Fine-tunings and renormalization of gluino bilinear operators in lattice SYM with Stout-Smeared links

TL;DR

This paper calculates renormalization factors for various operators in lattice N=1 SYM theory using improved actions and stout smearing, aiding precise lattice simulations.

Contribution

It introduces a one-loop perturbative method to determine renormalization factors with improved lattice actions and analyzes discretization effects for better calibration.

Findings

Identified optimal stout-smeared parameter for axial-current conservation.

Provided renormalization constants for gluino and gluon fields.

Guided fine-tuning procedures for lattice SYM simulations.

Abstract

In this paper, we compute the renormalization factors for the gluino and gluon fields, the gauge parameter, the coupling constant, as well as the scalar, pseudoscalar, and axial-vector gluino bilinear operators in N=1 supersymmetric Yang-Mills (SYM) theory, using improved lattice actions. Our lattice formulation employs clover fermions, a Symanzik-improved gauge action, and stout-smeared links, which suppress ultraviolet fluctuations and thus enable more accurate determinations of renormalization factors. Our methodology involves computing gauge-variant two-point and three-point Green's functions at one-loop order in lattice perturbation theory, in order to extract the multiplicative renormalization factors and the critical gluino mass. By analyzing lattice discretization effects on the axial current and their dependence on the stout-smearing and clover parameters, we identify a value of the smearing parameter that ensures axial-current conservation at one loop. The results presented in this work provide practical guidance for the fine-tuning procedures required to set up and calibrate lattice simulations of SYM.