A perturbative study of the chirally rotated Schr\"{o}dinger Functional in QCD

TL;DR

This paper performs a 1-loop perturbative analysis of the chirally rotated Schr"odinger functional in QCD, determining renormalization and boundary improvement coefficients to enable automatic $O(a)$ improvement and testing universality.

Contribution

It provides the first perturbative calculation of renormalization and boundary coefficients for the $ ext{chi}$SF, validating automatic $O(a)$ improvement and universality in QCD.

Findings

Successful determination of 1-loop renormalization coefficients.

Verification of automatic $O(a)$ improvement.

Confirmation of universality between SF formulations.

Abstract

The chirally rotated Schr\"odinger functional ($\chi$SF) renders the mechanism of automatic $O(a)$ improvement compatible with the Schr\"odinger functional (SF) formulation. Here we report on the determination to 1-loop order in perturbation theory of the renormalization coefficients necessary to achieve automatic $O(a)$ improvement and the boundary improvement coefficients needed to eliminate the extra boundary $O(a)$ effects present in any SF formulation. After this is done, we perform a set of tests of automatic $O(a)$ improvement and of the universality between standard and chirally rotated SF formulations.