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AM		 1///////////////////////////////////////////////////////////////////////////
2//
3// Copyright 2010
4//
5// This file is part of starlight.
6//
7// starlight is free software: you can redistribute it and/or modify
8// it under the terms of the GNU General Public License as published by
9// the Free Software Foundation, either version 3 of the License, or
10// (at your option) any later version.
11//
12// starlight is distributed in the hope that it will be useful,
13// but WITHOUT ANY WARRANTY; without even the implied warranty of
14// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15// GNU General Public License for more details.
16//
17// You should have received a copy of the GNU General Public License
18// along with starlight. If not, see <http://www.gnu.org/licenses/>.
19//
20///////////////////////////////////////////////////////////////////////////
21//
22// File and Version Information:
23// $Rev:: $: revision of last commit
24// $Author:: $: author of last commit
25// $Date:: $: date of last commit
26//
27// Description:
28//
29//
30///////////////////////////////////////////////////////////////////////////
31
32
33#include <iostream>
34#include <fstream>
35#include <cmath>
36
37#include "reportingUtils.h"
38#include "starlightconstants.h"
39#include "bessel.h"
40#include "photonNucleusCrossSection.h"
41
42
43using namespace std;
44using namespace starlightConstants;
45
46
47//______________________________________________________________________________
48photonNucleusCrossSection::photonNucleusCrossSection(const beamBeamSystem& bbsystem)
49 : _nWbins (inputParametersInstance.nmbWBins() ),
50 _nYbins (inputParametersInstance.nmbRapidityBins() ),
51 _wMin (inputParametersInstance.minW() ),
52 _wMax (inputParametersInstance.maxW() ),
53 _yMax (inputParametersInstance.maxRapidity() ),
54 _beamLorentzGamma (inputParametersInstance.beamLorentzGamma() ),
55 _bbs (bbsystem ),
56 _protonEnergy (inputParametersInstance.protonEnergy() ),
57 _particleType (inputParametersInstance.prodParticleType() ),
58 _beamBreakupMode (inputParametersInstance.beamBreakupMode() ),
59 _coherentProduction(inputParametersInstance.coherentProduction()),
60 _incoherentFactor (inputParametersInstance.incoherentFactor() ),
61 _productionMode (inputParametersInstance.productionMode() ),
62 _sigmaNucleus (_bbs.beam2().A() )
63{
64 // define luminosity for various beam particles in units of 10^{26} cm^{-2} sec^{-1}
65 switch(_bbs.beam1().Z()) {
66 case 1: // proton
67 _luminosity = 1.E8;
68 break;
69 case 8: // O
70 _luminosity = 980.;
71 break;
72 case 14: // Si
73 _luminosity = 440.;
74 break;
75 case 20: // Ca
76 _luminosity = 2000.;
77 break;
78 case 29: // Cu
79 _luminosity = 95.;
80 break;
81 case 49: // Indium, uses same as Iodine
82 _luminosity = 27.;
83 break;
84 case 53: // I
85 _luminosity = 27.;
86 break;
87 case 79: // Au
88 _luminosity = 2.0;
89 break;
90 case 82: // Pb
91 _luminosity = 1.;
92 break;
93 default:
94 printWarn << "luminosity is not defined for beam with Z = " << _bbs.beam1().Z()
95 << ". using " << _luminosity << " 10^{26} cm^{-2} sec^{-1}" << endl;
96 }
97
98 switch(_particleType) {
99 case RHO:
100 _slopeParameter = 11.0; // [(GeV/c)^{-2}]
101 _vmPhotonCoupling = 2.02;
102 _ANORM = -2.75;
103 _BNORM = 0.0;
104 _defaultC = 1.0;
105 _channelMass = 0.7685; // [GeV/c^2]
106 _width = 0.1507; // [GeV/c^2]
107 break;
108 case RHOZEUS:
109 _slopeParameter =11.0;
110 _vmPhotonCoupling=2.02;
111 _ANORM=-2.75;
112 _BNORM=1.84;
113 _defaultC=1.0;
114 _channelMass = 0.7685;
115 _width=0.1507;
116 break;
117 case FOURPRONG:
118 _slopeParameter = 11.0;
119 _vmPhotonCoupling = 2.02;
120 _ANORM = -2.75;
121 _BNORM = 0; // no coherent background component is implemented for four-prong
122 _defaultC = 11.0;
123 _channelMass = 1.350;
124 _width = 0.360;
125 break;
126 case OMEGA:
127 _slopeParameter=10.0;
128 _vmPhotonCoupling=23.13;
129 _ANORM=-2.75;
130 _BNORM=0.0;
131 _defaultC=1.0;
132 _channelMass=0.78194;
133 _width=0.00843;
134 break;
135 case PHI:
136 _slopeParameter=7.0;
137 _vmPhotonCoupling=13.71;
138 _ANORM=-2.75;
139 _BNORM=0.0;
140 _defaultC=1.0;
141 _channelMass=1.019413;
142 _width=0.00443;
143 break;
144 case JPSI:
145 case JPSI_ee:
146 case JPSI_mumu:
147 _slopeParameter=4.0;
148 _vmPhotonCoupling=10.45;
149 _ANORM=-2.75;//Artificial Breit-Wigner parameters--no direct pions
150 _BNORM=0.0;
151 _defaultC=1.0;
152 _channelMass=3.09692;//JN 3.09688
153 _width=0.000091;//JN 0.000087
154 break;
155 case JPSI2S:
156 case JPSI2S_ee:
157 case JPSI2S_mumu:
158 _slopeParameter=4.3;
159 _vmPhotonCoupling=26.39;
160 _ANORM=-2.75;//Artificial
161 _BNORM=0.0;
162 _defaultC=1.0;
163 _channelMass=3.686093;
164 _width=0.000337;
165 break;
166 case UPSILON:
167 case UPSILON_ee:
168 case UPSILON_mumu:
169 _slopeParameter=4.0;
170 _vmPhotonCoupling=125.37;
171 _ANORM=-2.75;//Artificial
172 _BNORM=0.0;
173 _defaultC=1.0;
174 _channelMass=9.46030;
175 _width=0.00005402;
176 break;
177 case UPSILON2S:
178 case UPSILON2S_ee:
179 case UPSILON2S_mumu:
180 _slopeParameter=4.0;
181 _vmPhotonCoupling=290.84;
182 _ANORM=-2.75;
183 _BNORM=0.0;
184 _defaultC=1.0;
185 _channelMass=10.02326;
186 _width=0.00003198;
187 break;
188 case UPSILON3S:
189 case UPSILON3S_ee:
190 case UPSILON3S_mumu:
191 _slopeParameter=4.0;
192 _vmPhotonCoupling=415.10;
193 _ANORM=-2.75;
194 _BNORM=0.0;
195 _defaultC=1.0;
196 _channelMass=10.3552;
197 _width=0.00002032;
198 break;
199 default:
200 cout <<"No sigma constants parameterized for pid: "<<_particleType
201 <<" GammaAcrosssection"<<endl;
202 }
203
204 double maxradius = (_bbs.beam1().nuclearRadius()<_bbs.beam2().nuclearRadius())?_bbs.beam2().nuclearRadius():_bbs.beam1().nuclearRadius();
205 _maxPhotonEnergy = 5. * _beamLorentzGamma * hbarc/maxradius;
206}
207
208
209//______________________________________________________________________________
210photonNucleusCrossSection::~photonNucleusCrossSection()
211{ }
212
213
214//______________________________________________________________________________
215void
216photonNucleusCrossSection::crossSectionCalculation(const double)
217{
218 cout << "Neither narrow/wide resonance cross-section calculation.--Derived" << endl;
219}
220
221
222//______________________________________________________________________________
223double
224photonNucleusCrossSection::getcsgA(const double Egamma,
225 const double W)
226{
227 //This function returns the cross-section for photon-nucleus interaction
228 //producing vectormesons
229
230 double Av,Wgp,cs,cvma;
231 double t,tmin,tmax;
232 double csgA,ax,bx;
233 int NGAUSS;
234
235 // DATA FOR GAUSS INTEGRATION
236 double xg[6] = {0, 0.1488743390, 0.4333953941, 0.6794095683, 0.8650633667, 0.9739065285};
237 double ag[6] = {0, 0.2955242247, 0.2692667193, 0.2190863625, 0.1494513492, 0.0666713443};
238 NGAUSS = 6;
239
240 // Find gamma-proton CM energy
241 Wgp = sqrt(2. * Egamma * (_protonEnergy
242 + sqrt(_protonEnergy * _protonEnergy - protonMass * protonMass))
243 + protonMass * protonMass);
244
245 //Used for d-A and A-A
246 tmin = (W * W / (4. * Egamma * _beamLorentzGamma)) * (W * W / (4. * Egamma * _beamLorentzGamma));
247
248 if ((_bbs.beam1().A() == 1) && (_bbs.beam2().A() == 1)) // proton-proton, no scaling needed
249 csgA = sigmagp(Wgp);
250 else if ((_bbs.beam2().Z() == 1) && (_bbs.beam2().A() == 2)) { // deuteron-A interaction
251 Av = _slopeParameter * sigmagp(Wgp);
252
253 tmax = tmin + 0.64; //0.64
254 ax = 0.5 * (tmax - tmin);
255 bx = 0.5 * (tmax + tmin);
256 csgA = 0.;
257
258 for (int k = 1; k < NGAUSS; ++k) {
259 t = ax * xg[k] + bx;
260 // We use beam2 here since the input stores the deuteron as nucleus 2
261 // and nucleus 2 is the pomeron field source
262 // Also this is the way sergey formatted the formfactor.
263 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t);
264 t = ax * (-xg[k]) + bx;
265 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t);
266 }
267 csgA = 0.5 * (tmax - tmin) * csgA;
268 csgA = Av * csgA;
269 } else if (!_coherentProduction &&
270 (!((_bbs.beam2().Z() == 1) && (_bbs.beam2().A() == 2)))) { // incoherent AA interactions
271 // For incoherent AA interactions, since incoherent treating it as gamma-p
272 // Calculate the differential V.M.+proton cross section
273 csgA = 1.E-4 * _incoherentFactor * _sigmaNucleus * _slopeParameter * sigmagp(Wgp);
274
275 } else { // coherent AA interactions
276 // For typical AA interactions.
277 // Calculate V.M.+proton cross section
278 cs = sqrt(16. * pi * _vmPhotonCoupling * _slopeParameter * hbarc * hbarc * sigmagp(Wgp) / alpha);
279
280 // Calculate V.M.+nucleus cross section
281 // cvma = _bbs.beam1().A()*cs;
282 cvma = sigma_A(cs);
283
284 // Calculate Av = dsigma/dt(t=0) Note Units: fm**s/Gev**2
285 Av = (alpha * cvma * cvma) / (16. * pi * _vmPhotonCoupling * hbarc * hbarc);
286
287 // Check if one or both beams are nuclei
288 int A_1 = _bbs.beam1().A();
289 int A_2 = _bbs.beam2().A();
290
291 tmax = tmin + 0.25;
292 ax = 0.5 * (tmax - tmin);
293 bx = 0.5 * (tmax + tmin);
294 csgA = 0.;
295 for (int k = 1; k < NGAUSS; ++k) {
296
297 t = ax * xg[k] + bx;
298 if( A_1 == 1 && A_2 != 1){
299 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
300 }else if(A_2 ==1 && A_1 != 1){
301 csgA = csgA + ag[k] * _bbs.beam1().formFactor(t) * _bbs.beam1().formFactor(t);
302 }else{
303 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
304 }
305
306 t = ax * (-xg[k]) + bx;
307 if( A_1 == 1 && A_2 != 1){
308 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
309 }else if(A_2 ==1 && A_1 != 1){
310 csgA = csgA + ag[k] * _bbs.beam1().formFactor(t) * _bbs.beam1().formFactor(t);
311 }else{
312 csgA = csgA + ag[k] * _bbs.beam2().formFactor(t) * _bbs.beam2().formFactor(t);
313 }
314 }
315 csgA = 0.5 * (tmax - tmin) * csgA;
316 csgA = Av * csgA;
317 }
318
319 return csgA;
320}
321
322
323//______________________________________________________________________________
324double
325photonNucleusCrossSection::photonFlux(const double Egamma)
326{
327 // This routine gives the photon flux as a function of energy Egamma
328 // It works for arbitrary nuclei and gamma; the first time it is
329 // called, it calculates a lookup table which is used on
330 // subsequent calls.
331 // It returns dN_gamma/dE (dimensions 1/E), not dI/dE
332 // energies are in GeV, in the lab frame
333 // rewritten 4/25/2001 by SRK
334
335 double lEgamma,Emin,Emax;
336 static double lnEmax, lnEmin, dlnE;
337 double stepmult,energy,rZ,rA;
338 int nbstep,nrstep,nphistep,nstep;
339 double bmin,bmax,bmult,biter,bold,integratedflux;
340 double fluxelement,deltar,riter;
341 double deltaphi,phiiter,dist;
342 static double dide[401];
343 double lnElt;
344 double rA2, rZ2;
345 double flux_r;
346 double Xvar;
347 int Ilt;
348 double RNuc=0.,RNuc2=0.,maxradius=0.;
349
350 RNuc=_bbs.beam1().nuclearRadius();
351 RNuc2=_bbs.beam2().nuclearRadius();
352 maxradius = (RNuc<RNuc2)?RNuc2:RNuc;
353 // static ->>> dide,lnEMax,lnEmin,dlnE
354 static int Icheck = 0;
355
356 //Check first to see if pp
357 if( _bbs.beam1().A()==1 && _bbs.beam2().A()==1 ){
358 int nbsteps = 400;
359 double bmin = 0.5;
360 double bmax = 5.0 + (5.0*_beamLorentzGamma*hbarc/Egamma);
361 double dlnb = (log(bmax)-log(bmin))/(1.*nbsteps);
362
363 double local_sum=0.0;
364
365 // Impact parameter loop
366 for (int i = 0; i<=nbsteps;i++){
367
368 double bnn0 = bmin*exp(i*dlnb);
369 double bnn1 = bmin*exp((i+1)*dlnb);
370 double db = bnn1-bnn0;
371
372 // double PofB0 = 1.0;
373 // if( bnn0 > 1.4 )PofB0=0.0;
374 // double PofB1 = 1.0;
375 // if( bnn1 > 1.4 )PofB1=0.0;
376
377 double ppslope = 19.0;
378 double GammaProfile = exp(-bnn0*bnn0/(2.*hbarc*hbarc*ppslope));
379 double PofB0 = 1. - (1. - GammaProfile)*(1. - GammaProfile);
380 GammaProfile = exp(-bnn1*bnn1/(2.*hbarc*hbarc*ppslope));
381 double PofB1 = 1. - (1. - GammaProfile)*(1. - GammaProfile);
382
383 double Xarg = Egamma*bnn0/(hbarc*_beamLorentzGamma);
384 double loc_nofe0 = (_bbs.beam1().Z()*_bbs.beam1().Z()*alpha)/
385 (pi*pi);
386 loc_nofe0 *= (1./(Egamma*bnn0*bnn0));
387 loc_nofe0 *= Xarg*Xarg*(bessel::dbesk1(Xarg))*(bessel::dbesk1(Xarg));
388
389 Xarg = Egamma*bnn1/(hbarc*_beamLorentzGamma);
390 double loc_nofe1 = (_bbs.beam1().Z()*_bbs.beam1().Z()*alpha)/
391 (pi*pi);
392 loc_nofe1 *= (1./(Egamma*bnn1*bnn1));
393 loc_nofe1 *= Xarg*Xarg*(bessel::dbesk1(Xarg))*(bessel::dbesk1(Xarg));
394
395 local_sum += loc_nofe0*(1. - PofB0)*bnn0*db;
396 local_sum += loc_nofe1*(1. - PofB1)*bnn1*db;
397
398 }
399 // End Impact parameter loop
400
401 // Note: 2*pi --> pi because of no factor 2 above
402 double flux_r=local_sum*pi;
403 return flux_r;
404
405 // bmin = nuclearRadius+nuclearRadius;
406 // flux_r = nepoint(Egamma,bmin);
407 // return flux_r;
408 }
409
410 // first call? - initialize - calculate photon flux
411 Icheck=Icheck+1;
412 if(Icheck > 1) goto L1000f;
413
414 rZ=double(_bbs.beam1().Z());
415 rA=double(_bbs.beam1().A());
416 rZ2=double(_bbs.beam2().Z()); //Sergey--dAu
417 rA2=double(_bbs.beam2().A()); //Sergey
418
419 // Nuclear breakup is done by PofB
420 // collect number of integration steps here, in one place
421
422 nbstep=1200;
423 nrstep=60;
424 nphistep=40;
425
426 // this last one is the number of energy steps
427 nstep=100;
428
429 // following previous choices, take Emin=10 keV at LHC, Emin = 1 MeV at RHIC
430 Emin=1.E-5;
431 if (_beamLorentzGamma < 500)
432 Emin=1.E-3;
433
434 // maximum energy is 6 times the cutoff
435 // Emax=12.*hbarc*_beamLorentzGamma/RNuc;
436 Emax=6.*hbarc*_beamLorentzGamma/maxradius;
437
438 // >> lnEmin <-> ln(Egamma) for the 0th bin
439 // >> lnEmax <-> ln(Egamma) for the last bin
440
441 lnEmin=log(Emin);
442 lnEmax=log(Emax);
443 dlnE=(lnEmax-lnEmin)/nstep;
444
445 cout<<" Calculating flux for photon energies from E= "<<Emin
446 <<" to "<<Emax<<" GeV (CM frame) "<<endl;
447
448
449 stepmult= exp(log(Emax/Emin)/double(nstep));
450 energy=Emin;
451
452 for (int j = 1; j<=nstep;j++){
453 energy=energy*stepmult;
454
455 // integrate flux over 2R_A < b < 2R_A+ 6* gamma hbar/energy
456 // use exponential steps
457
458 bmin=RNuc+RNuc2; //2.*nuclearRadius; Sergey
459 bmax=bmin + 6.*hbarc*_beamLorentzGamma/energy;
460
461 bmult=exp(log(bmax/bmin)/double(nbstep));
462 biter=bmin;
463 integratedflux=0.;
464
465 if (_bbs.beam2().Z()==1&&_bbs.beam1().A()==2){
466 //This is for deuteron-gold
467 Xvar = (RNuc+RNuc2)*energy/(hbarc*(_beamLorentzGamma));
468
469 fluxelement = (2.0/pi)*rZ*rZ*alpha/
470 energy*(Xvar*bessel::dbesk0(Xvar)*bessel::dbesk1(Xvar)-(1/2)*Xvar*Xvar*
471 (bessel::dbesk1(Xvar)*bessel::dbesk1(Xvar)-bessel::dbesk0(Xvar)*bessel::dbesk0(Xvar)));
472
473 integratedflux=integratedflux+fluxelement;
474 }else if( (_bbs.beam1().A() == 1 && _bbs.beam2().A() != 1) || (_bbs.beam2().A() == 1 && _bbs.beam1().A() != 1) ){
475 // This is pA
476 if( _productionMode == PHOTONPOMERONINCOHERENT ){
477 // This is pA incoherent
478 // cout<<" This is incoherent! "<<" j = "<<j<<endl;
479 double zproj = 0.0;
480 double localbmin = 0.0;
481 if( _bbs.beam1().A() == 1 ){
482 zproj = (_bbs.beam2().Z());
483 localbmin = _bbs.beam2().nuclearRadius() + 0.7;
484 }
485 if( _bbs.beam2().A() == 1 ){
486 zproj = (_bbs.beam1().Z());
487 localbmin = _bbs.beam1().nuclearRadius() + 0.7;
488 }
489 integratedflux = zproj*zproj*nepoint(energy,localbmin);
490 } else if ( _productionMode == PHOTONPOMERONNARROW || _productionMode == PHOTONPOMERONWIDE ){
491 // cout<<" This is pA coherent "<<" j= "<<j<<endl;
492 double localbmin = 0.0;
493 if( _bbs.beam1().A() == 1 ){
494 localbmin = _bbs.beam2().nuclearRadius() + 0.7;
495 }
496 if( _bbs.beam2().A() == 1 ){
497 localbmin = _bbs.beam1().nuclearRadius() + 0.7;
498 }
499 integratedflux = nepoint(energy,localbmin);
500 }
501 }else{
502 for (int jb = 1; jb<=nbstep;jb++){
503 bold=biter;
504 biter=biter*bmult;
505 // When we get to b>20R_A change methods - just take the photon flux
506 // at the center of the nucleus.
507 if (biter > (10.*RNuc))
508 {
509 // if there is no nuclear breakup or only hadronic breakup, which only
510 // occurs at smaller b, we can analytically integrate the flux from b~20R_A
511 // to infinity, following Jackson (2nd edition), Eq. 15.54
512 Xvar=energy*biter/(hbarc*_beamLorentzGamma);
513 // Here, there is nuclear breakup. So, we can't use the integrated flux
514 // However, we can do a single flux calculation, at the center of the nucleus
515 // Eq. 41 of Vidovic, Greiner and Soff, Phys.Rev.C47,2308(1993), among other places
516 // this is the flux per unit area
517 fluxelement = (rZ*rZ*alpha*energy)*
518 (bessel::dbesk1(Xvar))*(bessel::dbesk1(Xvar))/
519 ((pi*_beamLorentzGamma*hbarc)*
520 (pi*_beamLorentzGamma*hbarc));
521
522 }//if biter>10
523 else{
524 // integrate over nuclear surface. n.b. this assumes total shadowing -
525 // treat photons hitting the nucleus the same no matter where they strike
526 fluxelement=0.;
527 deltar=RNuc/double(nrstep);
528 riter=-deltar/2.;
529
530 for (int jr =1; jr<=nrstep;jr++){
531 riter=riter+deltar;
532 // use symmetry; only integrate from 0 to pi (half circle)
533 deltaphi=pi/double(nphistep);
534 phiiter=0.;
535
536 for( int jphi=1;jphi<= nphistep;jphi++){
537 phiiter=(double(jphi)-0.5)*deltaphi;
538 // dist is the distance from the center of the emitting nucleus to the point in question
539 dist=sqrt((biter+riter*cos(phiiter))*(biter+riter*
540 cos(phiiter))+(riter*sin(phiiter))*(riter*sin(phiiter)));
541 Xvar=energy*dist/(hbarc*_beamLorentzGamma);
542 flux_r = (rZ*rZ*alpha*energy)*
543 (bessel::dbesk1(Xvar)*bessel::dbesk1(Xvar))/
544 ((pi*_beamLorentzGamma*hbarc)*
545 (pi*_beamLorentzGamma*hbarc));
546
547 // The surface element is 2.* delta phi* r * delta r
548 // The '2' is because the phi integral only goes from 0 to pi
549 fluxelement=fluxelement+flux_r*2.*deltaphi*riter*deltar;
550 // end phi and r integrations
551 }//for(jphi)
552 }//for(jr)
553 // average fluxelement over the nuclear surface
554 fluxelement=fluxelement/(pi*RNuc*RNuc);
555 }//else
556 // multiply by volume element to get total flux in the volume element
557 fluxelement=fluxelement*2.*pi*biter*(biter-bold);
558 // modulate by the probability of nuclear breakup as f(biter)
559 if (_beamBreakupMode > 1){
560 fluxelement=fluxelement*_bbs.probabilityOfBreakup(biter);
561 }
562 integratedflux=integratedflux+fluxelement;
563
564 } //end loop over impact parameter
565 } //end of else (pp, pA, AA)
566
567 // In lookup table, store k*dN/dk because it changes less
568 // so the interpolation should be better
569 dide[j]=integratedflux*energy;
570
571 }//end loop over photon energy
572
573 // for 2nd and subsequent calls, use lookup table immediately
574
575 L1000f:
576
577 lEgamma=log(Egamma);
578 if (lEgamma < (lnEmin+dlnE) || lEgamma > lnEmax){
579 flux_r=0.0;
580 cout<<" ERROR: Egamma outside defined range. Egamma= "<<Egamma
581 <<" "<<lnEmax<<" "<<(lnEmin+dlnE)<<endl;
582 }
583 else{
584 // >> Egamma between Ilt and Ilt+1
585 Ilt = int((lEgamma-lnEmin)/dlnE);
586 // >> ln(Egamma) for first point
587 lnElt = lnEmin + Ilt*dlnE;
588 // >> Interpolate
589 flux_r = dide[Ilt] + ((lEgamma-lnElt)/dlnE)*(dide[Ilt+1]- dide[Ilt]);
590 flux_r = flux_r/Egamma;
591 }
592
593 return flux_r;
594}
595
596
597//______________________________________________________________________________
598double
599photonNucleusCrossSection::nepoint(const double Egamma,
600 const double bmin)
601{
602 // Function for the spectrum of virtual photons,
603 // dn/dEgamma, for a point charge q=Ze sweeping
604 // past the origin with velocity gamma
605 // (=1/SQRT(1-(V/c)**2)) integrated over impact
606 // parameter from bmin to infinity
607 // See Jackson eq15.54 Classical Electrodynamics
608 // Declare Local Variables
609 double beta,X,C1,bracket,nepoint_r;
610
611 beta = sqrt(1.-(1./(_beamLorentzGamma*_beamLorentzGamma)));
612 X = (bmin*Egamma)/(beta*_beamLorentzGamma*hbarc);
613
614 bracket = -0.5*beta*beta*X*X*(bessel::dbesk1(X)*bessel::dbesk1(X)
615 -bessel::dbesk0(X)*bessel::dbesk0(X));
616
617 bracket = bracket+X*bessel::dbesk0(X)*bessel::dbesk1(X);
618
619 // C1=(2.*double((_bbs.beam1().Z())*(_bbs.beam1().Z()))*
620 // alpha)/pi;
621
622 // Note: NO Z*Z!!
623 C1=(2.*alpha)/pi;
624
625 nepoint_r = C1*(1./beta)*(1./beta)*(1./Egamma)*bracket;
626
627 return nepoint_r;
628
629}
630
631
632//______________________________________________________________________________
633double
634photonNucleusCrossSection::sigmagp(const double Wgp)
635{
636 // >> Function for the gamma-proton --> VectorMeson
637 // >> cross section. Wgp is the gamma-proton CM energy.
638 // >> Unit for cross section: fm**2
639
640 double sigmagp_r=0.;
641
642 switch(_particleType)
643 {
644 case RHO:
645 case RHOZEUS:
646 case FOURPRONG:
647 sigmagp_r=1.E-4*(5.0*exp(0.22*log(Wgp))+26.0*exp(-1.23*log(Wgp)));
648 break;
649 case OMEGA:
650 sigmagp_r=1.E-4*(0.55*exp(0.22*log(Wgp))+18.0*exp(-1.92*log(Wgp)));
651 break;
652 case PHI:
653 sigmagp_r=1.E-4*0.34*exp(0.22*log(Wgp));
654 break;
655 case JPSI:
656 case JPSI_ee:
657 case JPSI_mumu:
658 sigmagp_r=(1.0-((_channelMass+protonMass)*(_channelMass+protonMass))/(Wgp*Wgp));
659 sigmagp_r*=sigmagp_r;
660 sigmagp_r*=1.E-4*0.00406*exp(0.65*log(Wgp));
661 // sigmagp_r=1.E-4*0.0015*exp(0.80*log(Wgp));
662 break;
663 case JPSI2S:
664 case JPSI2S_ee:
665 case JPSI2S_mumu:
666 sigmagp_r=(1.0-((_channelMass+protonMass)*(_channelMass+protonMass))/(Wgp*Wgp));
667 sigmagp_r*=sigmagp_r;
668 sigmagp_r*=1.E-4*0.00406*exp(0.65*log(Wgp));
669 sigmagp_r*=0.166;
670 // sigmagp_r=0.166*(1.E-4*0.0015*exp(0.80*log(Wgp)));
671 break;
672 case UPSILON:
673 case UPSILON_ee:
674 case UPSILON_mumu:
675 // >> This is W**1.7 dependence from QCD calculations
676 sigmagp_r=1.E-10*(0.060)*exp(1.70*log(Wgp));
677 break;
678 case UPSILON2S:
679 case UPSILON2S_ee:
680 case UPSILON2S_mumu:
681 sigmagp_r=1.E-10*(0.0259)*exp(1.70*log(Wgp));
682 break;
683 case UPSILON3S:
684 case UPSILON3S_ee:
685 case UPSILON3S_mumu:
686 sigmagp_r=1.E-10*(0.0181)*exp(1.70*log(Wgp));
687 break;
688 default: cout<< "!!! ERROR: Unidentified Vector Meson: "<< _particleType <<endl;
689 }
690 return sigmagp_r;
691}
692
693
694//______________________________________________________________________________
695double
696photonNucleusCrossSection::sigma_A(const double sig_N)
697{
698 // Nuclear Cross Section
699 // sig_N,sigma_A in (fm**2)
700
701 double sum;
702 double b,bmax,Pint,arg,sigma_A_r;
703
704 int NGAUSS;
705
706 double xg[17]=
707 {.0,
708 .0483076656877383162,.144471961582796493,
709 .239287362252137075, .331868602282127650,
710 .421351276130635345, .506899908932229390,
711 .587715757240762329, .663044266930215201,
712 .732182118740289680, .794483795967942407,
713 .849367613732569970, .896321155766052124,
714 .934906075937739689, .964762255587506430,
715 .985611511545268335, .997263861849481564
716 };
717
718 double ag[17]=
719 {.0,
720 .0965400885147278006, .0956387200792748594,
721 .0938443990808045654, .0911738786957638847,
722 .0876520930044038111, .0833119242269467552,
723 .0781938957870703065, .0723457941088485062,
724 .0658222227763618468, .0586840934785355471,
725 .0509980592623761762, .0428358980222266807,
726 .0342738629130214331, .0253920653092620595,
727 .0162743947309056706, .00701861000947009660
728 };
729
730 NGAUSS=16;
731
732 // Check if one or both beams are nuclei
733 int A_1 = _bbs.beam1().A();
734 int A_2 = _bbs.beam2().A();
735 if( A_1 == 1 && A_2 == 1)cout<<" This is pp, you should not be here..."<<endl;
736
737 // CALCULATE P(int) FOR b=0.0 - bmax (fm)
738 bmax = 25.0;
739 sum = 0.;
740 for(int IB=1;IB<=NGAUSS;IB++){
741
742 b = 0.5*bmax*xg[IB]+0.5*bmax;
743
744 if( A_1 == 1 && A_2 != 1){
745 arg=-sig_N*_bbs.beam2().rho0()*_bbs.beam2().thickness(b);
746 }else if(A_2 == 1 && A_1 != 1){
747 arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
748 }else{
749 arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
750 }
751
752 Pint=1.0-exp(arg);
753 sum=sum+2.*pi*b*Pint*ag[IB];
754
755
756 b = 0.5*bmax*(-xg[IB])+0.5*bmax;
757
758 if( A_1 == 1 && A_2 != 1){
759 arg=-sig_N*_bbs.beam2().rho0()*_bbs.beam2().thickness(b);
760 }else if(A_2 == 1 && A_1 != 1){
761 arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
762 }else{
763 arg=-sig_N*_bbs.beam1().rho0()*_bbs.beam1().thickness(b);
764 }
765
766 Pint=1.0-exp(arg);
767 sum=sum+2.*pi*b*Pint*ag[IB];
768
769 }
770
771 sum=0.5*bmax*sum;
772
773 sigma_A_r=sum;
774
775 return sigma_A_r;
776}
777
778//______________________________________________________________________________
779double
780photonNucleusCrossSection::sigma_N(const double Wgp)
781{
782 // Nucleon Cross Section in (fm**2)
783 double cs = sqrt(16. * pi * _vmPhotonCoupling * _slopeParameter * hbarc * hbarc * sigmagp(Wgp) / alpha);
784 return cs;
785}
786
787
788//______________________________________________________________________________
789double
790photonNucleusCrossSection::breitWigner(const double W,
791 const double C)
792{
793 // use simple fixed-width s-wave Breit-Wigner without coherent backgorund for rho'
794 // (PDG '08 eq. 38.56)
795 if(_particleType==FOURPRONG) {
796 if (W < 4.01 * pionChargedMass)
797 return 0;
798 const double termA = _channelMass * _width;
799 const double termA2 = termA * termA;
800 const double termB = W * W - _channelMass * _channelMass;
801 return C * _ANORM * _ANORM * termA2 / (termB * termB + termA2);
802 }
803
804 // Relativistic Breit-Wigner according to J.D. Jackson,
805 // Nuovo Cimento 34, 6692 (1964), with nonresonant term. A is the strength
806 // of the resonant term and b the strength of the non-resonant
807 // term. C is an overall normalization.
808
809 double ppi=0.,ppi0=0.,GammaPrim,rat;
810 double aa,bb,cc;
811
812 double nrbw_r;
813
814 // width depends on energy - Jackson Eq. A.2
815 // if below threshold, then return 0. Added 5/3/2001 SRK
816 // 0.5% extra added for safety margin
817 if( _particleType==RHO ||_particleType==RHOZEUS){
818 if (W < 2.01*pionChargedMass){
819 nrbw_r=0.;
820 return nrbw_r;
821 }
822 ppi=sqrt( ((W/2.)*(W/2.)) - pionChargedMass * pionChargedMass);
823 ppi0=0.358;
824 }
825
826 // handle phi-->K+K- properly
827 if (_particleType == PHI){
828 if (W < 2.*kaonChargedMass){
829 nrbw_r=0.;
830 return nrbw_r;
831 }
832 ppi=sqrt( ((W/2.)*(W/2.))- kaonChargedMass*kaonChargedMass);
833 ppi0=sqrt( ((_channelMass/2.)*(_channelMass/2.))-kaonChargedMass*kaonChargedMass);
834 }
835
836 //handle J/Psi-->e+e- properly
837 if (_particleType==JPSI || _particleType==JPSI2S){
838 if(W<2.*mel){
839 nrbw_r=0.;
840 return nrbw_r;
841 }
842 ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
843 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
844 }
845 if (_particleType==JPSI_ee){
846 if(W<2.*mel){
847 nrbw_r=0.;
848 return nrbw_r;
849 }
850 ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
851 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
852 }
853 if (_particleType==JPSI_mumu){
854 if(W<2.*muonMass){
855 nrbw_r=0.;
856 return nrbw_r;
857 }
858 ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
859 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
860 }
861 if (_particleType==JPSI2S_ee){
862 if(W<2.*mel){
863 nrbw_r=0.;
864 return nrbw_r;
865 }
866 ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
867 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
868 }
869 if (_particleType==JPSI2S_mumu){
870 if(W<2.*muonMass){
871 nrbw_r=0.;
872 return nrbw_r;
873 }
874 ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
875 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
876 }
877
878 if(_particleType==UPSILON || _particleType==UPSILON2S ||_particleType==UPSILON3S ){
879 if (W<2.*muonMass){
880 nrbw_r=0.;
881 return nrbw_r;
882 }
883 ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
884 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
885 }
886
887 if(_particleType==UPSILON_mumu || _particleType==UPSILON2S_mumu ||_particleType==UPSILON3S_mumu ){
888 if (W<2.*muonMass){
889 nrbw_r=0.;
890 return nrbw_r;
891 }
892 ppi=sqrt(((W/2.)*(W/2.))-muonMass*muonMass);
893 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-muonMass*muonMass);
894 }
895
896 if(_particleType==UPSILON_ee || _particleType==UPSILON2S_ee ||_particleType==UPSILON3S_ee ){
897 if (W<2.*mel){
898 nrbw_r=0.;
899 return nrbw_r;
900 }
901 ppi=sqrt(((W/2.)*(W/2.))-mel*mel);
902 ppi0=sqrt(((_channelMass/2.)*(_channelMass/2.))-mel*mel);
903 }
904
905 if(ppi==0.&&ppi0==0.)
906 cout<<"Improper Gammaacrosssection::breitwigner, ppi&ppi0=0."<<endl;
907
908 rat=ppi/ppi0;
909 GammaPrim=_width*(_channelMass/W)*rat*rat*rat;
910
911 aa=_ANORM*sqrt(GammaPrim*_channelMass*W);
912 bb=W*W-_channelMass*_channelMass;
913 cc=_channelMass*GammaPrim;
914
915 // First real part squared
916 nrbw_r = (( (aa*bb)/(bb*bb+cc*cc) + _BNORM)*( (aa*bb)/(bb*bb+cc*cc) + _BNORM));
917
918 // Then imaginary part squared
919 nrbw_r = nrbw_r + (( (aa*cc)/(bb*bb+cc*cc) )*( (aa*cc)/(bb*bb+cc*cc) ));
920
921 // Alternative, a simple, no-background BW, following J. Breitweg et al.
922 // Eq. 15 of Eur. Phys. J. C2, 247 (1998). SRK 11/10/2000
923 // nrbw_r = (_ANORM*_mass*GammaPrim/(bb*bb+cc*cc))**2
924
925 nrbw_r = C*nrbw_r;
926
927 return nrbw_r;
928}