Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the quartic couplings
Journal
Physical Review D
Date Issued
November 22, 2024
Author(s)
DOI
10.1103/PhysRevD.110.094515
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 naïve 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, Nc, the number of flavors, Nf, and the gauge parameter, α, which are left unspecified. Results for the specific case Nf=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.
Subjects