Quenched Chiral Perturbation Theory for Baryons

TL;DR

This paper develops a quenched chiral perturbation theory framework for baryons, calculating non-analytic mass contributions, and compares these theoretical results with lattice data to assess quenching errors.

Contribution

It introduces a formalism for quenched baryon chiral perturbation theory and computes novel mass correction terms due to quenched loops and the eta' hairpin effect.

Findings

Altered mass correction term proportional to m_q^{3/2} due to quenched loops

Identification of a new m_q^{1/2} correction from eta' hairpin vertex

Estimation of quenching errors in octet baryon masses from lattice data

Abstract

We develop quenched chiral perturbation theory for baryons using the graded-symmetry formalism of Bernard and Golterman and calculate non-analytic contributions to the baryon masses coming from quenched chiral loops. The usual term proportional to $m_{q}^{3/2}$ is substantially altered due to the cancellation of diagrams with internal quark loops. In addition, the $\eta'$ ``hairpin'' vertex leads to a new correction, proportional to $m_{q}^{1/2}$. We compare our results to numerical lattice data and use them to estimate the size of the quenching error in the octet baryon masses.