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

We study the mixing of the Gluino-Glue operator in 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 (MS) over bar 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, Nc, the gauge parameter, beta, and the clover coefficient, cSW, are left as free parameters.

Automated summary

The mixing and renormalization of the Gluino-Glue operator in N=1 Supersymmetric Yang-Mills theory has been studied using dimensional regularization and lattice methods. The calculations included one-loop quantum corrections for relevant Green's functions, allowing for determination of renormalization factors and mixing coefficients. The computations were performed with gluinos on lattice sites and gluons on lattice links, using Wilson's formulation with clover improvement.