Baryon Chiral Perturbation Theory in Partially Quenched Large-Nc QCD

Baryons of lower spin in partially quenched large-$N_c$ QCD are studied with particular emphasis to interpolation between standard unquenched and fully quenched limits. In large $N_c$ limit of partially quenched QCD, we calculate $\mathrm{\Delta }m$, the chiral one-loop correction to baryon masses. We find that leading order contribution to $\mathrm{\Delta }m$ is independent of number of ghost quarks introduced. For finite $N_c$, chiral correction $\mathrm{\Delta }m$ does satisfy the Bernard–Golterman’s third theorem and has no infared quenching singularity except for fully quenched limit. At large $N_c$ limit, however, we show that the third theorem is bypassed and nontrivial quenched chiral corrections do arise. In unquenched limit, we also show that standard chiral perturbation theory results are reproduced in which ${\eta }^{\mathrm{\prime }}$ loop contributions are explicitly taken into account.