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BSWModel.cc
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/**************************************************
* This file is a part of the Elegent package:
* http://elegent.hepforge.org/
*************************************************/
#include "interface/BSWModel.h"
#include "interface/Constants.h"
#include "interface/Math.h"
using namespace std;
using namespace Elegent;
//----------------------------------------------------------------------------------------------------
void BSWModel::Init(BSWModel::ModeType _mode, bool _presampled)
{
mode = _mode;
presampled = _presampled;
// Eq. (6) in [3]
c = 0.167;
cp = 0.748;
// Table 1 in [3]
m1 = 0.577; m1sq = m1*m1; // 0.333
m2 = 1.719; m2sq = m2*m2; // 2.955
f = 6.971;
a = 1.858; asq = a*a; // 3.452
// Table 2 in [3], b's given in text of section 3 in [3]
A2.Init( -24.269, 0., 0.357, 1., +1);
omega.Init( -167.329, 0., 0.323, 0.795, -1);
rho.Init( 124.919, 8.54, 0.320, 1., -1);
upper_bound_t = -500.; precision_t = 1E-15;
upper_bound_b = 50.; precision_b = 1E-12;
regge_fac(1., 0.);
// save value of S0(0)
S00 = S0(0.);
if (presampled)
BuildSample(25001);
}
//----------------------------------------------------------------------------------------------------
void BSWModel::Print() const
{
printf(">> BSWModel::Print\n");
printf("\tc=%.3f\tc'=%.3f\tm1=%.3f\tm2=%.3f\tf=%.3f\ta=%.3f\n", c, cp, m1, m2, f, a);
printf("\tA2: C=%.3f\tb=%.3f\talpha=%.3f\taplha'=%.3f\n", A2.C, A2.b, A2.a, A2.ap);
printf("\tomega: C=%.3f\tb=%.3f\talpha=%.3f\taplha'=%.3f\n", omega.C, omega.b, omega.a, omega.ap);
printf("\trho: C=%.3f\tb=%.3f\talpha=%.3f\taplha'=%.3f\n", rho.C, rho.b, rho.a, rho.ap);
printf("\n");
printf("\tpresampled = %u\n", presampled);
if (presampled)
printf("\t\tsample size = %u, db = %.1E\n", data_N, data_db);
printf("\n");
printf("\tintegration parameters:\n");
printf("\t\tt: upper bound = %.1E, precision = %.1E\n", upper_bound_t, precision_t);
printf("\t\tb: upper bound = %.1E, precision = %.1E\n", upper_bound_b, precision_b);
}
//----------------------------------------------------------------------------------------------------
string BSWModel::GetModeString() const
{
string ms = "unknown/";
if (mode == mPomReg) ms = "Pom+Reg";
if (mode == mPom) ms = "Pomeron";
if (mode == mReg) ms = "Regge";
if (presampled)
ms += "presampled";
//sprintf(str, "t:%.0f,%.0E b:%.0f,%.0E", upper_bound_t, precision_t, upper_bound_b, precision_b);
return ms;
}
//----------------------------------------------------------------------------------------------------
double BSWModel::Ft(double t) const
{
double G = 1. / (1. - t/m1sq) / (1. - t/m2sq);
return f*G*G* (asq + t) / (asq - t);
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Rt(Trajectory tr, double t) const
{
/// s0 = 1 GeV^2
double alpha = tr.a + tr.ap * t;
return tr.C * exp(tr.b * t + cnts->ln_s * alpha) * (1. + tr.sig * TComplex::Exp(-i*cnts->pi*alpha));
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::R0t(double t) const
{
return Rt(A2, t) + Rt(omega, t) + Rt(rho, t);
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::S0(double t) const
{
// the s term
TComplex term_s = pow(cnts->s, c) / pow(cnts->ln_s, cp);
// the u term
double u = 4.*cnts->proton_mass*cnts->proton_mass - cnts->s - t;
TComplex Lnu = TComplex(log(fabs(u)), -cnts->pi); // ambiguity in the article: which sign in +-pi?
double Lnu_rho2 = Lnu.Rho2();
double Lnu_theta = atan2(Lnu.Im(), Lnu.Re()); // atan2 results in (-pi, +pi)
TComplex LnLnu = TComplex(0.5*log(Lnu_rho2), Lnu_theta);
TComplex term_u = TComplex::Exp(c * Lnu) / TComplex::Exp(cp * LnLnu);
#ifdef DEBUG
printf(">> BSWModel::S0\n");
printf("\ts=%E, u=%E\n", cnts->s, u);
printf("\tLn u=%E +i%E\n", Lnu.Re(), Lnu.Im());
printf("\tLn Ln u=%E +i%E\n", LnLnu.Re(), LnLnu.Im());
printf("\tterm_s: %E + i%E\n", term_s.Re(), term_s.Im());
printf("\tterm_u: %E + i%E\n", term_u.Re(), term_u.Im());
#endif
return term_s + term_u;
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Omega0t(double t) const
{
// S00 = S0(0) instead of S0(t) is used here, valid for high s only !!
switch (mode) {
case mPomReg:
return S00*Ft(t) + R0t(t) / cnts->s / regge_fac;
case mPom:
return S00*Ft(t);
case mReg:
return R0t(t);
}
return TComplex(0, 0);
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Omega0t_J0(double *t, double *b, const void *obj)
{
return ((BSWModel *)obj)->Omega0t(t[0]) * TMath::BesselJ0(b[0] * sqrt(-t[0]));
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Omega0b(double b) const
{
// the 1/2 factor is consequence of dt integration (instead of q dq)
return 0.5 * CmplxInt(this, Omega0t_J0, upper_bound_t, 0., &b, precision_t);
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::prf0(double b) const
{
return 1. - TComplex::Exp( - Omega0b(b) );
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Prf(double b) const
{
return prf0(b / cnts->hbarc) * i / 2.;
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::prf0_J0(double *b, double *q, const void *obj)
{
BSWModel *m = (BSWModel *) obj;
if (m->presampled)
return m->SampleEval(b[0]) * b[0] * TMath::BesselJ0(b[0] * q[0]);
else
return m->prf0(b[0]) * b[0] * TMath::BesselJ0(b[0] * q[0]);
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::Amp(double t) const
{
double q = sqrt(-t);
return i * cnts->p_cms * cnts->sqrt_s * CmplxInt(this, prf0_J0, 0., upper_bound_b, &q, precision_b);
}
//----------------------------------------------------------------------------------------------------
void BSWModel::BuildSample(unsigned int samples)
{
printf(">> BSWModel::BuildSample > Building %u samples...\n", samples);
data_re.clear();
data_re.reserve(samples);
data_im.clear();
data_im.reserve(samples);
#ifdef DEBUG
data_b.clear();
data_b.reserve(samples);
#endif
double db = upper_bound_b / (samples - 1);
data_db = db;
data_N = samples;
double b = 0.;
for (unsigned int i = 0; i < samples; i++, b += db)
{
TComplex v = prf0(b);
#ifdef DEBUG
//printf("v=%.5f: re=%E, im=%E\n", b, v.Re(), v.Im());
data_b.push_back(b);
#endif
data_re.push_back(v.Re());
data_im.push_back(v.Im());
}
}
//----------------------------------------------------------------------------------------------------
TComplex BSWModel::SampleEval(double b)
{
unsigned int idx = (int)(b / data_db);
if (idx + 1 > data_N - 1)
return TComplex(0, 0);
double f = b/data_db - idx;
return TComplex(
(data_re[idx+1] - data_re[idx])*f + data_re[idx],
(data_im[idx+1] - data_im[idx])*f + data_im[idx]
);
}

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