Gauge Symmetry Breaking through Soft Masses in Supersymmetric Gauge Theories

TL;DR

This paper investigates how soft supersymmetry breaking terms, including negative squark mass squared, influence symmetry breaking, spectrum, and phase transitions in N=1 supersymmetric QCD with various flavor and color configurations.

Contribution

It provides a detailed analysis of symmetry breaking patterns and spectrum in supersymmetric QCD with soft breaking terms, including negative squark masses, across different flavor regimes.

Findings

Negative squark mass squared can induce spontaneous symmetry breaking.

Mass spectrum varies smoothly across Higgs and confining phases.

The analysis applies to both N_f < N_c and N_f > N_c+1 regimes.

Abstract

We analyze the effects of soft supersymmetry breaking terms on N=1 supersymmetric QCD with $N_f$ flavors and color gauge group $SU(N_c)$. The mass squared of some squarks may be negative, as long as vacuum stability is ensured by a simple mass inequality. For $N_f<N_c$, we include the dynamics of the non-perturbative superpotential and use the original (s)quark and gauge fields, while for $N_f>N_c+1$, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group $SU(N_f-N_c)$. The presence of negative squark mass squared terms leads to spontaneous breakdown of flavor and color symmetry. We determine this breaking pattern, derive the spectrum, and argue that the masses vary smoothly as one crosses from the Higgs phase into the confining phase.