Renormalization of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons

Starting from a relativistic Lagrangian for pseudoscalar Goldstone bosons and vector mesons in the antisymmetric tensor representation, a one-loop calculation is performed to pin down the divergent structures that appear for the effective low-energy action at chiral orders ${Q}^{2}$ and ${Q}^{4}$. The corresponding renormalization-scale dependencies of all low-energy constants up to chiral order ${Q}^{4}$ are determined. Calculations are carried out for both the pseudoscalar octet and the pseudoscalar nonet, the latter in the framework of chiral perturbation theory in the limit of a large number of colors.