# Chiral Lagrangians for mesons with a single heavy quark

## TL;DR

This paper develops relativistic chiral Lagrangians for heavy-light mesons up to fourth order, detailing the number of independent terms and relations between low-energy constants, advancing effective field theory descriptions of these particles.

## Contribution

It provides a comprehensive construction of chiral Lagrangians for heavy-light mesons at high order, including flavor and heavy quark symmetry considerations.

## Key findings

- Constructed Lagrangians up to $ ext{O}(p^4)$ for $Qar{q}$ mesons.
- Counted independent terms for $SU(2)$ and $SU(3)$ cases.
- Derived relations between low-energy constants based on heavy quark symmetry.

## Abstract

We construct the relativistic chiral Lagrangians for heavy-light mesons $(Q\bar{q})$ to the $\mathcal{O}(p^4)$ order. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 17, 67, and 404 independent terms in the flavor $SU(2)$ case and 20, 84, and 655 independent terms in the flavor $SU(3)$ case. The Lagrangians in the heavy quark limit are also obtained. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 7, 25, and 136 independent terms in the flavor $SU(2)$ case and 8, 33, and 212 independent terms in the flavor $SU(3)$ case. The relations between low-energy constants based on the heavy quark symmetry are also given up to the $\mathcal{O}(p^3)$ order.