Light Pseudoscalar Meson and Heavy Meson Scattering Lengths

TL;DR

This paper systematically calculates S-wave scattering lengths for light and heavy pseudoscalar mesons using chiral perturbation theory, predicting unmeasured values and highlighting the attractive DK interaction relevant to charm-strange scalar states.

Contribution

It provides a comprehensive calculation and prediction of meson scattering lengths up to ${ m O}(p^3)$, incorporating lattice data to estimate low-energy constants.

Findings

DK scattering length is positive, indicating attractive interaction.

Predicted unmeasured scattering lengths for various meson pairs.

Analytical expressions useful for future meson interaction studies.

Abstract

We have performed a systematical calculation of the pion ($\pi, K, \eta$) and heavy pseudoscalar meson S-wave scattering lengths up to ${\cal O}(p^3)$ in the chiral perturbation theory in the heavy quark symmetry limit. With the three scattering lengths from the lattice simulations as input we estimate the unknown low-energy constants. Then we predict all the other unmeasured scattering lengths. The analytical expressions and predictions may be helpful to future investigations. Especially we note that the DK scattering length is positive. Therefore their interaction is attractive, which helps to lower the mass of the "bare" charm-strange scalar state in the quark model through the couple-channel effect.