Quenched chiral perturbation theory for baryons

Abstract

We develop chiral perturbation theory for baryons in quenched QCD. Quenching (the elimination of diagrams containing virtual quark loops) is achieved by extending the Lagrangian method of Bernard and Golterman, and is implemented in a theory where baryons are treated as fixed velocity sources. Our method requires that the octet baryons be represented by a three index tensor rather than by the usual matrix field. We calculate the leading nonanalytic corrections to the masses of octet and decuplet baryons. In QCD these are proportional to $M_{\pi }^3$. We find that quenching alters the $M_{\pi }^3$ terms, but does not completely remove them. In addition, we find nonanalytic contributions to baryon masses proportional to $M_{\pi }$ and $M_{\pi }^2\ln M_{\pi }$. These terms, which are artifacts of quenching, dominate over the $M_{\pi }^3$ terms for sufficiently small quark masses. This pattern of corrections is different from that in most mesonic quantities, where the leading nonanalytic terms in QCD (proportional to $M_{\pi }^4\ln M_{\pi }$) are removed by quenching. We also point out various peculiarities of the quenched theory, most notably that the $\Delta$ baryon can decay (if kinematically allowed), in the sense that its two point function will be dominated at long Euclidean times by a nucleon plus pion intermediate state.