Quenched and Partially Quenched Chiral Perturbation Theory for Vector and Tensor Mesons

Quenched and partially quenched chiral perturbation theory for vector mesons is developed and is used to extract chiral loop correction to the $\rho$ meson mass. Connections to fully quenched and totally unquenched chiral perturbation theory results are discussed. It is also shown that (partially) quenched perturbation theory for tensor mesons can be formulated analogously, and the chiral corrections for tensor meson masses are directly proportional to their counterparts in the vector meson sector. Utilizing this observation and non-relativistic quark model, we point out that mass difference $(m_{a_2} - {3 \over 2} m_\rho)$ is ``quenching-insensitive'' in large-$N_c$ limit. This quantity may be used for normalization of mass scale in lattice QCD calculations.