Elegent::CoulombInterference Class Reference

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

enum Elegent::CoulombInterference::CIMode

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)

enum Elegent::CoulombInterference::FFType

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

t	in GeV^2, negative

TComplex Elegent::CoulombInterference::Amp_pure

(

double

t

)

const

pure Coulomb amplitude (PC).

Parameters

t	in 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

t	in 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

t	in 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

t	in 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

t	in GeV^2, negative

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

inline

d/dt of the effective form factor square.

Parameters

t	in GeV^2, negative

TComplex Elegent::CoulombInterference::Phase

(

double

t

)

const

interference phase WITH the alpha factor.

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

Parameters

t	in 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

t	in 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

t	in GeV^2, negative

TComplex Elegent::CoulombInterference::R

(

double

t

)

const

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

Parameters

t	in 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

t	in GeV^2, negative
cutoff	in GeV^2, negative

TComplex Elegent::CoulombInterference::Z

(

double

t

)

const

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

Parameters

t	in GeV^2, negative

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

• src/libElegent/interface/CoulombInterference.h
• src/libElegent/src/CoulombInterference.cc