Fine-Tuning of the Yukawa and Quartic Couplings in Supersymmetric QCD
Date Issued
August 8, 2022
Author(s)
DOI
10.48550/arXiv.2210.03695
Abstract
In this work, we investigate the fine tuning of parameters in N = 1 Supersymmetric QCD, discretized on a Euclidean lattice. Specifically, we study the renormalization of the Yukawa (gluino-quark-squark interactions) and the quartic (four-squark interactions) couplings. At the quantum level, these interactions suffer from mixing with other operators which have the same transformation properties. We exploit the symmetries of the action, such as charge conjugation and parity, in order to reduce the allowed mixing patterns. To deduce the renormalizations and the mixing coefficients we compute, perturbatively to one-loop and to the lowest order in the lattice spacing, the relevant three-point and four-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. We obtain analytic expressions for the renormalization and mixing coefficients of the Yukawa couplings; they are functions of the number of colors Nc, the gauge parameter α, and the gauge coupling g. Furthermore, preliminary results on the quartic couplings are also presented. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).