Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons

TL;DR

This paper analyzes the low-energy constants in the chiral Lagrangian for charmed mesons, comparing resonance estimates, positivity constraints, and lattice data fits, highlighting tensions and the need for more data.

Contribution

It provides a comprehensive comparison of different methods to determine low-energy constants in the chiral Lagrangian for charmed mesons, including resonance exchange, positivity constraints, and lattice data.

Findings

Tensions between estimates and lattice data values.

More lattice and experimental data needed for precise constants.

Estimated coupling constant g_{DDa_2} via QCD sum rules.

Abstract

We investigate the numerical values of the low-energy constants in the chiral effective Lagrangian for the interactions between the charmed mesons and the lightest pseudoscalar mesons, the Goldstone bosons of the spontaneous breaking of chiral symmetry for QCD. This problem is tackled from two sides: estimates using the resonance exchange model, and positivity constraints from the general properties of the $S$-matrix including analyticity, crossing symmetry and unitarity. These estimates and constraints are compared with the values determined from fits to lattice data of the scattering lengths. Tensions are found, and possible reasons are discussed. We conclude that more data from lattice calculations and experiments are necessary to fix these constants better. As a by-product, we also estimate the coupling constant $g_{DDa_2}$, with $a_2$ the light tensor meson, via the QCD sum rule approach.