Non-perturbative renormalization of the axial current with dynamical Wilson fermions

TL;DR

This work tackles the non-perturbative renormalization of the isovector axial current in two-flavor Wilson lattice QCD using a mass-aware PCAC relation within the Schrödinger functional. By deriving a mass-dependent normalization condition and employing boundary-to-boundary correlators, the authors obtain $Z_A(g_0^2)$ and $Z_V(g_0^2)$ across a range of couplings with ${O}(a^2)$ precision, and demonstrate reduced mass dependence in the chiral limit. They provide interpolating formulas for $Z_A(g_0^2)$ and $Z_V(g_0^2)$, compare with perturbative expectations, and show the new condition yields mass-stable extrapolations, essential for precise determinations of decay constants and quark masses. The results pave the way for reliable physical predictions from dynamical Wilson fermion simulations and can be extended to the ${N_f=3}$ theory and different gauge actions.

Abstract

We present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor Z_A. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schroedinger functional setup we calculate Z_A(g_0^2) as well as the vector current normalization factor Z_V(g_0^2) for beta = 6/g_0^2 >= 5.2.