# Quenched Chiral Perturbation Theory for Baryons

## TL;DR

This paper develops a quenched chiral perturbation theory framework for baryons, revealing how quenching modifies mass corrections and introduces artifacts, with implications for lattice QCD calculations.

## Contribution

It extends chiral perturbation theory to quenched QCD for baryons using a tensor representation and calculates leading non-analytic mass corrections.

## Key findings

- Quenching alters the $M_b3$ terms in baryon mass corrections.
- Non-analytic contributions proportional to $M_b1$ and $M_b1^2 \,\log M_b1$ are introduced by quenching.
- The $b4$ baryon can decay into a nucleon and pion in the quenched approximation.

## 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 non-analytic 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 non-analytic contributions to baryon masses proportional to $M_\pi$ and $M_\pi^2 \log M_\pi$. These terms, which are artifacts of quenching, dominate over the $M_\pi^3$ terms for sufficiently small quark masses. We also point out various pecularities 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.