Detailed Description

The lineshape was first described by S.M.Flatté in Phys. Lett B. 63, 224 (1976), and describes a single, isolated resonance that couples to a pair of channels, which can have a large impact on the lineshape if the opening of one of the channels is near to the mass of the resonance. This lineshape can be considered a special case of the K matrix or coupled channel formalisms, and is explicitly implemented with the couplings and channels for the \(f_{0}(980)^{0}\) and \(a_{0}(980)^{0}\) resonances, which couple to the channels \(\pi\pi\) and \(KK\) for the \(f_{0}(980)^{0}\) and \(\pi\eta\) and \(KK\) for the \(a_{0}(980)^{0}\). In particular, the opening of the \(KK\) threshold close to the resonance mass strongly distorts the lineshape. For a generic implementation of a coupled channel, see the CoupledChannel lineshape.

\[ \mathcal{A}(s) = \frac{1}{ m^2 - s - i m \Gamma(s) }, \]

where the running width is given by

\[ \Gamma(s) = \frac{ g_{\pi\pi} }{s} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\pi}^2) + \frac{g_{KK}}{g_{\pi\pi}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right) \]

or

\[ \Gamma(s) = \frac{ g_{\pi\eta}}{s} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\eta}^2) + \frac{g_{KK}}{g_{\pi\eta}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right) \]

for the \(f_0(980)^{0}\) and the \(a_0(980)^{0}\), respectively.

Definition at line 297 of file Lineshapes.h.

Public Member Functions
	Flatte ()

AmpGen::Expression	get (const AmpGen::Expression &s, const AmpGen::Expression &s1, const AmpGen::Expression &s2, const std::string &particleName, const unsigned int &L, const std::string &lineshapeModifier, AmpGen::DebugSymbols *dbexpressions=0) const override

AmpGen::Expression	get (const AmpGen::Particle &p, const std::string &lineshapeModifier, AmpGen::DebugSymbols *dbexpressions=nullptr) const override

virtual Expression	get (const Expression &s, const Expression &s1, const Expression &s2, const std::string &particleName, const unsigned &L, const std::string &lineshapeModifier, DebugSymbols *dbexpressions=nullptr) const =0

Base *	create ()

Inheritance diagram for AmpGen::Lineshape::Flatte:

Constructor & Destructor Documentation

◆ Flatte()

AmpGen::Lineshape::Flatte::Flatte ( )

inline

Definition at line 297 of file Lineshapes.h.

Member Function Documentation

◆ create()

Base * AmpGen::Lineshape::Base::create ( )

inlineinherited

Definition at line 98 of file Lineshapes.h.

◆ get() [1/3]

virtual Expression AmpGen::Lineshape::Base::get	(	const Expression &	s,
		const Expression &	s1,
		const Expression &	s2,
		const std::string &	particleName,
		const unsigned &	L,
		const std::string &	lineshapeModifier,
		DebugSymbols *	dbexpressions = nullptr ) const

pure virtualinherited

◆ get() [2/3]

AmpGen::Expression AmpGen::Lineshape::Flatte::get	(	const AmpGen::Expression &	s,
		const AmpGen::Expression &	s1,
		const AmpGen::Expression &	s2,
		const std::string &	particleName,
		const unsigned int &	L,
		const std::string &	lineshapeModifier,
		AmpGen::DebugSymbols *	dbexpressions = 0 ) const

override

◆ get() [3/3]

AmpGen::Expression AmpGen::Lineshape::Flatte::get	(	const AmpGen::Particle &	p,
		const std::string &	lineshapeModifier,
		AmpGen::DebugSymbols *	dbexpressions = nullptr ) const

overridevirtual

Implements AmpGen::Lineshape::Base.

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

/github/workspace/AmpGen/Lineshapes.h