Renormalisation of quark bilinears with Nf=2 Wilson fermions and tree-level improved gauge action

TL;DR

The paper addresses non-perturbative renormalisation of quark bilinears in $N_f=2$ twisted mass Wilson lattice QCD using a tree-level Symanzik gauge action. It introduces a novel two-regularisation method combining twisted mass and Osterwalder-Seiler valence quarks to extract scale-independent RCs ($Z_A$ and $Z_P/Z_S$) and complements this with an RI-MOM program for all RCs, including a Goldstone-pole subtraction to control infrared contamination. The authors report precise determinations of $Z_V$, $Z_A$, and $Z_P/Z_S$ from the scale-independent analysis and provide RI-MOM results for $Z_A$, $Z_V$, $Z_P$, $Z_S$, and $Z_T$ at $ u_0=a^{-1}$ across three lattice spacings, with consistent extrapolations to the chiral limit and $oxed{O(a^2)}$-improved behavior at maximal twist. The work yields robust, non-perturbative RCs for widely used lattice setups, enabling accurate normalization of hadronic matrix elements and cross-method validation in lattice QCD phenomenology.

Abstract

We present results for the renormalisation constants of bilinear quark operators, using the Nf=2 twisted mass Wilson action at maximal twist (which guarantees automatic O(a) improvement) and the tree-level Symanzik improved gauge action. The scale-independent renormalisation constants are computed with a new method, which makes use of both standard twisted mass and Osterwalder-Seiler fermions. Moreover, the results from an RI-MOM calculation are presented for both scale independent and scale dependent renormalisation constants.

Figures (2)

• Figure 1: Asymptotic behaviour of scale independent normalisation constants
• Figure 2: Goldstone pole subtraction at $\beta=3.90$; $Z_{\Gamma}(a\mu_0)$ of Eq. (\ref{['ZG']}) is plotted against $(a\mu)^2$.