Renormalization and mixing of the Gluino-Glue operator on the lattice

M Costa,H Herodotou,P Philippides,H Panagopoulos

doi:10.1140/epjc/s10052-021-09173-x

Abstract

We study the mixing of the Gluino-Glue operator in mathcal{N}=1 Supersymmetric Yang–Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not merely 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{mathrm{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_{mathrm{SW}}, are left as free parameters.

Highlights

A most appropriate prototype theory, exhibiting all the above features and including both gauge and matter fields, is Supersymmetric Quantum Chromodynamics (SQCD)
We present the renormalization factors and mixing coefficients in the lattice regularization and the MS scheme
We briefly introduce the notation used in this paper and we present all candidate operators that may mix with OGg

Summary

Introduction

A most appropriate prototype theory, exhibiting all the above features and including both gauge and matter fields, is Supersymmetric Quantum Chromodynamics (SQCD). The study of composite operators and their mixing is presently out of reach, especially at the nonperturbative level. A simpler theory, and an important forerunner to the more complex models, is the Supersymmetric Yang–Mills theory (SYM). It contains only gauge fields and it exhibits an interesting spectrum of bound states, in particular particles made of gluino (λ) and gluon (uμ) fields. Preliminary nonperturbative investigations in this direction were performed in Refs. A fundamental ingredient in these investigations is the “Gluino-Glue” composite operator, OGg. In the present work we study thoroughly the

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Conclusion