+++ /dev/null
-///////////////////////////////////////////////////////////////////////////
-//
-// Copyright 2010
-//
-// This file is part of starlight.
-//
-// starlight is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// starlight is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with starlight. If not, see <http://www.gnu.org/licenses/>.
-//
-///////////////////////////////////////////////////////////////////////////
-//
-// File and Version Information:
-// $Rev:: $: revision of last commit
-// $Author:: $: author of last commit
-// $Date:: $: date of last commit
-//
-// Description:
-//
-//
-///////////////////////////////////////////////////////////////////////////
-
-
-#include <iostream>
-#include <fstream>
-#include <cmath>
-
-#include "reportingUtils.h"
-#include "starlightconstants.h"
-#include "bessel.h"
-#include "photonNucleusCrossSection.h"
-
-
-using namespace std;
-using namespace starlightConstants;
-
-
-//______________________________________________________________________________
-photonNucleusCrossSection::photonNucleusCrossSection(const beamBeamSystem& bbsystem)
- : _nWbins (inputParametersInstance.nmbWBins() ),
- _nYbins (inputParametersInstance.nmbRapidityBins() ),
- _wMin (inputParametersInstance.minW() ),
- _wMax (inputParametersInstance.maxW() ),
- _yMax (inputParametersInstance.maxRapidity() ),
- _beamLorentzGamma (inputParametersInstance.beamLorentzGamma() ),
- _bbs (bbsystem ),
- _protonEnergy (inputParametersInstance.protonEnergy() ),
- _particleType (inputParametersInstance.prodParticleType() ),
- _beamBreakupMode (inputParametersInstance.beamBreakupMode() ),
- _coherentProduction(inputParametersInstance.coherentProduction()),
- _incoherentFactor (inputParametersInstance.incoherentFactor() ),
- _productionMode (inputParametersInstance.productionMode() ),
- _sigmaNucleus (_bbs.beam2().A() )
-{
- // define luminosity for various beam particles in units of 10^{26} cm^{-2} sec^{-1}
- switch(_bbs.beam1().Z()) {
- case 1: // proton
- _luminosity = 1.E8;
- break;
- case 8: // O
- _luminosity = 980.;
- break;
- case 14: // Si
- _luminosity = 440.;
- break;
- case 20: // Ca
- _luminosity = 2000.;
- break;
- case 29: // Cu
- _luminosity = 95.;
- break;
- case 49: // Indium, uses same as Iodine
- _luminosity = 27.;
- break;
- case 53: // I
- _luminosity = 27.;
- break;
- case 79: // Au
- _luminosity = 2.0;
- break;
- case 82: // Pb
- _luminosity = 1.;
- break;
- default:
- printWarn << "luminosity is not defined for beam with Z = " << _bbs.beam1().Z()
- << ". using " << _luminosity << " 10^{26} cm^{-2} sec^{-1}" << endl;
- }
-
- switch(_particleType) {
- case RHO:
- _slopeParameter = 11.0; // [(GeV/c)^{-2}]
- _vmPhotonCoupling = 2.02;
- _ANORM = -2.75;
- _BNORM = 0.0;
- _defaultC = 1.0;
- _channelMass = 0.7685; // [GeV/c^2]
- _width = 0.1507; // [GeV/c^2]
- break;
- case RHOZEUS:
- _slopeParameter =11.0;
- _vmPhotonCoupling=2.02;
- _ANORM=-2.75;
- _BNORM=1.84;
- _defaultC=1.0;
- _channelMass = 0.7685;
- _width=0.1507;
- break;
- case FOURPRONG:
- _slopeParameter = 11.0;
- _vmPhotonCoupling = 2.02;
- _ANORM = -2.75;
- _BNORM = 0; // no coherent background component is implemented for four-prong
- _defaultC = 11.0;
- _channelMass = 1.350;
- _width = 0.360;
- break;
- case OMEGA:
- _slopeParameter=10.0;
- _vmPhotonCoupling=23.13;
- _ANORM=-2.75;
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=0.78194;
- _width=0.00843;
- break;
- case PHI:
- _slopeParameter=7.0;
- _vmPhotonCoupling=13.71;
- _ANORM=-2.75;
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=1.019413;
- _width=0.00443;
- break;
- case JPSI:
- case JPSI_ee:
- case JPSI_mumu:
- _slopeParameter=4.0;
- _vmPhotonCoupling=10.45;
- _ANORM=-2.75;//Artificial Breit-Wigner parameters--no direct pions
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=3.09692;//JN 3.09688
- _width=0.000091;//JN 0.000087
- break;
- case JPSI2S:
- case JPSI2S_ee:
- case JPSI2S_mumu:
- _slopeParameter=4.3;
- _vmPhotonCoupling=26.39;
- _ANORM=-2.75;//Artificial
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=3.686093;
- _width=0.000337;
- break;
- case UPSILON:
- case UPSILON_ee:
- case UPSILON_mumu:
- _slopeParameter=4.0;
- _vmPhotonCoupling=125.37;
- _ANORM=-2.75;//Artificial
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=9.46030;
- _width=0.00005402;
- break;
- case UPSILON2S:
- case UPSILON2S_ee:
- case UPSILON2S_mumu:
- _slopeParameter=4.0;
- _vmPhotonCoupling=290.84;
- _ANORM=-2.75;
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=10.02326;
- _width=0.00003198;
- break;
- case UPSILON3S:
- case UPSILON3S_ee:
- case UPSILON3S_mumu:
- _slopeParameter=4.0;
- _vmPhotonCoupling=415.10;
- _ANORM=-2.75;
- _BNORM=0.0;
- _defaultC=1.0;
- _channelMass=10.3552;
- _width=0.00002032;
- break;
- default:
- cout <<"No sigma constants parameterized for pid: "<<_particleType
- <<" GammaAcrosssection"<<endl;
- }
-
- double maxradius = (_bbs.beam1().nuclearRadius()<_bbs.beam2().nuclearRadius())?_bbs.beam2().nuclearRadius():_bbs.beam1().nuclearRadius();
- _maxPhotonEnergy = 5. * _beamLorentzGamma * hbarc/maxradius;
-}
-
-
-//______________________________________________________________________________
-photonNucleusCrossSection::~photonNucleusCrossSection()
-{ }
-
-
-//______________________________________________________________________________
-void
-photonNucleusCrossSection::crossSectionCalculation(const double)
-{
- cout << "Neither narrow/wide resonance cross-section calculation.--Derived" << endl;
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::getcsgA(const double Egamma,
- const double W)
-{
- //This function returns the cross-section for photon-nucleus interaction
- //producing vectormesons
-
- double Av,Wgp,cs,cvma;
- double t,tmin,tmax;
- double csgA,ax,bx;
- int NGAUSS;
-
- // DATA FOR GAUSS INTEGRATION
- double xg[6] = {0, 0.1488743390, 0.4333953941, 0.6794095683, 0.8650633667, 0.9739065285};
- double ag[6] = {0, 0.2955242247, 0.2692667193, 0.2190863625, 0.1494513492, 0.0666713443};
- NGAUSS = 6;
-
- // Find gamma-proton CM energy
- Wgp = sqrt(2. * Egamma * (_protonEnergy
- + sqrt(_protonEnergy * _protonEnergy - protonMass * protonMass))
- + protonMass * protonMass);
-
- //Used for d-A and A-A
- tmin = (W * W / (4. * Egamma * _beamLorentzGamma)) * (W * W / (4. * Egamma * _beamLorentzGamma));
-
- if ((_bbs.beam1().A() == 1) && (_bbs.beam2().A() == 1)) // proton-proton, no scaling needed
- csgA = sigmagp(Wgp);
- else if ((_bbs.beam2().Z() == 1) && (_bbs.beam2().A() == 2)) { // deuteron-A interaction
- Av = _slopeParameter * sigmagp(Wgp);
-
- tmax = tmin + 0.64; //0.64
- ax = 0.5 * (tmax - tmin);
- bx = 0.5 * (tmax + tmin);
- csgA = 0.;
-
- for (int k = 1; k < NGAUSS; ++k) {
- t = ax * xg[k] + bx;
- // We use beam2 here since the input stores the deuteron as nucleus 2
- // and nucleus 2 is the pomeron field source
- // Also this is the way sergey formatted the formfactor.
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t);
- t = ax * (-xg[k]) + bx;
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t);
- }
- csgA = 0.5 * (tmax - tmin) * csgA;
- csgA = Av * csgA;
- } else if (!_coherentProduction &&
- (!((_bbs.beam2().Z() == 1) && (_bbs.beam2().A() == 2)))) { // incoherent AA interactions
- // For incoherent AA interactions, since incoherent treating it as gamma-p
- // Calculate the differential V.M.+proton cross section
- csgA = 1.E-4 * _incoherentFactor * _sigmaNucleus * _slopeParameter * sigmagp(Wgp);
-
- } else { // coherent AA interactions
- // For typical AA interactions.
- // Calculate V.M.+proton cross section
- cs = sqrt(16. * pi * _vmPhotonCoupling * _slopeParameter * hbarc * hbarc * sigmagp(Wgp) / alpha);
-
- // Calculate V.M.+nucleus cross section
- // cvma = _bbs.beam1().A()*cs;
- cvma = sigma_A(cs);
-
- // Calculate Av = dsigma/dt(t=0) Note Units: fm**s/Gev**2
- Av = (alpha * cvma * cvma) / (16. * pi * _vmPhotonCoupling * hbarc * hbarc);
-
- // Check if one or both beams are nuclei
- int A_1 = _bbs.beam1().A();
- int A_2 = _bbs.beam2().A();
-
- tmax = tmin + 0.25;
- ax = 0.5 * (tmax - tmin);
- bx = 0.5 * (tmax + tmin);
- csgA = 0.;
- for (int k = 1; k < NGAUSS; ++k) {
-
- t = ax * xg[k] + bx;
- if( A_1 == 1 && A_2 != 1){
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
- }else if(A_2 ==1 && A_1 != 1){
- csgA = csgA + ag[k] * _bbs.beam1().formFactor(t) * _bbs.beam1().formFactor(t);
- }else{
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
- }
-
- t = ax * (-xg[k]) + bx;
- if( A_1 == 1 && A_2 != 1){
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
- }else if(A_2 ==1 && A_1 != 1){
- csgA = csgA + ag[k] * _bbs.beam1().formFactor(t) * _bbs.beam1().formFactor(t);
- }else{
- csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
- }
- }
- csgA = 0.5 * (tmax - tmin) * csgA;
- csgA = Av * csgA;
- }
-
- return csgA;
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::photonFlux(const double Egamma)
-{
- // This routine gives the photon flux as a function of energy Egamma
- // It works for arbitrary nuclei and gamma; the first time it is
- // called, it calculates a lookup table which is used on
- // subsequent calls.
- // It returns dN_gamma/dE (dimensions 1/E), not dI/dE
- // energies are in GeV, in the lab frame
- // rewritten 4/25/2001 by SRK
-
- double lEgamma,Emin,Emax;
- static double lnEmax, lnEmin, dlnE;
- double stepmult,energy,rZ,rA;
- int nbstep,nrstep,nphistep,nstep;
- double bmin,bmax,bmult,biter,bold,integratedflux;
- double fluxelement,deltar,riter;
- double deltaphi,phiiter,dist;
- static double dide[401];
- double lnElt;
- double rA2, rZ2;
- double flux_r;
- double Xvar;
- int Ilt;
- double RNuc=0.,RNuc2=0.,maxradius=0.;
-
- RNuc=_bbs.beam1().nuclearRadius();
- RNuc2=_bbs.beam2().nuclearRadius();
- maxradius = (RNuc<RNuc2)?RNuc2:RNuc;
- // static ->>> dide,lnEMax,lnEmin,dlnE
- static int Icheck = 0;
-
- //Check first to see if pp
- if( _bbs.beam1().A()==1 && _bbs.beam2().A()==1 ){
- int nbsteps = 400;
- double bmin = 0.5;
- double bmax = 5.0 + (5.0*_beamLorentzGamma*hbarc/Egamma);
- double dlnb = (log(bmax)-log(bmin))/(1.*nbsteps);
-
- double local_sum=0.0;
-
- // Impact parameter loop
- for (int i = 0; i<=nbsteps;i++){
-
- double bnn0 = bmin*exp(i*dlnb);
- double bnn1 = bmin*exp((i+1)*dlnb);
- double db = bnn1-bnn0;
-
- // double PofB0 = 1.0;
- // if( bnn0 > 1.4 )PofB0=0.0;
- // double PofB1 = 1.0;
- // if( bnn1 > 1.4 )PofB1=0.0;
-
- double ppslope = 19.0;
- double GammaProfile = exp(-bnn0*bnn0/(2.*hbarc*hbarc*ppslope));
- double PofB0 = 1. - (1. - GammaProfile)*(1. - GammaProfile);
- GammaProfile = exp(-bnn1*bnn1/(2.*hbarc*hbarc*ppslope));
- double PofB1 = 1. - (1. - GammaProfile)*(1. - GammaProfile);
-
- double Xarg = Egamma*bnn0/(hbarc*_beamLorentzGamma);
- double loc_nofe0 = (_bbs.beam1().Z()*_bbs.beam1().Z()*alpha)/
- (pi*pi);
- loc_nofe0 *= (1./(Egamma*bnn0*bnn0));
- loc_nofe0 *= Xarg*Xarg*(bessel::dbesk1(Xarg))*(bessel::dbesk1(Xarg));
-
- Xarg = Egamma*bnn1/(hbarc*_beamLorentzGamma);
- double loc_nofe1 = (_bbs.beam1().Z()*_bbs.beam1().Z()*alpha)/
- (pi*pi);
- loc_nofe1 *= (1./(Egamma*bnn1*bnn1));
- loc_nofe1 *= Xarg*Xarg*(bessel::dbesk1(Xarg))*(bessel::dbesk1(Xarg));
-
- local_sum += loc_nofe0*(1. - PofB0)*bnn0*db;
- local_sum += loc_nofe1*(1. - PofB1)*bnn1*db;
-
- }
- // End Impact parameter loop
-
- // Note: 2*pi --> pi because of no factor 2 above
- double flux_r=local_sum*pi;
- return flux_r;
-
- // bmin = nuclearRadius+nuclearRadius;
- // flux_r = nepoint(Egamma,bmin);
- // return flux_r;
- }
-
- // first call? - initialize - calculate photon flux
- Icheck=Icheck+1;
- if(Icheck > 1) goto L1000f;
-
- rZ=double(_bbs.beam1().Z());
- rA=double(_bbs.beam1().A());
- rZ2=double(_bbs.beam2().Z()); //Sergey--dAu
- rA2=double(_bbs.beam2().A()); //Sergey
-
- // Nuclear breakup is done by PofB
- // collect number of integration steps here, in one place
-
- nbstep=1200;
- nrstep=60;
- nphistep=40;
-
- // this last one is the number of energy steps
- nstep=100;
-
- // following previous choices, take Emin=10 keV at LHC, Emin = 1 MeV at RHIC
- Emin=1.E-5;
- if (_beamLorentzGamma < 500)
- Emin=1.E-3;
-
- // maximum energy is 6 times the cutoff
- // Emax=12.*hbarc*_beamLorentzGamma/RNuc;
- Emax=6.*hbarc*_beamLorentzGamma/maxradius;
-
- // >> lnEmin <-> ln(Egamma) for the 0th bin
- // >> lnEmax <-> ln(Egamma) for the last bin
-
- lnEmin=log(Emin);
- lnEmax=log(Emax);
- dlnE=(lnEmax-lnEmin)/nstep;
-
- cout<<" Calculating flux for photon energies from E= "<<Emin
- <<" to "<<Emax<<" GeV (CM frame) "<<endl;
-
-
- stepmult= exp(log(Emax/Emin)/double(nstep));
- energy=Emin;
-
- for (int j = 1; j<=nstep;j++){
- energy=energy*stepmult;
-
- // integrate flux over 2R_A < b < 2R_A+ 6* gamma hbar/energy
- // use exponential steps
-
- bmin=RNuc+RNuc2; //2.*nuclearRadius; Sergey
- bmax=bmin + 6.*hbarc*_beamLorentzGamma/energy;
-
- bmult=exp(log(bmax/bmin)/double(nbstep));
- biter=bmin;
- integratedflux=0.;
-
- if (_bbs.beam2().Z()==1&&_bbs.beam1().A()==2){
- //This is for deuteron-gold
- Xvar = (RNuc+RNuc2)*energy/(hbarc*(_beamLorentzGamma));
-
- fluxelement = (2.0/pi)*rZ*rZ*alpha/
- energy*(Xvar*bessel::dbesk0(Xvar)*bessel::dbesk1(Xvar)-(1/2)*Xvar*Xvar*
- (bessel::dbesk1(Xvar)*bessel::dbesk1(Xvar)-bessel::dbesk0(Xvar)*bessel::dbesk0(Xvar)));
-
- integratedflux=integratedflux+fluxelement;
- }else if( (_bbs.beam1().A() == 1 && _bbs.beam2().A() != 1) || (_bbs.beam2().A() == 1 && _bbs.beam1().A() != 1) ){
- // This is pA
- if( _productionMode == PHOTONPOMERONINCOHERENT ){
- // This is pA incoherent
- // cout<<" This is incoherent! "<<" j = "<<j<<endl;
- double zproj = 0.0;
- double localbmin = 0.0;
- if( _bbs.beam1().A() == 1 ){
- zproj = (_bbs.beam2().Z());
- localbmin = _bbs.beam2().nuclearRadius() + 0.7;
- }
- if( _bbs.beam2().A() == 1 ){
- zproj = (_bbs.beam1().Z());
- localbmin = _bbs.beam1().nuclearRadius() + 0.7;
- }
- integratedflux = zproj*zproj*nepoint(energy,localbmin);
- } else if ( _productionMode == PHOTONPOMERONNARROW || _productionMode == PHOTONPOMERONWIDE ){
- // cout<<" This is pA coherent "<<" j= "<<j<<endl;
- double localbmin = 0.0;
- if( _bbs.beam1().A() == 1 ){
- localbmin = _bbs.beam2().nuclearRadius() + 0.7;
- }
- if( _bbs.beam2().A() == 1 ){
- localbmin = _bbs.beam1().nuclearRadius() + 0.7;
- }
- integratedflux = nepoint(energy,localbmin);
- }
- }else{
- for (int jb = 1; jb<=nbstep;jb++){
- bold=biter;
- biter=biter*bmult;
- // When we get to b>20R_A change methods - just take the photon flux
- // at the center of the nucleus.
- if (biter > (10.*RNuc))
- {
- // if there is no nuclear breakup or only hadronic breakup, which only
- // occurs at smaller b, we can analytically integrate the flux from b~20R_A
- // to infinity, following Jackson (2nd edition), Eq. 15.54
- Xvar=energy*biter/(hbarc*_beamLorentzGamma);
- // Here, there is nuclear breakup. So, we can't use the integrated flux
- // However, we can do a single flux calculation, at the center of the nucleus
- // Eq. 41 of Vidovic, Greiner and Soff, Phys.Rev.C47,2308(1993), among other places
- // this is the flux per unit area
- fluxelement = (rZ*rZ*alpha*energy)*
- (bessel::dbesk1(Xvar))*(bessel::dbesk1(Xvar))/
- ((pi*_beamLorentzGamma*hbarc)*
- (pi*_beamLorentzGamma*hbarc));
-
- }//if biter>10
- else{
- // integrate over nuclear surface. n.b. this assumes total shadowing -
- // treat photons hitting the nucleus the same no matter where they strike
- fluxelement=0.;
- deltar=RNuc/double(nrstep);
- riter=-deltar/2.;
-
- for (int jr =1; jr<=nrstep;jr++){
- riter=riter+deltar;
- // use symmetry; only integrate from 0 to pi (half circle)
- deltaphi=pi/double(nphistep);
- phiiter=0.;
-
- for( int jphi=1;jphi<= nphistep;jphi++){
- phiiter=(double(jphi)-0.5)*deltaphi;
- // dist is the distance from the center of the emitting nucleus to the point in question
- dist=sqrt((biter+riter*cos(phiiter))*(biter+riter*
- cos(phiiter))+(riter*sin(phiiter))*(riter*sin(phiiter)));
- Xvar=energy*dist/(hbarc*_beamLorentzGamma);
- flux_r = (rZ*rZ*alpha*energy)*
- (bessel::dbesk1(Xvar)*bessel::dbesk1(Xvar))/
- ((pi*_beamLorentzGamma*hbarc)*
- (pi*_beamLorentzGamma*hbarc));
-
- // The surface element is 2.* delta phi* r * delta r
- // The '2' is because the phi integral only goes from 0 to pi
- fluxelement=fluxelement+flux_r*2.*deltaphi*riter*deltar;
- // end phi and r integrations
- }//for(jphi)
- }//for(jr)
- // average fluxelement over the nuclear surface
- fluxelement=fluxelement/(pi*RNuc*RNuc);
- }//else
- // multiply by volume element to get total flux in the volume element
- fluxelement=fluxelement*2.*pi*biter*(biter-bold);
- // modulate by the probability of nuclear breakup as f(biter)
- if (_beamBreakupMode > 1){
- fluxelement=fluxelement*_bbs.probabilityOfBreakup(biter);
- }
- integratedflux=integratedflux+fluxelement;
-
- } //end loop over impact parameter
- } //end of else (pp, pA, AA)
-
- // In lookup table, store k*dN/dk because it changes less
- // so the interpolation should be better
- dide[j]=integratedflux*energy;
-
- }//end loop over photon energy
-
- // for 2nd and subsequent calls, use lookup table immediately
-
- L1000f:
-
- lEgamma=log(Egamma);
- if (lEgamma < (lnEmin+dlnE) || lEgamma > lnEmax){
- flux_r=0.0;
- cout<<" ERROR: Egamma outside defined range. Egamma= "<<Egamma
- <<" "<<lnEmax<<" "<<(lnEmin+dlnE)<<endl;
- }
- else{
- // >> Egamma between Ilt and Ilt+1
- Ilt = int((lEgamma-lnEmin)/dlnE);
- // >> ln(Egamma) for first point
- lnElt = lnEmin + Ilt*dlnE;
- // >> Interpolate
- flux_r = dide[Ilt] + ((lEgamma-lnElt)/dlnE)*(dide[Ilt+1]- dide[Ilt]);
- flux_r = flux_r/Egamma;
- }
-
- return flux_r;
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::nepoint(const double Egamma,
- const double bmin)
-{
- // Function for the spectrum of virtual photons,
- // dn/dEgamma, for a point charge q=Ze sweeping
- // past the origin with velocity gamma
- // (=1/SQRT(1-(V/c)**2)) integrated over impact
- // parameter from bmin to infinity
- // See Jackson eq15.54 Classical Electrodynamics
- // Declare Local Variables
- double beta,X,C1,bracket,nepoint_r;
-
- beta = sqrt(1.-(1./(_beamLorentzGamma*_beamLorentzGamma)));
- X = (bmin*Egamma)/(beta*_beamLorentzGamma*hbarc);
-
- bracket = -0.5*beta*beta*X*X*(bessel::dbesk1(X)*bessel::dbesk1(X)
- -bessel::dbesk0(X)*bessel::dbesk0(X));
-
- bracket = bracket+X*bessel::dbesk0(X)*bessel::dbesk1(X);
-
- // C1=(2.*double((_bbs.beam1().Z())*(_bbs.beam1().Z()))*
- // alpha)/pi;
-
- // Note: NO Z*Z!!
- C1=(2.*alpha)/pi;
-
- nepoint_r = C1*(1./beta)*(1./beta)*(1./Egamma)*bracket;
-
- return nepoint_r;
-
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::sigmagp(const double Wgp)
-{
- // >> Function for the gamma-proton --> VectorMeson
- // >> cross section. Wgp is the gamma-proton CM energy.
- // >> Unit for cross section: fm**2
-
- double sigmagp_r=0.;
-
- switch(_particleType)
- {
- case RHO:
- case RHOZEUS:
- case FOURPRONG:
- sigmagp_r=1.E-4*(5.0*exp(0.22*log(Wgp))+26.0*exp(-1.23*log(Wgp)));
- break;
- case OMEGA:
- sigmagp_r=1.E-4*(0.55*exp(0.22*log(Wgp))+18.0*exp(-1.92*log(Wgp)));
- break;
- case PHI:
- sigmagp_r=1.E-4*0.34*exp(0.22*log(Wgp));
- break;
- case JPSI:
- case JPSI_ee:
- case JPSI_mumu:
- sigmagp_r=(1.0-((_channelMass+protonMass)*(_channelMass+protonMass))/(Wgp*Wgp));
- sigmagp_r*=sigmagp_r;
- sigmagp_r*=1.E-4*0.00406*exp(0.65*log(Wgp));
- // sigmagp_r=1.E-4*0.0015*exp(0.80*log(Wgp));
- break;
- case JPSI2S:
- case JPSI2S_ee:
- case JPSI2S_mumu:
- sigmagp_r=(1.0-((_channelMass+protonMass)*(_channelMass+protonMass))/(Wgp*Wgp));
- sigmagp_r*=sigmagp_r;
- sigmagp_r*=1.E-4*0.00406*exp(0.65*log(Wgp));
- sigmagp_r*=0.166;
- // sigmagp_r=0.166*(1.E-4*0.0015*exp(0.80*log(Wgp)));
- break;
- case UPSILON:
- case UPSILON_ee:
- case UPSILON_mumu:
- // >> This is W**1.7 dependence from QCD calculations
- sigmagp_r=1.E-10*(0.060)*exp(1.70*log(Wgp));
- break;
- case UPSILON2S:
- case UPSILON2S_ee:
- case UPSILON2S_mumu:
- sigmagp_r=1.E-10*(0.0259)*exp(1.70*log(Wgp));
- break;
- case UPSILON3S:
- case UPSILON3S_ee:
- case UPSILON3S_mumu:
- sigmagp_r=1.E-10*(0.0181)*exp(1.70*log(Wgp));
- break;
- default: cout<< "!!! ERROR: Unidentified Vector Meson: "<< _particleType <<endl;
- }
- return sigmagp_r;
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::sigma_A(const double sig_N)
-{
- // Nuclear Cross Section
- // sig_N,sigma_A in (fm**2)
-
- double sum;
- double b,bmax,Pint,arg,sigma_A_r;
-
- int NGAUSS;
-
- double xg[17]=
- {.0,
- .0483076656877383162,.144471961582796493,
- .239287362252137075, .331868602282127650,
- .421351276130635345, .506899908932229390,
- .587715757240762329, .663044266930215201,
- .732182118740289680, .794483795967942407,
- .849367613732569970, .896321155766052124,
- .934906075937739689, .964762255587506430,
- .985611511545268335, .997263861849481564
- };
-
- double ag[17]=
- {.0,
- .0965400885147278006, .0956387200792748594,
- .0938443990808045654, .0911738786957638847,
- .0876520930044038111, .0833119242269467552,
- .0781938957870703065, .0723457941088485062,
- .0658222227763618468, .0586840934785355471,
- .0509980592623761762, .0428358980222266807,
- .0342738629130214331, .0253920653092620595,
- .0162743947309056706, .00701861000947009660
- };
-
- NGAUSS=16;
-
- // Check if one or both beams are nuclei
- int A_1 = _bbs.beam1().A();
- int A_2 = _bbs.beam2().A();
- if( A_1 == 1 && A_2 == 1)cout<<" This is pp, you should not be here..."<<endl;
-
- // CALCULATE P(int) FOR b=0.0 - bmax (fm)
- bmax = 25.0;
- sum = 0.;
- for(int IB=1;IB<=NGAUSS;IB++){
-
- b = 0.5*bmax*xg[IB]+0.5*bmax;
-
- if( A_1 == 1 && A_2 != 1){
- arg=-sig_N*_bbs.beam2().rho0()*_bbs.beam2().thickness(b);
- }else if(A_2 == 1 && A_1 != 1){
- arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
- }else{
- arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
- }
-
- Pint=1.0-exp(arg);
- sum=sum+2.*pi*b*Pint*ag[IB];
-
-
- b = 0.5*bmax*(-xg[IB])+0.5*bmax;
-
- if( A_1 == 1 && A_2 != 1){
- arg=-sig_N*_bbs.beam2().rho0()*_bbs.beam2().thickness(b);
- }else if(A_2 == 1 && A_1 != 1){
- arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
- }else{
- arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
- }
-
- Pint=1.0-exp(arg);
- sum=sum+2.*pi*b*Pint*ag[IB];
-
- }
-
- sum=0.5*bmax*sum;
-
- sigma_A_r=sum;
-
- return sigma_A_r;
-}
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::sigma_N(const double Wgp)
-{
- // Nucleon Cross Section in (fm**2)
- double cs = sqrt(16. * pi * _vmPhotonCoupling * _slopeParameter * hbarc * hbarc * sigmagp(Wgp) / alpha);
- return cs;
-}
-
-
-//______________________________________________________________________________
-double
-photonNucleusCrossSection::breitWigner(const double W,
- const double C)
-{
- // use simple fixed-width s-wave Breit-Wigner without coherent backgorund for rho'
- // (PDG '08 eq. 38.56)
- if(_particleType==FOURPRONG) {
- if (W < 4.01 * pionChargedMass)
- return 0;
- const double termA = _channelMass * _width;
- const double termA2 = termA * termA;
- const double termB = W * W - _channelMass * _channelMass;
- return C * _ANORM * _ANORM * termA2 / (termB * termB + termA2);
- }
-
- // Relativistic Breit-Wigner according to J.D. Jackson,
- // Nuovo Cimento 34, 6692 (1964), with nonresonant term. A is the strength
- // of the resonant term and b the strength of the non-resonant
- // term. C is an overall normalization.
-
- double ppi=0.,ppi0=0.,GammaPrim,rat;
- double aa,bb,cc;
-
- double nrbw_r;
-
- // width depends on energy - Jackson Eq. A.2
- // if below threshold, then return 0. Added 5/3/2001 SRK
- // 0.5% extra added for safety margin
- if( _particleType==RHO ||_particleType==RHOZEUS){
- if (W < 2.01*pionChargedMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt( ((W/2.)*(W/2.)) - pionChargedMass * pionChargedMass);
- ppi0=0.358;
- }
-
- // handle phi-->K+K- properly
- if (_particleType == PHI){
- if (W < 2.*kaonChargedMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt( ((W/2.)*(W/2.))- kaonChargedMass*kaonChargedMass);
- ppi0=sqrt( ((_channelMass/2.)*(_channelMass/2.))-kaonChargedMass*kaonChargedMass);
- }
-
- //handle J/Psi-->e+e- properly
- if (_particleType==JPSI || _particleType==JPSI2S){
- if(W<2.*mel){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
- }
- if (_particleType==JPSI_ee){
- if(W<2.*mel){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
- }
- if (_particleType==JPSI_mumu){
- if(W<2.*muonMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
- }
- if (_particleType==JPSI2S_ee){
- if(W<2.*mel){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
- }
- if (_particleType==JPSI2S_mumu){
- if(W<2.*muonMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
- }
-
- if(_particleType==UPSILON || _particleType==UPSILON2S ||_particleType==UPSILON3S ){
- if (W<2.*muonMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
- }
-
- if(_particleType==UPSILON_mumu || _particleType==UPSILON2S_mumu ||_particleType==UPSILON3S_mumu ){
- if (W<2.*muonMass){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
- }
-
- if(_particleType==UPSILON_ee || _particleType==UPSILON2S_ee ||_particleType==UPSILON3S_ee ){
- if (W<2.*mel){
- nrbw_r=0.;
- return nrbw_r;
- }
- ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
- ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
- }
-
- if(ppi==0.&&ppi0==0.)
- cout<<"Improper Gammaacrosssection::breitwigner, ppi&ppi0=0."<<endl;
-
- rat=ppi/ppi0;
- GammaPrim=_width*(_channelMass/W)*rat*rat*rat;
-
- aa=_ANORM*sqrt(GammaPrim*_channelMass*W);
- bb=W*W-_channelMass*_channelMass;
- cc=_channelMass*GammaPrim;
-
- // First real part squared
- nrbw_r = (( (aa*bb)/(bb*bb+cc*cc) + _BNORM)*( (aa*bb)/(bb*bb+cc*cc) + _BNORM));
-
- // Then imaginary part squared
- nrbw_r = nrbw_r + (( (aa*cc)/(bb*bb+cc*cc) )*( (aa*cc)/(bb*bb+cc*cc) ));
-
- // Alternative, a simple, no-background BW, following J. Breitweg et al.
- // Eq. 15 of Eur. Phys. J. C2, 247 (1998). SRK 11/10/2000
- // nrbw_r = (_ANORM*_mass*GammaPrim/(bb*bb+cc*cc))**2
-
- nrbw_r = C*nrbw_r;
-
- return nrbw_r;
-}
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