Lineshapes

Detailed Description

The lineshapes are stored in a static factory and can be accessed by key from anywhere in the program. For example, consider a \(K^{*}(892)^{0}\) resonance decaying into a kaon and a pion, the propagation of which could be described using the Relativistic Breit Wigner (BW) lineshape. The corresponding decay descriptor would be

K*(892)[BW]{K+,pi-}

where in this case, the BW is redundant, as this the default if no alternative is specified. Now consider the broad scalar \(K^{*}(1430)^{0}\) meson, which cannot readily be described by a simple Breit Wigner due to a quasi nonresonant amplitude (alternatively, due to the presence of an additional very broad scalar at lower masses, the \(\kappa(800)\)). One alternative parameterisation of this system is the LASS lineshape which can be used as

K(0)*(1430)[LASS]{K+,pi-}

Lineshapes for describing different systems are detailed below. Some, such as the LASS shape or kMatrix, pertain to the specific particles and final states. Others, such as CoupledChannel or Spline can flexibly describe a variety of systems, but therefore require a more detailed specification by the user.

Generally, the relativistic Breit-Wigner a sufficient description for many purposes for nonscalar resonances that decay to a single two-body final state or are relatively far from relevant thresholds.More complex systems require more specialised descriptions.

Namespaces
namespace	AmpGen::Lineshape
	Namespace that contains all lineshapes, i.e.

Classes
class	AmpGen::Lineshape::CoupledChannel
	Description of a resonance that decays to multiple two and three-body final states. More...
class	AmpGen::Lineshape::BW
	Simple two-body Breit-Wigner lineshape that describes relatively narrow, isolated resonances that couple to a single channel / orbital configuration. More...
class	AmpGen::Lineshape::SBW
	Breit-Wigner lineshape with fixed width. More...
class	AmpGen::Lineshape::NonRelBW
	Nonrelativistic Breit-Wigner lineshape. More...
class	AmpGen::Lineshape::GounarisSakurai
	Gounaris-Sakurai lineshape models dispersive corrections to the \(I=1,J=1\) \(\pi\pi\) propagator. More...
class	AmpGen::Lineshape::LASS
	Description of the \( K\pi \) S-wave, based on the fits to scattering data. More...
class	AmpGen::Lineshape::GLASS
	Generalised description of the \( K\pi\) S-wave, taken from BABAR / BELLE analysis of \( D^{0} \to K_{S}^{0} \pi^{+} \pi^{-} \) https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.112012. More...
class	AmpGen::Lineshape::Flatte
	Lineshape to describe resonances with coupled channels such as \(f_{0}(980)^{0} / a_{0}(980) \). More...
class	AmpGen::Lineshape::Gaussian
	Gaussian shape for (relatively) long lived states that are limited by experimental resolution, rather than natural width. More...
class	AmpGen::Lineshape::PolyNR
	Polynominal shape \( \mathcal{A}(s) = \sum^n_i c_i s^{i} \) where the sum is to lineshapeModifier::Degree, and the free parameters of the shape are lineshapeModifier_ci. More...
class	AmpGen::Lineshape::Poly
	Polynominal shape \( \mathcal{A}(s) = \sqrt{ \sum_{ij} c_{ij} s^{i} (s^\prime)^{j} } \) where the sum is to lineshapeModifier::Degree, and the free parameters of the shape are lineshapeModifier_cij. More...
class	AmpGen::Lineshape::FOCUS
	K matrix amplitudes used for I=1/2 and I=3/2 in the description of the \( K\pi \) S-wave in the analysis of \( D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}\) https://arxiv.org/abs/0705.2248. More...
class	AmpGen::Lineshape::kMatrixSimple
	Simple and flexible K matrix that implements a variable number of scalar channels and poles. More...
class	AmpGen::Lineshape::MIPWA
	Model-Independent Partial Wave parameterisation using cubic splines. More...
class	AmpGen::Lineshape::GSpline
	Lineshape with an arbitrary running width determined from a spline. More...
class	AmpGen::Lineshape::GenericKmatrix
	Implementation of a generic K-matrix. More...
class	AmpGen::Lineshape::EtaDalitz
	Empirical Dalitz plot distribution for \( \eta \rightarrow \pi^{+}\pi^{-}\pi^{0} \). More...
class	AmpGen::Lineshape::TD
	(Linear) time dependence More...

Functions
	AmpGen::Lineshape::DECLARE_LINESHAPE (kMatrix)
	Anisovich-Sarantsev Isoscalar K-matrix from https://arxiv.org/abs/hep-ph/0204328.

Function Documentation

DECLARE_LINESHAPE()

AmpGen::Lineshape::DECLARE_LINESHAPE

(

kMatrix

)

Describes the isoscalar \( \pi\pi, KK, 4\pi \eta\eta, \eta\eta^\prime\) S-wave in terms of a five-by-five K-matrix and corresponding P-vector couplings. Includes a large number of parameters that can be fixed from the above publication. These parameters can be found in the options directory, which in turn can be includes in the fit by adding

Import $AMPGENROOT/options/kMatrix.opt

to the user configuration file.