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.