Renormalization and Mixing of the Gluino-Glue Operator on the Lattice

TL;DR

This paper investigates the renormalization and operator mixing of the Gluino-Glue operator in ${ m N}=1$ Supersymmetric Yang-Mills theory, providing one-loop calculations in both dimensional and lattice regularizations to determine renormalization factors and mixing coefficients.

Contribution

It presents the first detailed one-loop calculation of the renormalization and mixing of the Gluino-Glue operator on the lattice, including the effects of operator mixing with non-gauge invariant operators.

Findings

Calculated renormalization factors in the $ar{MS}$ scheme.

Determined mixing coefficients with non-gauge invariant operators.

Performed computations using Wilson's lattice discretization with clover improvement.

Abstract

We study the mixing of the Gluino-Glue operator in ${\cal N}$=1 Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green's functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $\overline{\textrm{MS}}$ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson's formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $N_c$, the gauge parameter, $\beta$, and the clover coefficient, $c_{\rm SW}$, are left as free parameters.