Gauge-invariant Renormalization of the Gluino-Glue operator

We study the Gluino-Glue operator in the context of Supersymmetric ${\cal N}{=}1$ Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Green's function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to $\overline{\rm MS}$. This conversion factor can be used in order to convert to $\overline{\rm MS}$ Green's functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.