available. if (!is.good()) { printErr("Error in PomH1Jets::init: cannot read from stream", infoPtr); isSet = false; return; } // Read in x and Q grids. Do interpolation logarithmically in Q2. for (int i = 0; i < 100; ++i) { is >> setw(13) >> xGrid[i]; } for (int j = 0; j < 88; ++j) { is >> setw(13) >> Q2Grid[j]; Q2Grid[j] = log( Q2Grid[j] ); } // Read in gluon data grid. for (int j = 0; j < 88; ++j) { for (int i = 0; i < 100; ++i) { is >> setw(13) >> gluonGrid[i][j]; } } // Read in singlet data grid. for (int j = 0; j < 88; ++j) { for (int i = 0; i < 100; ++i) { is >> setw(13) >> singletGrid[i][j]; } } // Read in charm data grid. for (int j = 0; j < 88; ++j) { for (int i = 0; i < 100; ++i) { is >> setw(13) >> charmGrid[i][j]; } } // Check for errors during read-in of files. if (!is) { printErr("Error in PomH1Jets::init: could not read data file", infoPtr); isSet = false; return; } // Done. isSet = true; } //-------------------------------------------------------------------------- void PomH1Jets::xfUpdate(int , double x, double Q2) { // Find position in x array. double xLog = log(x); int i = 0; double dx = 0.; if (xLog <= xGrid[0]); else if (xLog >= xGrid[99]) { i = 98; dx = 1.; } else { while (xLog > xGrid[i]) ++i; --i; dx = (xLog - xGrid[i]) / (xGrid[i + 1] - xGrid[i]); } // Find position in y array. double Q2Log = log(Q2); int j = 0; double dQ2 = 0.; if (Q2Log <= Q2Grid[0]); else if (Q2Log >= Q2Grid[87]) { j = 86; dQ2 = 1.; } else { while (Q2Log > Q2Grid[j]) ++j; --j; dQ2 = (Q2Log - Q2Grid[j]) / (Q2Grid[j + 1] - Q2Grid[j]); } // Extrapolate to small x values for gluon, singlet and charm PDF. double gl, sn, ch; if (xLog < xGrid[0] && doExtraPol) { double dlx = (xLog - xGrid[0]) / (xGrid[1] - xGrid[0]) ; gl = (1. - dQ2) * gluonGrid[0][j] * pow( gluonGrid[1][j] / gluonGrid[0][j], dlx) + dQ2 * gluonGrid[0][j + 1] * pow( gluonGrid[1][j + 1] / gluonGrid[0][j + 1], dlx); sn = (1. - dQ2) * singletGrid[0][j] * pow( singletGrid[1][j] / singletGrid[0][j], dlx) + dQ2 * singletGrid[0][j + 1] * pow( singletGrid[1][j + 1] / singletGrid[0][j + 1], dlx); ch = (1. - dQ2) * charmGrid[0][j] * pow( charmGrid[1][j] / charmGrid[0][j], dlx) + dQ2 * charmGrid[0][j + 1] * pow( charmGrid[1][j + 1] / charmGrid[0][j + 1], dlx); } else { // Interpolate to derive gluon PDF. gl = (1. - dx) * (1. - dQ2) * gluonGrid[i][j] + dx * (1. - dQ2) * gluonGrid[i + 1][j] + (1. - dx) * dQ2 * gluonGrid[i][j + 1] + dx * dQ2 * gluonGrid[i + 1][j + 1]; // Interpolate to derive singlet PDF. (Sum of u, d, s, ubar, dbar, sbar.) sn = (1. - dx) * (1. - dQ2) * singletGrid[i][j] + dx * (1. - dQ2) * singletGrid[i + 1][j] + (1. - dx) * dQ2 * singletGrid[i][j + 1] + dx * dQ2 * singletGrid[i + 1][j + 1]; // Interpolate to derive charm PDF. (Charge-square times c and cbar.) ch = (1. - dx) * (1. - dQ2) * charmGrid[i][j] + dx * (1. - dQ2) * charmGrid[i + 1][j] + (1. - dx) * dQ2 * charmGrid[i][j + 1] + dx * dQ2 * charmGrid[i + 1][j + 1]; } // Update values. xg = rescale * gl; xu = rescale * sn / 6.; xd = xu; xubar = xu; xdbar = xu; xs = xu; xsbar = xu; xc = rescale * ch * 9./8.; xb = 0.; // Subdivision of valence and sea. xuVal = 0.; xuSea = xu; xdVal = 0.; xdSea = xd; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // Gives electron (or muon, or tau) parton distribution. // Constants: alphaEM(0), m_e, m_mu, m_tau. const double Lepton::ALPHAEM = 0.00729735; const double Lepton::ME = 0.0005109989; const double Lepton::MMU = 0.10566; const double Lepton::MTAU = 1.77699; void Lepton::xfUpdate(int id, double x, double Q2) { // Squared mass of lepton species: electron, muon, tau. if (!isInit) { double mLep = ME; if (abs(id) == 13) mLep = MMU; if (abs(id) == 15) mLep = MTAU; m2Lep = pow2( mLep ); isInit = true; } // Electron inside electron, see R. Kleiss et al., in Z physics at // LEP 1, CERN 89-08, p. 34 double xLog = log(max(1e-10,x)); double xMinusLog = log( max(1e-10, 1. - x) ); double Q2Log = log( max(3., Q2/m2Lep) ); double beta = (ALPHAEM / M_PI) * (Q2Log - 1.); double delta = 1. + (ALPHAEM / M_PI) * (1.5 * Q2Log + 1.289868) + pow2(ALPHAEM / M_PI) * (-2.164868 * Q2Log*Q2Log + 9.840808 * Q2Log - 10.130464); double fPrel = beta * pow(1. - x, beta - 1.) * sqrtpos( delta ) - 0.5 * beta * (1. + x) + 0.125 * beta*beta * ( (1. + x) * (-4. * xMinusLog + 3. * xLog) - 4. * xLog / (1. - x) - 5. - x); // Zero distribution for very large x and rescale it for intermediate. if (x > 1. - 1e-10) fPrel = 0.; else if (x > 1. - 1e-7) fPrel *= pow(1000.,beta) / (pow(1000.,beta) - 1.); xlepton = x * fPrel; // Photons with restricted virtuality. double sCM = infoPtr->s(); double m2s = 4 * m2Lep / sCM; double Q2minGamma = 2. * m2Lep * pow2(x) / ( 1. - x - m2s + sqrt(1. - m2s) * sqrt( pow2(1. - x) - m2s ) ); xgamma = (0.5 * ALPHAEM / M_PI) * (1. + pow2(1. - x)) * log( Q2maxGamma / Q2minGamma ); // idSav = 9 to indicate that all flavours reset. idSav = 9; } //========================================================================== // The NNPDF class. // Code for handling NNPDF2.3 QCD+QED LO // Code provided by Juan Rojo and Stefano Carrazza. //-------------------------------------------------------------------------- // Freeze PDFs below XMINGRID const double NNPDF::fXMINGRID = 1e-9; //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void NNPDF::init(int iFitIn, string xmlPath, Info* infoPtr) { // Choice of fit among possibilities. iFit = iFitIn; // Select which data file to read for current fit. if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; string fileName = " "; // NNPDF2.3 LO QCD+QED, for two values of alphas if (iFit == 1) fileName = "NNPDF23_lo_as_0130_qed_mem0.grid"; if (iFit == 2) fileName = "NNPDF23_lo_as_0119_qed_mem0.grid"; // NNPDF2.3 NLO QCD+QED if (iFit == 3) fileName = "NNPDF23_nlo_as_0119_qed_mc_mem0.grid"; // NNPDF2.4 NLO QCD+QED if (iFit == 4) fileName = "NNPDF23_nnlo_as_0119_qed_mc_mem0.grid"; // Open data file. fstream f; f.open( (xmlPath + fileName).c_str(),ios::in); if (f.fail()) { printErr("Error in NNPDF::init: did not find data file ", infoPtr); isSet = false; return; } // Initialization with a stream. init(f, infoPtr); f.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void NNPDF::init(istream& f, Info* infoPtr) { // Check that data stream is available. if (!f.good()) { printErr("Error in NNPDF::init: cannot read from stream", infoPtr); isSet = false; return; } // Reading grid: removing header. string tmp; for (;;) { getline(f,tmp); if (tmp.find("NNPDF20intqed") != string::npos) { getline(f,tmp); break; } } // Get nx and x grid. f >> fNX; fXGrid = new double[fNX]; for (int ix = 0; ix < fNX; ix++) f >> fXGrid[ix]; fLogXGrid = new double[fNX]; for (int ix = 0; ix < fNX; ix++) fLogXGrid[ix] = log(fXGrid[ix]); // Get nQ2 and Q2 grid (ignorming first value). f >> fNQ2; f >> tmp; fQ2Grid = new double[fNQ2]; for (int iq = 0; iq < fNQ2; iq++) f >> fQ2Grid[iq]; fLogQ2Grid = new double[fNQ2]; for (int iq = 0; iq < fNQ2; iq++) fLogQ2Grid[iq] = log(fQ2Grid[iq]); // Prepare grid array. fPDFGrid = new double**[fNFL]; for (int i = 0; i < fNFL; i++) { fPDFGrid[i] = new double*[fNX]; for (int j = 0; j < fNX; j++) { fPDFGrid[i][j] = new double[fNQ2]; for (int z = 0; z < fNQ2; z++) fPDFGrid[i][j][z] = 0.0; } } // Check values of number of grid entries. if (fNX<= 0 || fNX>100 || fNQ2<=0 || fNQ2>50) { cout << "Error in NNPDF::init, Invalid grid values" << endl << "fNX = " << fNX << endl << "fNQ2 = " << fNQ2 << endl << "fNFL = " <> tmp; for (int ix = 0; ix < fNX; ix++) for (int iq = 0; iq < fNQ2; iq++) for (int fl = 0; fl < fNFL; fl++) f >> fPDFGrid[fl][ix][iq]; // Other vectors. fRes = new double[fNFL]; } //-------------------------------------------------------------------------- void NNPDF::xfUpdate(int , double x, double Q2) { // Update using NNPDF routine, within allowed (x, q) range. xfxevolve(x,Q2); // Then transfer to Pythia8 notation. xg = fRes[6]; xu = fRes[8]; xd = fRes[7]; xubar = fRes[4]; xdbar = fRes[5]; xs = fRes[9]; xsbar = fRes[3]; xc = fRes[10]; xb = fRes[11]; xgamma = fRes[13]; // Subdivision of valence and sea. xuVal = xu - xubar; xuSea = xubar; xdVal = xd - xdbar; xdSea = xdbar; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- void NNPDF::xfxevolve(double x, double Q2) { // Freeze outside x-Q2 grid. if (x < fXMINGRID || x > fXGrid[fNX-1]) { if (x < fXMINGRID) x = fXMINGRID; if (x > fXGrid[fNX-1]) x = fXGrid[fNX-1]; } if (Q2 < fQ2Grid[0] || Q2 > fQ2Grid[fNQ2-1]) { if (Q2 < fQ2Grid[0]) Q2 = fQ2Grid[0]; if (Q2 > fQ2Grid[fNQ2-1]) Q2 = fQ2Grid[fNQ2-1]; } // Find nearest points in the x-Q2 grid. int minx = 0; int maxx = fNX; while (maxx-minx > 1) { int midx = (minx+maxx)/2; if (x < fXGrid[midx]) maxx = midx; else minx = midx; } int ix = minx; int minq = 0; int maxq = fNQ2; while (maxq-minq > 1) { int midq = (minq+maxq)/2; if (Q2 < fQ2Grid[midq]) maxq = midq; else minq = midq; } int iq2 = minq; // Assign grid for interpolation. M,N -> order of polyN interpolation. int ix1a[fM], ix2a[fN]; double x1a[fM], x2a[fN]; double ya[fM][fN]; for (int i = 0; i < fM; i++) { if (ix+1 >= fM/2 && ix+1 <= (fNX-fM/2)) ix1a[i] = ix+1 - fM/2 + i; if (ix+1 < fM/2) ix1a[i] = i; if (ix+1 > (fNX-fM/2)) ix1a[i] = (fNX-fM) + i; // Check grids. if (ix1a[i] < 0 || ix1a[i] >= fNX) { cout << "Error in grids! i, ixia[i] = " << i << "\t" << ix1a[i] << endl; return; } } for (int j = 0; j < fN; j++) { if (iq2+1 >= fN/2 && iq2+1 <= (fNQ2-fN/2)) ix2a[j] = iq2+1 - fN/2 + j; if (iq2+1 < fN/2) ix2a[j] = j; if (iq2+1 > (fNQ2-fN/2)) ix2a[j] = (fNQ2-fN) + j; // Check grids. if (ix2a[j] < 0 || ix2a[j] >= fNQ2) { cout << "Error in grids! j, ix2a[j] = " << j << "\t" << ix2a[j] << endl; return; } } const double xch = 1e-1; double x1; if (x < xch) x1 = log(x); else x1 = x; double x2 = log(Q2); for (int ipdf = 0; ipdf < fNFL; ipdf++) { fRes[ipdf] = 0.0; for (int i = 0; i < fM; i++) { if (x < xch) x1a[i] = fLogXGrid[ix1a[i]]; else x1a[i] = fXGrid[ix1a[i]]; for (int j = 0; j < fN; j++) { x2a[j] = fLogQ2Grid[ix2a[j]]; ya[i][j] = fPDFGrid[ipdf][ix1a[i]][ix2a[j]]; } } // 2D polynomial interpolation. double y = 0, dy = 0; polin2(x1a,x2a,ya,x1,x2,y,dy); fRes[ipdf] = y; } } //-------------------------------------------------------------------------- // 1D polynomial interpolation. void NNPDF::polint(double xa[], double yal[], int n, double x, double& y, double& dy) { int ns = 0; double dif = abs(x-xa[0]); double c[fM > fN ? fM : fN]; double d[fM > fN ? fM : fN]; for (int i = 0; i < n; i++) { double dift = abs(x-xa[i]); if (dift < dif) { ns = i; dif = dift; } c[i] = yal[i]; d[i] = yal[i]; } y = yal[ns]; ns--; for (int m = 1; m < n; m++) { for (int i = 0; i < n-m; i++) { double ho = xa[i]-x; double hp = xa[i+m]-x; double w = c[i+1]-d[i]; double den = ho-hp; if (den == 0) { cout << "NNPDF::polint, failure" << endl; return; } den = w/den; d[i] = hp*den; c[i] = ho*den; } if (2*(ns+1) < n-m) dy = c[ns+1]; else { dy = d[ns]; ns--; } y+=dy; } } //-------------------------------------------------------------------------- // 2D polynomial interpolation. void NNPDF::polin2(double x1al[], double x2al[], double yal[][fN], double x1, double x2, double& y, double& dy) { double yntmp[fN]; double ymtmp[fM]; for (int j = 0; j < fM; j++) { for (int k = 0; k < fN; k++) yntmp[k] = yal[j][k]; polint(x2al,yntmp,fN,x2,ymtmp[j],dy); } polint(x1al,ymtmp,fM,x1,y,dy); } //========================================================================== // LHAPDF plugin interface. //-------------------------------------------------------------------------- // Constructor. LHAPDF::LHAPDF(int idIn, string pSet, Info* infoPtrIn) : pdfPtr(0), infoPtr(infoPtrIn) { isSet = false; if (!infoPtr) return; // Determine the plugin library name. if (pSet.size() < 8) { printErr("Error in LHAPDF::LHAPDF: invalid pSet " + pSet, infoPtr); return; } libName = pSet.substr(0, 7); if (libName != "LHAPDF5" && libName != "LHAPDF6") { printErr("Error in LHAPDF::LHAPDF: invalid pSet " + pSet, infoPtr); return; } libName = "libpythia8lhapdf" + libName.substr(6) + ".so"; // Determine the PDF set and member. string set = pSet.substr(8); int mem = 0; size_t pos = set.find_last_of("/"); if (pos != string::npos) { istringstream memStream(set.substr(pos + 1)); memStream >> mem; } set = set.substr(0, pos); // Load the PDF. NewLHAPDF* newLHAPDF = (NewLHAPDF*)symbol("newLHAPDF"); if (!newLHAPDF) return; pdfPtr = newLHAPDF(idIn, set, mem, infoPtr); isSet = true; } //-------------------------------------------------------------------------- // Destructor. LHAPDF::~LHAPDF() { if (!infoPtr) return; if (!isSet) return; // Delete the PDF. DeleteLHAPDF* deleteLHAPDF = (DeleteLHAPDF*)symbol("deleteLHAPDF"); if (deleteLHAPDF) deleteLHAPDF(pdfPtr); // Close the plugin library if not needed by other instances. map >::iterator plugin = infoPtr->plugins.find(libName); if (plugin == infoPtr->plugins.end()) return; --plugin->second.second; if (plugin->second.first && plugin->second.second == 0) { dlclose(plugin->second.first); dlerror(); infoPtr->plugins.erase(plugin); } } //-------------------------------------------------------------------------- // Access a plugin library symbol. LHAPDF::Symbol LHAPDF::symbol(string symName) { void *lib(0); Symbol sym(0); const char* error(0); if (!infoPtr) return sym; // Load the library if not loaded. map >::iterator plugin = infoPtr->plugins.find(libName); if (plugin == infoPtr->plugins.end()) { lib = dlopen(libName.c_str(), RTLD_LAZY); error = dlerror(); } if (error) { printErr("Error in LHAPDF::symbol: " + string(error), infoPtr); return sym; } if (plugin == infoPtr->plugins.end()) infoPtr->plugins[libName] = pair(lib, 1); else { lib = plugin->second.first; ++plugin->second.second; } dlerror(); // Load the symbol. sym = (Symbol)dlsym(lib, symName.c_str()); error = dlerror(); if (error) printErr("Error in LHAPDF::symbol: " + string(error), infoPtr); dlerror(); return sym; } //========================================================================== // Gives the CJKL leading order parton distribution function set // in parametrized form for the real photons. Authors: F.Cornet, P.Jankowski, // M.Krawczyk and A.Lorca, Phys. Rev. D68: 014010, 2003. // Valid for 10^(-5) < x < 1 and 1 < Q^2 < 2*10^5 GeV^2. // Below Q^2 = 1 a logarithmic approximation in Q^2 is used. // Constants related to the fit. const double CJKL::ALPHAEM = 0.007297353080; const double CJKL::Q02 = 0.25; const double CJKL::Q2MIN = 0.05; const double CJKL::Q2REF = 1.0; const double CJKL::LAMBDA = 0.221; const double CJKL::MC = 1.3; const double CJKL::MB = 4.3; //-------------------------------------------------------------------------- void CJKL::xfUpdate(int , double x, double Q2) { // Parameters: double lambda2 = pow2(LAMBDA); // When below reference scale calculate first with the reference scale and // later scale with log(Q^2). double Q2Save = Q2; bool belowRef = (Q2 < Q2REF); if ( belowRef) Q2 = Q2REF; // Evolution variable. double s = log( log(Q2/lambda2)/log(Q02/lambda2) ); double plLog = 9.0/(4.0*M_PI)*log(Q2/lambda2); // Point-like contributions. double plGluon = pointlikeG(x,s); double plUp = pointlikeU(x,s); double plDown = pointlikeD(x,s); double plStrange = plDown; // Hadron-like contributions. double hlGluon = hadronlikeG(x,s); double hlVal = hadronlikeVal(x,s); double hlSea = hadronlikeSea(x,s); // Heavy quarks. Undo the ACOT_X rescaling for DIS kinematics. double xMaxC = 1 - 6.76/(6.76 + Q2); double xMaxB = 1 - 73.96/(73.96 + Q2); double plCharm = pointlikeC(x*xMaxC,s,Q2)*xMaxC; double plBottom = pointlikeB(x*xMaxB,s,Q2)*xMaxB; double hlCharm = hadronlikeC(x*xMaxC,s,Q2)*xMaxC; double hlBottom = hadronlikeB(x*xMaxB,s,Q2)*xMaxB; // Sum different contributions together. xg = ALPHAEM*( plLog*plGluon + hlGluon ); xu = ALPHAEM*( plLog*plUp + 0.5*hlVal + hlSea ); xd = ALPHAEM*( plLog*plDown + 0.5*hlVal + hlSea ); xubar = xu; xdbar = xd; xs = ALPHAEM*( plLog*plStrange + hlSea ); xsbar = xs; xc = ALPHAEM*( plLog*plCharm + hlCharm ); xb = ALPHAEM*( plLog*plBottom + hlBottom ); xgamma = 0; // Subdivision of valence and sea. xuVal = ALPHAEM*( plLog*plUp + 0.5*hlVal ); xuSea = ALPHAEM*( hlSea ); xdVal = ALPHAEM*( plLog*plDown + 0.5*hlVal ); xdSea = ALPHAEM*( hlSea ); xsVal = ALPHAEM*( plLog*plStrange ); xsSea = ALPHAEM*( hlSea ); xcVal = ALPHAEM*( plLog*plCharm ); xcSea = ALPHAEM*( hlCharm ); xbVal = ALPHAEM*( plLog*plBottom ); xbSea = ALPHAEM*( hlBottom ); // When below valid Q^2 values approximate scale evolution with log(Q^2). // Approximation derived by integrating xf over x and calculating the // derivative at Q2REF. if ( belowRef) { double logApprox = max( log(Q2Save/Q2MIN) / log(Q2REF/Q2MIN ), 0.); // Scale the PDFs according to log(Q^2) approx. xg *= logApprox; xd *= logApprox; xu *= logApprox; xubar *= logApprox; xdbar *= logApprox; xs *= logApprox; xsbar *= logApprox; xc *= logApprox; xb *= logApprox; xuVal *= logApprox; xuSea *= logApprox; xdVal *= logApprox; xdSea *= logApprox; xsVal *= logApprox; xsSea *= logApprox; xcVal *= logApprox; xcSea *= logApprox; xbVal *= logApprox; xbSea *= logApprox; } // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- // Returns the x-dependence decoupled from the logarithmic scale // dependence to approximate the PDFs from below for ISR. // Currently flat in x (no second argument), could be improved. double CJKL::gammaPDFxDependence(int id, double) { if (abs(id) == 1) return 0.013 * ALPHAEM; else if (abs(id) == 2) return 0.026 * ALPHAEM; else if (abs(id) == 3) return 0.010 * ALPHAEM; else if (abs(id) == 4) return 0.020 * ALPHAEM; else if (abs(id) == 5) return 0.010 * ALPHAEM; else return 0; } //-------------------------------------------------------------------------- // Returns the reference scale for the logarithmic scale dependence to // approximate the PDFs in ISR. Mass squared for heavy quarks and 0.2 // for others. double CJKL::gammaPDFRefScale(int id) { if (abs(id) == 4) return pow2(MC); else if (abs(id) == 5) return pow2(MB); else return 0.20; } //-------------------------------------------------------------------------- // Set valence content of the photon beam using parametrized Q2-dependence. int CJKL::sampleGammaValFlavor(double Q2) { // Freeze the scale below the initial scale. if(Q2 < Q02) Q2 = Q02; // Calculate the x-integrated valence part of hadron-like contribution. double lambda2 = pow2(LAMBDA); double s = log( log(Q2/lambda2)/log(Q02/lambda2) ); double a = 1.0898 + 0.38087 * s; double b = 0.42654 - 1.2128 * s; double c = -1.6576 + 1.7075 * s; double d = 0.96155 + 1.8441 * s; double aa = 0.78391 - 0.06872 * s; double a1 = tgamma(1+aa)*tgamma(1+d)/tgamma(2+aa+d); double b1 = tgamma(1.5+aa)*tgamma(1+d)/tgamma(2.5+aa+d); double c1 = tgamma(2+aa)*tgamma(1+d)/tgamma(3+aa+d); double xfValHad = ALPHAEM*a*(a1 + b*b1 + c*c1); // Set the reference scales and charges. double mq2[5] = { Q02, Q02, Q02, pow2(MC), pow2(MB) }; double eq2[5] = { 1.0/9.0, 4.0/9.0, 1.0/9.0, 4.0/9.0, 1.0/9.0 }; // For u- and d-quarks valence contribution from hadron-like part. double qEvo[5] = { xfValHad/2, xfValHad/2, 0, 0, 0 }; double qEvoTot = 0; // Normalization of the point-like part. double plNorm = 0.000936; // Logarithmic Q^2 evolution of gamma -> qqbar splitting for each flavor. for(int i = 0;i < 5;++i) { qEvo[i] += plNorm*eq2[i]*max(0.0,log(Q2/mq2[i])); qEvoTot += qEvo[i]; } // Sample the valence flavor. double qEvoRand = qEvoTot*rndmPtr->flat(); for(int i = 0; i < 5; ++i) { qEvoRand -= qEvo[i]; if(qEvoRand <= 0.0) { idVal1 = i+1; idVal2 = -idVal1; break; } } return idVal1; } //-------------------------------------------------------------------------- // Sum of integrated PDFs \int dx x f(x,Q^2) at given scale Q^2. // Integrals parametrized as a0 + a1*log(Q^2/Q0^2). double CJKL::xfIntegratedTotal(double Q2){ // Freeze the scale below the initial scale. if(Q2 < Q02) Q2 = Q02; // Set the reference scales and relative contributions. // Gluons and u/d quarks has some non-perturbative contribution, others // only radiative contributions. Derived by fitting by eye to // a0 + a1*log(Q^2/Q0^2). double fq0[6] = { 0.0018, 0.0006, 0.0006, 0., 0., 0. }; double mq2[6] = { Q02, Q02, Q02, Q02, pow2(MC), pow2(MB) }; double eq2[6] = { 3.0/9.0, 1.0/9.0, 4.0/9.0, 1.0/9.0, 4.0/9.0, 1.0/9.0 }; double a1 = 0.000981; // Logarithmic Q^2 evolution for each flavor. quarks two times, gluon // coefficents scaled appropriately. double xIntegrated = 0; for(int i = 0;i < 6;++i) { xIntegrated += fq0[i] + 2*a1*eq2[i]*max(0.0,log(Q2/mq2[i])); } return xIntegrated; } //-------------------------------------------------------------------------- // Returns the point-like part of the gluon. double CJKL::pointlikeG(double x, double s) { // Exponents. double alpha1 = -0.43865; double alpha2 = 2.7174; double beta = 0.36752; // Scale dependent parameters. double a = 0.086893 - 0.34992 * s; double b = 0.010556 + 0.049525 * s; double c = -0.099005 + 0.34830 * s; double d = 1.0648 + 0.143421 * s; double e = 3.6717 + 2.5071 * s; double f = 2.1944 + 1.9358 * s; double aa = 0.23679 - 0.11849 * s; double bb = -0.19994 + 0.028124 * s; // Point-like gluon parametrization. return max(0.0,( pow(s,alpha1)*pow(x,aa)*( a + b*sqrt(x) + c*pow(x,bb) ) + pow(s,alpha2)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) * pow(1-x,d) ); } //-------------------------------------------------------------------------- // Returns the point-like part of the u-quark. double CJKL::pointlikeU(double x, double s) { // Exponents. double alpha1 = -1.0711; double alpha2 = 3.1320; double beta = 0.69243; // Scale dependent parameters. double a = -0.058266 + 0.20506 * s; double b = 0.0097377 - 0.10617 * s; double c = -0.0068345 + 0.15211 * s; double d = 0.22297 + 0.013567 * s; double e = 6.4289 + 2.2802 * s; double f = 1.7302 + 0.76997 * s; double aa = 0.87940 - 0.110241 * s; double bb = 2.6878 - 0.040252 * s; // Point-like u-quark parametrization. return max(0.0, ( pow(s,alpha1)*pow(x,aa)*( a + b*sqrt(x) + c*pow(x,bb) ) + pow(s,alpha2)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) * pow(1-x,d) ); } //-------------------------------------------------------------------------- // Returns the point-like part of the d-quark. double CJKL::pointlikeD(double x, double s) { // Exponents. double alpha1 = -1.1357; double alpha2 = 3.1187; double beta = 0.66290; // Scale dependent parameters. double a = 0.098814 - 0.067300 * s; double b = -0.092892 + 0.049949 * s; double c = -0.0066140 + 0.020427 * s; double d = -0.31385 - 0.0037558 * s; double e = 6.4671 + 2.2834 * s; double f = 1.6996 + 0.84262 * s; double aa = 11.777 + 0.034760 * s; double bb = -11.124 - 0.20135 * s; // Regulate the x->1 divergence of (1-x)^d in the parameterization. if(x > 0.995) x = 0.995; // Point-like d-quark parametrization. return max( 0.0, ( pow(s,alpha1)*pow(x,aa)*( a + b*sqrt(x) + c*pow(x,bb) ) + pow(s,alpha2)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) * pow(1-x,d) ); } //-------------------------------------------------------------------------- // Returns the point-like part of the c-quark. double CJKL::pointlikeC(double x, double s, double Q2) { // Scaled variable for c quarks with m = 1.3 GeV. double y = x + 1 - Q2/(Q2 + 6.76); // Kinematic boundary. if (y >= 1.0) return 0; // Declaration of parameters. double alpha1, alpha2, beta, a, b, c, d, e, f, aa, bb; // Parameters for Q^2 <= 10 GeV^2. if (Q2 <= 10) { // Exponents. alpha1 = 2.9808; alpha2 = 28.682; beta = 2.4863; // Scale dependent parameters. a = -0.18826 + 0.13565 * s; b = 0.18508 - 0.11764 * s; c = -0.0014153 - 0.011510 * s; d = -0.48961 + 0.18810 * s; e = 0.20911 - 2.8544 * s + 14.256 *s*s; f = 2.7644 + 0.93717 * s; aa = -7.6307 + 5.6807 * s; bb = 394.58 - 541.82 * s + 200.82 *s*s; // Parameters for Q^2 > 10 GeV^2. } else { // Exponents. alpha1 = -1.8095; alpha2 = 7.9399; beta = 0.041563; // Scale dependent parameters. a = -0.54831 + 0.33412 * s; b = 0.19484 + 0.041562 * s; c = -0.39046 + 0.37194 * s; d = 0.12717 + 0.059280 * s; e = 8.7191 + 3.0194 * s; f = 4.2616 + 0.73993 * s; aa = -0.30307 + 0.29430 * s; bb = 7.2383 - 1.5995 * s; } // Point-like c-quark parametrization. return max( 0.0, ( pow(s,alpha1)*pow(y,aa)*( a + b*sqrt(y) + c*pow(y,bb) ) + pow(s,alpha2)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) * pow(1-y,d) ); } //-------------------------------------------------------------------------- // Returns the point-like part of the b-quark. double CJKL::pointlikeB(double x, double s, double Q2) { //Scaled variable for b quarks with m = 4.3 GeV. double y = x + 1 - Q2/(Q2 + 73.96); // Kinematic boundary. if (y >= 1.0) return 0; // Declaration of parameters. double alpha1, alpha2, beta, a, b, c, d, e, f, aa, bb; // Parameters for Q^2 <= 100 GeV^2. if (Q2 <= 100) { // Exponents. alpha1 = 2.2849; alpha2 = 6.0408; beta = -0.11577; // Scale dependent parameters. a = -0.26971 + 0.17942 * s; b = 0.27033 - 0.18358 * s + 0.0061059 *s*s; c = 0.0022862 - 0.0016837 * s; d = 0.30807 - 0.10490 * s; e = 14.812 - 1.2977 * s; f = 1.7148 + 2.3532 * s + 0.053734 *sqrt(s); aa = 3.8140 - 1.0514 * s; bb = 2.2292 + 20.194 * s; // Parameters for Q^2 > 100 GeV^2. } else { // Exponents. alpha1 = -5.0607; alpha2 = 16.590; beta = 0.87190; // Scale dependent parameters. a = -0.72790 + 0.36549 * s; b = -0.62903 + 0.56817 * s; c = -2.4467 + 1.6783 * s; d = 0.56575 - 0.19120 * s; e = 1.4687 + 9.6071 * s; f = 1.1706 + 0.99674 * s; aa = -0.084651 - 0.083206 * s; bb = 9.6036 - 3.4864 * s; } // Point-like b-quark parametrization. return max( 0.0, ( pow(s,alpha1)*pow(y,aa)*( a + b*sqrt(y) + c*pow(y,bb) ) + pow(s,alpha2)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) * pow(1-y,d) ); } //-------------------------------------------------------------------------- // Returns the hadron-like part of the gluon pdf. double CJKL::hadronlikeG(double x, double s) { // Exponents. double alpha = 0.59945; double beta = 1.1285; // Scale dependent parameters. double a = -0.19898 + 0.57414 * s; double b = 1.9942 - 1.8306 * s; double c = -1.9848 + 1.4136 * s; double d = 0.21294 + 2.7450 * s; double e = 1.2287 + 2.4447 * s; double f = 4.9230 + 0.18526 * s; double aa = -0.34948 + 0.47058 * s; // Hadron-like gluon parametrization. return max( 0.0, pow(1-x,d)*( pow(x,aa)*( a + b*sqrt(x) + c*x ) + pow(s,alpha)*exp( -e + sqrt( f*pow(s,beta)*log(1.0/x) ) ) ) ); } //-------------------------------------------------------------------------- // Returns the hadron-like part of the valence quarks. double CJKL::hadronlikeVal(double x, double s) { // Scale dependent parameters. double a = 1.0898 + 0.38087 * s; double b = 0.42654 - 1.2128 * s; double c = -1.6576 + 1.7075 * s; double d = 0.96155 + 1.8441 * s; double aa = 0.78391 - 0.068720 * s; // Hadron-like valence quarks parametrization. return max( 0.0, pow(1-x,d)*pow(x,aa)*a*( 1 + b*sqrt(x) + c*x ) ); } //-------------------------------------------------------------------------- // Returns the hadron-like part of the sea quarks. double CJKL::hadronlikeSea(double x, double s) { // Exponents. double alpha = 0.71660; double beta = 1.0497; // Scale dependent parameters. double a = 0.60478 + 0.036160 * s; double b = 4.2106 - 0.85835 * s; double d = 4.1494 + 0.34866 * s; double e = 4.5179 + 1.9219 * s; double f = 5.2812 - 0.15200 * s; double aa = 0.72289 - 0.21562 * s; // Pre-calculate the logarithm. double logx = log(1.0/x); // Hadron-like sea quark parametrization. return max( 0.0, pow(1-x,d)*pow(s,alpha)*( 1 + a*sqrt(x) + b*x ) * exp( -e + sqrt( f*pow(s,beta)*logx ) )*pow(logx,-aa) ); } //-------------------------------------------------------------------------- // Returns the hadron-like part of the c-quarks. double CJKL::hadronlikeC(double x, double s, double Q2) { //Scaled variable for c quarks with m = 1.3 GeV. double y = x + 1 - Q2/(Q2 + 6.76); // Kinematic boundary. if (y >= 1.0) return 0; // Pre-calculate the logarithm. double logx = log(1.0/x); // Declaration of parameters. double alpha, beta, a, b, d, e, f, aa; // Parameters for Q^2 <= 10 GeV^2. if (Q2 <= 10) { // Exponents. alpha = 5.6729; beta = 1.4575; // Scale dependent parameters. a = -2586.4 + 1910.1 * s; b = 2695.0 - 1688.2 * s; d = 1.5146 + 3.1028 * s; e = -3.9185 + 11.738 * s; f = 3.6126 - 1.0291 * s; aa = 1.6248 - 0.70433 * s; // Parameters for Q^2 > 10 GeV^2. } else { // Exponents. alpha = -1.6470; beta = 0.72738; // Scale dependent parameters. a = -2.0561 + 0.75576 * s; b = 2.1266 + 0.66383 * s; d = 3.0301 - 1.7499 * s + 1.6466 *s*s; e = 4.1282 + 1.6929 * s - 0.26292 *s*s; f = 0.89599 + 1.2761 * s - 0.15061 *s*s; aa = -0.78809 + 0.90278 * s; } // Hadron-like c-quark parametrization. Note typo in the CJKL paper. return max( 0.0, pow(1-y,d)*pow(s,alpha)*( 1 + a*sqrt(y) + b*y ) * exp( -e + f*sqrt( pow(s,beta)*logx ) )*pow(logx,-aa) ); } //-------------------------------------------------------------------------- // Returns the hadron-like part of the b-quarks. double CJKL::hadronlikeB(double x, double s, double Q2) { // Scaled variable for b quarks with m = 4.3 GeV. double y = x + 1 - Q2/(Q2 + 73.96); // Kinematic boundary. if (y >= 1.0) return 0; // Pre-calculate the logarithm. double logx = log(1.0/x); // Declaration of parameters. double alpha, beta, a, b, d, e, f, aa; // Parameters for Q^2 <= 100 GeV^2. if (Q2 <= 100) { // Exponents. alpha = -10.210; beta = -2.2296; // Scale dependent parameters. a = -99.613 + 171.25 * s; b = 492.61 - 420.45 * s; d = 3.3917 + 0.084256 * s; e = 5.6829 - 0.23571 * s; f = -2.0137 + 4.6955 * s; aa = 0.82278 + 0.081818 * s; // Parameters for Q^2 > 100 GeV^2. } else { // Exponents. alpha = 2.4198; beta = 0.40703; // Scale dependent parameters. a = -2.1109 + 1.2711 * s; b = 9.0196 - 3.6082 * s; d = 3.6455 - 4.1353 * s + 2.3615 *s*s; e = 4.6196 + 2.4212 * s; f = 0.66454 + 1.1109 * s; aa = -0.98933 + 0.42366 * s + 0.15817 *s*s; } // Hadron-like b-quark parametrization. Note typo in the CJKL paper. return max( 0.0, pow(1-y,d)*pow(s,alpha)*( 1 + a*sqrt(y) + b*y ) * exp( -e + f*sqrt( pow(s,beta)*logx ) )*pow(logx,-aa) ); } //========================================================================== // The LHAGrid1 class. // Codes to read files i the LHAPDF6 lhagrid1 format, // assuming that the same x grid is used for all Q subgrids. // Results are not identical with LHAPDF6, owing to different interpolation. //-------------------------------------------------------------------------- // Initialize PDF: select data file and open stream. void LHAGrid1::init(string pdfWord, string xmlPath, Info* infoPtr) { // Identify whether file number or name. if (pdfWord.length() > 9 && toLower(pdfWord).substr(0,9) == "lhagrid1:") pdfWord = pdfWord.substr(9, pdfWord.length() - 9); istringstream pdfStream(pdfWord); int pdfSet = 0; pdfStream >> pdfSet; // Input is file name. string dataFile = ""; if ( xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; if (pdfWord[0] == '/') dataFile = pdfWord; else if (pdfSet == 0) dataFile = xmlPath + pdfWord; // Input is fit number. Current selection for NNPDF3.1 only. else if (pdfSet == 17) dataFile = xmlPath+"NNPDF31_lo_as_0130_0000.dat"; else if (pdfSet == 18) dataFile = xmlPath+"NNPDF31_lo_as_0118_0000.dat"; else if (pdfSet == 19) dataFile = xmlPath+"NNPDF31_nlo_as_0118_0000.dat"; else if (pdfSet == 20) dataFile = xmlPath+"NNPDF31_nnlo_as_0118_0000.dat"; // Open files from which grids should be read in. ifstream is( dataFile.c_str() ); if (!is.good()) { printErr("Error in LHAGrid1::init: did not find data file", infoPtr); isSet = false; return; } // Initialization with a stream. init( is, infoPtr); is.close(); } //-------------------------------------------------------------------------- // Initialize PDF: read in data grid from stream and set up interpolation. void LHAGrid1::init(istream& is, Info* infoPtr) { // Check that data stream is available. if (!is.good()) { printErr("Error in LHAGrid1::init: cannot read from stream", infoPtr); isSet = false; return; } // Some local variables. string line; vector idlines, pdflines; int nqNow, idNow, idNowMap; double xNow, qNow, pdfNow; // Skip lines of header, until ---. Probe for next subgrid in Q space. nqSub = 0; do getline( is, line); while (line.find("---") == string::npos); if (!is.good()) { printErr("Error in LHAGrid1::init: could not read data file", infoPtr); isSet = false; return; } while (getline( is, line)) { ++nqSub; // Read in x grid; save for first, check it matches for later ones. istringstream isx(line); if (nqSub == 1) { while (isx >> xNow) { xGrid.push_back( xNow); lnxGrid.push_back( log(xNow)); } nx = xGrid.size(); xMin = xGrid.front(); xMax = xGrid.back(); } else { int ixc = -1; while (isx >> xNow) if ( abs(log(xNow) - lnxGrid[++ixc]) > 1e-5) { printErr("Error in LHAGrid1::init: mismatched subgrid x spacing", infoPtr); isSet = false; return; } } // Read in Q grid; append as needed. Check that subgrids match. getline( is, line); istringstream isq(line); nqNow = 0; while (isq >> qNow) { ++nqNow; qGrid.push_back( qNow); lnqGrid.push_back( log(qNow)); } if (nqSub > 1) { if (abs(qGrid[nq] / qGrid[nq-1] - 1.) > 1e-5) { printErr("Error in LHAGrid1::init: mismatched subgrid Q borders", infoPtr); isSet = false; return; } qGrid[nq-1] = 0.5 * (qGrid[nq-1] + qGrid[nq]); qGrid[nq] = qGrid[nq-1]; } nq = qGrid.size(); qMin = qGrid.front(); qMax = qGrid.back(); nqSum.push_back(nq); qDiv.push_back(qMax); // Read in and store flavour mapping and pdf data. Separator line. getline( is, line); idlines.push_back( line); for (int ixq = 0; ixq < nx * nqNow; ++ixq) { getline( is, line); pdflines.push_back( line); } getline( is, line); } // Create array big enough to hold (flavour, x, Q) grid. pdfGrid = new double**[12]; for (int iid = 0; iid < 12; ++iid) { pdfGrid[iid] = new double*[nx]; for (int ix = 0; ix < nx; ++ix) { pdfGrid[iid][ix] = new double[nq]; for (int iq = 0; iq < nq; ++iq) pdfGrid[iid][ix][iq] = 0.; } } // Second pass through the Q subranges. int iln = -1; for (int iqSub = 0; iqSub < nqSub; ++iqSub) { vector idGridMap; // Study flavour grid and decide flavour mapping. istringstream isid( idlines[iqSub] ); while (isid >> idNow) { idNowMap = -1; if (idNow == 21 || idNow == 0) idNowMap = 0; if (idNow > 0 && idNow < 6) idNowMap = idNow; if (idNow < 0 && idNow > -6) idNowMap = 5 - idNow; if (idNow == 22) idNowMap = 11; idGridMap.push_back( idNowMap); } int nid = idGridMap.size(); // Read in data grid, line by line. int iq0 = (iqSub == 0) ? 0 : nqSum[iqSub - 1]; for (int ix = 0; ix < nx; ++ix) for (int iq = iq0; iq < nqSum[iqSub]; ++iq) { istringstream ispdf( pdflines[++iln] ); for (int iid = 0; iid < nid; ++iid) { ispdf >> pdfNow; if (idGridMap[iid] >= 0) pdfGrid[idGridMap[iid]][ix][iq] = pdfNow; } } } // For extrapolation to small x: create array for b values of x^b shape. pdfSlope = new double*[12]; for (int iid = 0; iid < 12; ++iid) { pdfSlope[iid] = new double[nq]; for (int iq = 0; iq < nq; ++iq) { pdfSlope[iid][iq] = ( min( pdfGrid[iid][0][iq], pdfGrid[iid][1][iq]) > 1e-5) ? ( log(pdfGrid[iid][1][iq]) - log(pdfGrid[iid][0][iq]) ) / (lnxGrid[1] - lnxGrid[0]) : 0.; } } } //-------------------------------------------------------------------------- void LHAGrid1::xfUpdate(int , double x, double Q2) { // No PDF values if not properly set up. if (!isSet) { xg = xu = xd = xubar = xdbar = xs = xsbar = xc = xb = xgamma = xuVal = xuSea = xdVal = xdSea = 0.; return; } // Update within allowed (x, q) range. xfxevolve( x, Q2); // Then transfer to Pythia8 notation. xg = pdfVal[0]; xu = pdfVal[2]; xd = pdfVal[1]; xubar = pdfVal[7]; xdbar = pdfVal[6]; xs = pdfVal[3]; xsbar = pdfVal[8]; xc = 0.5 * (pdfVal[4] + pdfVal[9]); xb = 0.5 * (pdfVal[5] + pdfVal[10]); xgamma = pdfVal[11]; // Subdivision of valence and sea. xuVal = xu - xubar; xuSea = xubar; xdVal = xd - xdbar; xdSea = xdbar; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- void LHAGrid1::xfxevolve(double x, double Q2) { // Find if (x, Q) inside our outside grid. double q = sqrt(Q2); int inx = (x <= xMin) ? -1 : ((x >= xMax) ? 1 : 0); int inq = (q <= qMin) ? -1 : ((q >= qMax) ? 1 : 0); // Set up default for x interpolation. int minx = 0; int maxx = nx - 1; int m3x = 0; double wx[4] = {1., 1., 1., 1.}; // Find grid value on either side of x. if (inx == 0) { int midx; while (maxx - minx > 1) { midx = (minx + maxx) / 2; if (x < xGrid[midx]) maxx = midx; else minx = midx; } // Weights for cubic interpolation in ln(x). double lnx = log(x); if (minx == 0) m3x = 0; else if (maxx == nx - 1) m3x = nx - 4; else m3x = minx - 1; for (int i3 = 0; i3 < 4; ++i3) for (int j = 0; j < 4; ++j) if (j != i3) wx[i3] *= (lnx - lnxGrid[m3x+j]) / (lnxGrid[m3x+i3] - lnxGrid[m3x+j]); } // Find q subgrid and set up default for q interpolation. int iqDiv = 0; for (int iqSub = 1; iqSub < nqSub; ++iqSub) if (q > qDiv[iqSub - 1]) iqDiv = iqSub; int minS = (iqDiv == 0) ? 0 : nqSum[iqDiv - 1]; int maxS = nqSum[iqDiv] - 1; int minq = minS; int maxq = maxS; int n3q = 4; int m3q = 0.; double wq[4] = {1., 1., 1., 1.}; // Find grid value on either side of q. if (inq == 0) { int midq; while (maxq - minq > 1) { midq = (minq + maxq) / 2; if (q < qGrid[midq]) maxq = midq; else minq = midq; } // Weights for linear or cubic interpolation in ln(q). double lnq = log(q); if (maxS - minS < 3) { n3q = 2; m3q = minq; wq[1] = (lnq - lnqGrid[minq]) / (lnqGrid[maxq] - lnqGrid[minq]); wq[0] = 1. - wq[1]; } else { if (minq == minS) m3q = minS; else if (maxq == maxS) m3q = maxS - 3; else m3q = minq - 1; for (int i3 = 0; i3 < 4; ++i3) for (int j = 0; j < 4; ++j) if (j != i3) wq[i3] *= (lnq - lnqGrid[m3q+j]) / (lnqGrid[m3q+i3] - lnqGrid[m3q+j]); } // Freeze at border of q range. } else { n3q = 1; if (inq == 1) m3q = nq - 1; } // Interpolate between grid elements, normally bicubic, or simpler in ln(q). for (int iid = 0; iid < 12; ++iid) pdfVal[iid] = 0.; if (inx == 0) { for (int iid = 0; iid < 12; ++iid) for (int i3x = 0; i3x < 4; ++i3x) for (int i3q = 0; i3q < n3q; ++i3q) pdfVal[iid] += wx[i3x] * wq[i3q] * pdfGrid[iid][m3x+i3x][m3q+i3q]; // Special: extrapolate to small x. (Let vanish at large x, so no such code.) } else if (inx == -1) { for (int iid = 0; iid < 12; ++iid) for (int i3q = 0; i3q < n3q; ++i3q) pdfVal[iid] += wq[i3q] * pdfGrid[iid][0][m3q+i3q] * (doExtraPol ? pow( x / xMin, pdfSlope[iid][m3q+i3q]) : 1.); } } //========================================================================== // Convolution with photon flux from leptons and photon PDFs. // Contains a pointer to a photon PDF set and samples the // convolution integral event-by-event basis. // Includes also a overestimate for the PDF set in order to set up // the phase-space sampling correctly. // Constants related to the fit. const double Lepton2gamma::ALPHAEM = 0.007297353080; const double Lepton2gamma::Q2MIN = 1.; //-------------------------------------------------------------------------- // Update PDFs and sample a value for x_gamma. void Lepton2gamma::xfUpdate(int , double x, double Q2){ // Find the maximum x value at given Q2max and sqrt(s). double sCM = infoPtr->s(); double xGamMax = ( 2. - 2. * Q2max / sCM - 8. * m2lepton / sCM ) / ( 1. + sqrt( (1. + 4. * m2lepton / Q2max) * (1. - 4. * m2lepton/sCM) ) ); // If outside allowed x values set PDFs to zero. if ( x > xGamMax ) { xg = 0.; xd = 0.; xu = 0.; xs = 0.; xc = 0.; xb = 0.; xubar = 0.; xdbar = 0.; xsbar = 0.; xGm = 1.; return; } // Pre-calculate some logs. double log2x = pow2( log( Q2max / (m2lepton * pow2(x)) ) ); double log2xMax = pow2( log( Q2max / (m2lepton * pow2(xGamMax)) ) ); // Sample x_gamma. if ( sampleXgamma) { xGm = sqrt( (Q2max / m2lepton) * exp( -sqrt( log2x + rndmPtr->flat() * (log2xMax - log2x) ) ) ); } // Evaluate the PDFs at x/x_gamma. double xInGamma = x/xGm; double xgGm = gammaPDFPtr->xf(21, xInGamma, Q2); double xdGm = gammaPDFPtr->xf(1 , xInGamma, Q2); double xuGm = gammaPDFPtr->xf(2 , xInGamma, Q2); double xsGm = gammaPDFPtr->xf(3 , xInGamma, Q2); double xcGm = gammaPDFPtr->xf(4 , xInGamma, Q2); double xbGm = gammaPDFPtr->xf(5 , xInGamma, Q2); // Calculate the Q^2_min for sampled x_gamma. double m2s = 4. * m2lepton / sCM; double Q2min = 2. * m2lepton * pow2(xGm) / ( 1. - xGm - m2s + sqrt(1. - m2s) * sqrt( pow2(1. - xGm) - m2s ) ); // Correct with weight. double alphaLog = (ALPHAEM / (2. * M_PI)) * (1. + pow2(1. - xGm) ) * 0.25 * (log2x - log2xMax) * log(Q2max / Q2min) / log( Q2max / ( m2lepton * pow2(xGm) ) ); // Calculate the PDF value. xg = alphaLog * xgGm; xd = alphaLog * xdGm; xu = alphaLog * xuGm; xs = alphaLog * xsGm; xc = alphaLog * xcGm; xb = alphaLog * xbGm; xubar = xu; xdbar = xd; xsbar = xs; // Photon inside electron not currently implemented (Use point-like lepton). xgamma = 0; // idSav = 9 to indicate that all flavours reset. idSav = 9; } //-------------------------------------------------------------------------- // Approximate the maximum of convoluted PDF to correctly set up the // sampling of the phase space. double Lepton2gamma::xfMax(int id, double x, double Q2){ // Find the maximum x value at given Q2max and sqrt(s). double sCM = infoPtr->s(); double xGamMax = ( 2. - 2. * Q2max / sCM - 8. * m2lepton / sCM ) / ( 1. + sqrt( (1. + 4. * m2lepton / Q2max) * (1. - 4. * m2lepton/sCM) ) ); // Set PDFs to zero outside allowed x values. if ( x > xGamMax ) return 0; // Pre-calculate some logs. double log2x = pow2( log( Q2max / (m2lepton * pow2(x)) ) ); double log2xMax = pow2( log( Q2max / (m2lepton * pow2(xGamMax)) ) ); // Find approximate x-behaviour for each flavour. Optimized for CJKL. double xApprox = 0.; int idAbs = abs(id); if (idAbs == 21 || idAbs == 0) xApprox = 2.35; else if (idAbs == 1) xApprox = (pow(x, 0.2) + pow(1. - x, -0.15)) * 0.8; else if (idAbs == 2) xApprox = (pow(x, 1.0) + pow(1. - x, -0.4)) * 0.4; else if (idAbs == 3) xApprox = (pow(x, 0.2) + pow(1. - x, -0.5)) * 0.5; else if (idAbs == 4) xApprox = (pow(x, 1.0) + pow(1. - x, -0.4)) * 0.7; else if (idAbs == 5) xApprox = (pow(x, 0.2) + pow(1. -x, -0.5)) * 0.5; else xApprox = 0.; // Direct photons in usual lepton PDFs. if ( idAbs == 22 ) return 0; // Return the approximation. return (ALPHAEM / (2. * M_PI)) * (log2x - log2xMax) * 0.5 * gammaPDFPtr->xf(id, x, Q2) / xApprox; } //-------------------------------------------------------------------------- // Return PDF without sampling x_gamma values to compute cross section with // rescaled sHat. Not very elegant but no need to modify the xfUpdate call. double Lepton2gamma::xfSame(int id, double x, double Q2){ sampleXgamma = false; xfUpdate(id, x, Q2); double xfNow = xf(id, x, Q2); sampleXgamma = true; return xfNow; } //========================================================================== } // end namespace Pythia8