Dynamical light vector mesons in low-energy scattering of Goldstone bosons

TL;DR

This paper models low-energy Goldstone boson scattering using a chiral Lagrangian with vector mesons, achieving good agreement with experimental phase shifts up to 1.2 GeV through a coupled-channel approach.

Contribution

It introduces a novel coupled-channel framework incorporating vector mesons in the tensor field representation, constrained by micro-causality and unitarity, to analyze scattering data.

Findings

Good agreement with empirical phase shifts up to 1.2 GeV

Only two free parameters needed for the model

Effective implementation of unitarity and causality constraints

Abstract

We present a study of Goldstone boson scattering based on the flavor SU(3) chiral Lagrangian formulated with vector mesons in the tensor field representation. A coupled-channel channel computation is confronted with the empirical s- and p-wave phase shifts, where good agreement with the data set is obtained up to about 1.2 GeV. There are two relevant free parameters only, the chiral limit value of the pion decay constant and the coupling constant characterizing the decay of the rho meson into a pair of pions. We apply a recently suggested approach that implements constraints from micro- causality and coupled-channel unitarity. Generalized potentials are obtained from the chiral Lagrangian and are expanded in terms of suitably constructed conformal variables. The partial-wave scattering amplitudes are defined as solutions of non-linear integral equations that are solved by means of an N/D ansatz.