Chiral Lagrangians for singly heavy baryons to $\mathcal{O}(p^4)$ order

Abstract

The chiral Lagrangians for singly heavy baryons are constructed up to the $\mathcal{O}(p^4)$ order. The involved baryons may be in a flavor antitriplet with spin-1/2, a flavor sextet with spin-$1/2$, or a flavor sextet with spin-3/2 when one considers three light flavors. For the relativistic version of Lagrangian, from $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there exist 48, 199, and 1242 independent terms in the $SU(2)$ case and 59, 307, and 2454 independent terms in the $SU(3)$ case, respectively. For the Lagrangian in the heavy quark limit, from $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, the numbers of independent terms are reduced to 16, 64, and 412 in the $SU(2)$ case and to 17, 88, and 714 in the $SU(3)$ case, respectively. We obtain the low-energy constant relations between the relativistic case and the heavy-quark case up to the $\mathcal{O}(p^3)$ order. The relations between low-energy constants of independent relativistic terms are also presented up to this order by using the heavy quark symmetry.

51 pages

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