Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the quartic couplings

Abstract

In this work we calculate the renormalization of counterterms which arise in the lattice action of $N = 1$ Supersymmetric QCD (SQCD). In particular, the fine-tunings for quartic couplings are studied in detail through both continuum and lattice perturbation theory at one-loop level. For the lattice version of SQCD we make use of the Wilson gauge action for gluon fields and the Wilson fermion action for fermion fields (quarks, gluinos); for squark fields we use na\"ive discretization. On the lattice, different components of squark fields mix among themselves and a total of ten quartic terms arise at the quantum level. Consequently, the renormalization conditions must take into account these effects in order to appropriately fine-tune all quartic couplings. All our results for Green's functions and renormalization factors exhibit an explicit analytic dependence on the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $\alpha$, which are left unspecified. Results for the specific case $N_f=1$ are also presented, where the symmetries allow only five linearly independent quartic terms. For the calculation of the Green's functions, we consider both one-particle reducible and one-particle irreducible Feynman diagrams. Knowledge of these renormalization factors is necessary in order to relate numerical results, coming from nonperturbative studies, to ``physical'' observables.