Fine-tunings and renormalization of gluino bilinear operators in lattice SYM with stout-smeared links

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 $${\mathcal {N}} =1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> 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.