Elegent is hosted by Hepforge, IPPP Durham
Elegent

Coulomb hadron interference for elastic scattering. More...

#include <CoulombInterference.h>

Public Types

enum  CIMode {
  mPC, mPH, mWY, mSWY,
  mKL
}
 the mode of coulomb interference More...
 
enum  FFType {
  ffNone, ffDipole, ffHofstadter, ffBorkowski,
  ffKelly, ffArrington, ffPuckett, ffPuckettEl
}
 form factor type More...
 

Public Member Functions

std::string GetModeString () const
 
double GetT ()
 
void Print () const
 print the parameters
 
double A_term (double t) const
 A: \(\int_{t_{min}}^0 \log(t'/t) * d/dt(FF^2(t'))\). More...
 
double I_integral (double t, double tp) const
 
TComplex B_term (double t) const
 B: \({1 / 2\pi} \int_{t_{min}}^0 [ F^N(t') / F^N(t) - 1] I(t, t')\). More...
 
double C_term (double t) const
 C: the correction for non-vanishing form factors at t_min. More...
 
std::string GetFFName () const
 
double FF_dipole (double t) const
 dipole form factor
 
double FF_e (double t) const
 eletric form factor. More...
 
double FF_m (double t) const
 magnetic form factor. More...
 
double FF_sq (double t) const
 square of the effective form factor. More...
 
double FF_sq_prime (double t) const
 d/dt of the effective form factor square. More...
 
TComplex Phi_WY (double t) const
 full West-Yennie phase (with alpha factor). More...
 
TComplex Phi_SWY (double t) const
 simplified West-Yennie phase
 
TComplex Psi_KL (double t) const
 Kundrat-Lokajicek phase (with alpha factor). More...
 
TComplex Phase (double t) const
 interference phase WITH the alpha factor. More...
 
TComplex Amp_pure (double t) const
 pure Coulomb amplitude (PC). More...
 
TComplex Amp_WY (double t) const
 
TComplex Amp_SWY (double t) const
 
TComplex Amp_KL (double t) const
 
TComplex Amp (double t) const
 total Amplitude according to the choice in `mode'
 
TComplex R (double t) const
 ratio (|KL|^2 - |WY|^2) / |KL|^2. More...
 
TComplex R_with_cutoff (double t, double cutoff) const
 for |t| < |cutoff|: (|KL|^2 - |WY|^2) / |KL|^2, otherwise (|KL|^2 - |PH|^2) / |KL|^2. More...
 
TComplex Z (double t) const
 ratio (|KL|^2 - |PH|^2 - |PC|^2) / |KL|^2. More...
 
TComplex C (double t) const
 ratio (|KL|^2 - |PH|^2) / |PH|^2. More...
 

Public Attributes

enum Elegent::CoulombInterference::CIMode mode
 
enum Elegent::CoulombInterference::FFType ffType
 
double tau
 the size of the region around t=t' which is cut off from integration, see B_term method
 
double T
 the upper bound of the integration in A_term and B_term is |t|+T
 
double precision
 precision of the integration
 
unsigned long integ_workspace_size
 
gsl_integration_workspace * integ_workspace
 
gsl_integration_workspace * integ_workspace2
 

Static Protected Member Functions

static double A_integrand (double tt, double *par, const void *vobj)
 the integrand of the A term
 
static double I_integrand (double phi, double *par, const void *vobj)
 the integrand of I(t, t') integral
 
static TComplex B_integrand (double tp, double *par, const void *vobj)
 the integrand of the B term
 

Detailed Description

Coulomb hadron interference for elastic scattering.

Member Enumeration Documentation

the mode of coulomb interference

Enumerator
mPC 

pure electromagnetic amplitude (Born/OPE approximation) [default]

mPH 

pure hadronic amplitude

mWY 

WY formula.

mSWY 

simplified WY formula

mKL 

(corrected) KL formula (includes the one of Cahn)

form factor type

Enumerator
ffNone 

form factor = 1

ffDipole 

dipole form factor, in G_eff, G_E and G_M (G_M(0) = 1)

ffHofstadter 

Hofstader et al.: Rev. Mod. Phys. 30 (1958)

ffBorkowski 

Borkowski et al.: Nucl. Phys. B93 (1975)

ffKelly 

Kelly: Phys. Rev. C70 (2004)

ffArrington 

Arrington et al.: Phys. Rev C76 (2007)

ffPuckett 

Puckett et al.: arXiv 1008.0855v1 [default].

ffPuckettEl 

only electric form-factor of Puckett et al.

Member Function Documentation

double Elegent::CoulombInterference::A_term ( double  t) const

A: \(\int_{t_{min}}^0 \log(t'/t) * d/dt(FF^2(t'))\).

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::Amp_pure ( double  t) const

pure Coulomb amplitude (PC).

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::B_term ( double  t) const

B: \({1 / 2\pi} \int_{t_{min}}^0 [ F^N(t') / F^N(t) - 1] I(t, t')\).

Parameters
tin GeV^2, negative

Function B_integrand(t', t) has problems at point t' = t. It is not defined there (left and right limits are different), it is not continuous at the point. To avoid problems, we cut out a small interval (t-tau, t+tau), tau > 0 from the the integration region (t_min, 0). The second note concerns exponential fall off of B_integrand as one goes with t' away from t. Thus one can take (t-T, 0) instead of (t_min, 0). Of course, T must be suffciently large.

In fact, one must be careful with lower bound t+tau, since it must be less than 0. Otherwise contribution from the region (t+tau, 0) isn't present.

TComplex Elegent::CoulombInterference::C ( double  t) const

ratio (|KL|^2 - |PH|^2) / |PH|^2.

Parameters
tin GeV^2, negative
double Elegent::CoulombInterference::C_term ( double  t) const

C: the correction for non-vanishing form factors at t_min.

\(FF^2(t_{min} \log(t/t_{min}))\)

Parameters
tin GeV^2, negative
double Elegent::CoulombInterference::FF_e ( double  t) const

eletric form factor.

normalized such FF_e(0) = 1, t negative

t is negative

double Elegent::CoulombInterference::FF_m ( double  t) const

magnetic form factor.

normalized such FF_m(0) = 1, t negative

t is negative

double Elegent::CoulombInterference::FF_sq ( double  t) const

square of the effective form factor.

Parameters
tin GeV^2, negative
double Elegent::CoulombInterference::FF_sq_prime ( double  t) const
inline

d/dt of the effective form factor square.

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::Phase ( double  t) const

interference phase WITH the alpha factor.

returns either \(-\Phi\) or \(\Psi\)

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::Phi_WY ( double  t) const

full West-Yennie phase (with alpha factor).

that is the \(\alpha\Phi\) in the decomposition \(F^{C+H} = F^C e^{i \alpha \Phi} + F^H\)

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::Psi_KL ( double  t) const

Kundrat-Lokajicek phase (with alpha factor).

that is the \(\alpha\Phi\) in the decomposition \(F^{C+H} = F^C + F^H * e^{i \alpha \Psi}\)

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::R ( double  t) const

ratio (|KL|^2 - |WY|^2) / |KL|^2.

Parameters
tin GeV^2, negative
TComplex Elegent::CoulombInterference::R_with_cutoff ( double  t,
double  cutoff 
) const

for |t| < |cutoff|: (|KL|^2 - |WY|^2) / |KL|^2, otherwise (|KL|^2 - |PH|^2) / |KL|^2.

Parameters
tin GeV^2, negative
cutoffin GeV^2, negative
TComplex Elegent::CoulombInterference::Z ( double  t) const

ratio (|KL|^2 - |PH|^2 - |PC|^2) / |KL|^2.

Parameters
tin GeV^2, negative

The documentation for this class was generated from the following files: