Chiral Lagrangians for mesons with a single heavy quark

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.