Lineshapes for composite particles with unstable constituents

TL;DR

This paper derives general formulas for the lineshapes of composite particles with an unstable constituent, applicable in various regimes, including narrow and broad widths, using a coupled-channel formalism.

Contribution

It provides a unified framework for describing lineshapes of composite particles with unstable constituents without assuming narrow widths.

Findings

Derived general lineshape expressions for unstable constituents

Identified parameters controlling narrow vs. broad width regimes

Connected existing narrow-width formulas to a broader formalism

Abstract

We discuss on very general grounds possible lineshapes of composite particles with one unstable constituent. Expressions are derived in a coupled-channel formalism for constituents interacting in an S-wave with no assumption made on the width of one of them. We show how easy-to-use formulae, already existing in the literature, emerge for narrow constituents and identify the parameter that controls the regime of their applicability.