Supersymmetric QCD on the Lattice: Fine-Tuning of the Yukawa Couplings

TL;DR

This paper calculates the one-loop perturbative fine-tuning of Yukawa couplings in supersymmetric QCD discretized on a lattice, addressing complex mixing and symmetry considerations to connect nonperturbative results to physical Green's functions.

Contribution

It provides the first detailed perturbative analysis of Yukawa coupling renormalization and mixing in lattice supersymmetric QCD, including explicit analytic expressions for renormalization factors.

Findings

Derived analytic expressions for renormalization factors

Analyzed mixing of squark fields at quantum level

Established conditions for Yukawa coupling fine-tuning

Abstract

We determine the fine-tuning of the Yukawa couplings of supersymmetric QCD, discretized on a lattice. We use perturbation theory at one-loop level. The Modified Minimal Subtraction scheme ($\overline{{\rm MS}}$) is employed; by its definition, this scheme requires perturbative calculations, in the continuum and/or on the lattice. On the lattice, we utilize the Wilson formulation for gluon, quark and gluino fields; for squark fields we use na\"ive discretization. The sheer difficulties of this study lie in the fact that different components of squark fields mix among themselves at the quantum level and the action's symmetries, such as parity and charge conjugation, allow an additional Yukawa coupling. Consequently, for an appropriate fine-tuning of the Yukawa terms, these mixings must be taken into account in the renormalization conditions. All Green's functions and renormalization factors are analytic expressions depending on the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $\alpha$, which are left unspecified. Knowledge of these renormalization factors is necessary in order to relate numerical results, coming from nonperturbative studies, to the renormalized, ``physical" Green's functions of the theory.