Quark sector effects and glueball mass sensitivity estimates in Lorentz-violating supersymmetric QCD-like theories

TL;DR

This work extends the SYM–CFJ framework to include SUSY QCD matter, encoded by a spurion chiral superfield S with a purely spacelike v_μ that induces a topological gauge-mass scale m_A ∼ |v|. The authors classify LV deformations in the quark sector into CPT-even mass-type terms and CPT-odd derivative (SME-like) couplings, yielding parametric quantities such as δm_q and b_μ that feed into quark/squark propagators and, consequently, into glueball correlators. Glueball observables are treated nonperturbatively only insofar as their parametric dependence on LV is constrained by symmetry and dimensional analysis, using lattice YM glueball masses as infrared benchmarks to extract naturalness estimates for |v| and to forecast anisotropies or multiplet splittings as clean LV signatures. The framework provides a path toward nonperturbative lattice implementations and suggests complementary strategies, including ML-based surrogates, to map LV sensitivity across glueball and hybrid channels in LV SUSY gauge theories.

Abstract

The $N=1$ supersymmetric Yang--Mills--Carroll--Field--Jackiw (SYM--CFJ) model is extended to include the quark sector of supersymmetric quantum chromodynamics (SQCD) in the presence of Lorentz--symmetry violation (LSV). The Lorentz--violating data are carried by a spurion chiral superfield whose components define a purely spacelike background vector $v_μ$ and fermionic bilinears, inducing a topological mass scale in the gauge sector. Working within a spurion effective field theory (EFT) and a small--LSV expansion, we classify the allowed parametric dependence of glueball observables on the induced mass scales. Using lattice Yang--Mills (YM) glueball masses only as a reference hadronic scale, we provide parametric sensitivity estimates and naturalness ranges for the topological mass $|v|$ relative to $Λ_{\rm YM}$.

Figures (4)

• Figure 1: Naturalness estimate for the spacelike CFJ background magnitude $|\bm v|$ as a function of the glueball response coefficient $\alpha_{0^{++}}$, obtained from Eq. \ref{['eq:v_naturalness']} for representative tolerances $\Delta=0.05,\,0.1,\,0.2~\mathrm{GeV}$.
• Figure 2: Theoretical behavior of the glueball mass shift $\Delta m_G(|\bm v|)$. Left: $\chi_G=1$, linear term allowed. Right: $\chi_G=0$, leading correction quadratic.
• Figure 3: Crossover between linear and quadratic LSV contributions as a function of the EFT coefficients $(\alpha_G,\gamma_G)$.
• Figure 4: Angular dependence of the glueball energy $E_G(\bm p)$ at fixed $|\bm p|$, illustrating the anisotropy induced by a spacelike CFJ background.