One-loop calculations in Supersymmetric Lattice QCD

TL;DR

This paper performs one-loop perturbative calculations of self energies and renormalization functions in supersymmetric QCD on the lattice, providing analytic results for various fields and exploring operator mixing effects.

Contribution

It introduces a detailed one-loop analysis of supersymmetric QCD on the lattice, including renormalization functions and operator mixing, which advances understanding of lattice supersymmetry.

Findings

Analytic expressions for renormalization functions of quark, gluon, gluino, and squark fields.

Results from dimensional regularization are presented; lattice results are forthcoming.

Identification of operator mixing patterns in quark bilinear operators.

Abstract

We study the self energies of all particles which appear in a lattice regularization of supersymmetric QCD (${\cal N}=1$). We compute, perturbatively to one-loop, the relevant two-point Green's functions using both the dimensional and the lattice regularizations. Our lattice formulation employs the Wilson fermion acrion for the gluino and quark fields. The gauge group that we consider is $SU(N_c)$ while the number of colors, $N_c$ and the number of flavors, $N_f$, are kept as generic parameters. We have also searched for relations among the propagators which are computed from our one-loop results. We have obtained analytic expressions for the renormalization functions of the quark field ($Z_\psi$), gluon field ($Z_u$), gluino field ($Z_\lambda$) and squark field ($Z_{A_\pm}$). We present here results from dimensional regularization, relegating to a forthcoming publication our results along with a more complete list of references. Part of the lattice study regards also the renormalization of quark bilinear operators which, unlike the non-supersymmetric case, exhibit a rich pattern of operator mixing at the quantum level.