A dynamical study of the chirally rotated Schr\"odinger functional in QCD

TL;DR

This paper investigates the chirally rotated Schr"odinger functional in QCD with two dynamical quark flavors, demonstrating how to compute renormalization factors and confirming the effectiveness of automatic O(a) improvement.

Contribution

First dynamical results for renormalization factors in the chirally rotated Schr"odinger functional in QCD with two flavors, including a precise determination of Z_A.

Findings

Renormalization factors obtained from simple ratios of two-point functions.

Automatic O(a) improvement is confirmed in the dynamical setup.

Precise determination of the non-singlet axial current renormalization Z_A.

Abstract

The chirally rotated Schr\"odinger functional for Wilson-fermions allows for finite-volume, mass-independent renormalization schemes compatible with automatic O($a$) improvement. So far, in QCD, the set-up has only been studied in the quenched approximation. Here we present first results for $N_{\rm f} = 2$ dynamical quark-flavours for several renormalization factors of quark-bilinears. We discuss how these renormalization factors can be easily obtained from simple ratios of two-point functions, and show how automatic O($a$) improvement is at work. As a by-product of this investigation the renormalization of the non-singlet axial current, $Z_A$, is determined very precisely.