Exploring two non-perturbative definitions of $c_A$

TL;DR

This paper compares two non-perturbative methods to determine the coefficient $c_A$ in quenched QCD, highlighting the ambiguity's significance at certain lattice couplings.

Contribution

It introduces and compares two distinct non-perturbative definitions of $c_A$ in quenched QCD, clarifying their consistency and the ambiguity's impact.

Findings

Both methods yield consistent $c_A$ values.

The $O(a)$ ambiguity becomes relevant near $eta oughly 6.0$.

Results confirm previous findings about the ambiguity's significance.

Abstract

We present two determinations of the coefficient $c_A$ in quenched QCD, needed to build the $O(a)$ improved axial current. The first condition used is the requirement that the PCAC quark mass, as a function of $x_0$, stays flat for a non-trivial spatial phase for the fermions in the Schr\"odinger functional. The second condition is that the PCAC relation for the ground-state and the first excited state at finite L give the same quark mass. Our results confirm previous findings that in the quenched theory the intrinsic $O(a)$ ambiguity of $c_A$ gets relevant around $\beta\simeq6.0$.