Fine-Tuning of the Yukawa and Quartic Couplings in Supersymmetric QCD

TL;DR

This paper analyzes the renormalization and mixing of Yukawa and quartic couplings in lattice supersymmetric QCD, providing analytic expressions for their coefficients at one-loop order.

Contribution

It presents a perturbative calculation of the renormalization and mixing coefficients for Yukawa and quartic couplings in lattice supersymmetric QCD, including analytic formulas and preliminary results.

Findings

Analytic expressions for Yukawa coupling renormalization and mixing coefficients.

Perturbative one-loop calculations in lattice supersymmetric QCD.

Initial results on quartic coupling renormalization.

Abstract

In this work, we investigate the fine tuning of parameters in $\mathcal{N} = 1$ 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 na\"ive discretization. We obtain analytic expressions for the renormalization and mixing coefficients of the Yukawa couplings; they are functions of the number of colors $N_c$, the gauge parameter $\alpha$, and the gauge coupling $g$. Furthermore, preliminary results on the quartic couplings are also presented.