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.
Categories: hep-ph