On the spectrum of mesons in quenched $Sp(2N)$ gauge theories

TL;DR

This paper investigates the meson spectra in quenched lattice gauge theories with symplectic groups, providing foundational results for future dynamical studies and exploring phenomenological implications for composite models.

Contribution

It presents the first extensive lattice study of meson spectra in quenched $Sp(2N)$ gauge theories across multiple representations and sets the groundwork for future unquenched analyses.

Findings

Spectra computed for $Sp(4)$, $Sp(6)$, and $Sp(8)$ gauge groups.

Application of Wilson flow for scale setting and chiral perturbation theory for continuum extrapolation.

Initial insights into large-$N$ behavior and Weinberg sum rules in symplectic gauge theories.

Abstract

We report the findings of our extensive study of the spectra of flavoured mesons in lattice gauge theories with symplectic gauge group and fermion matter content treated in the quenched approximation. For the $Sp(4)$, $Sp(6)$, and $Sp(8)$ gauge groups, the (Dirac) fermions transform in either the fundamental, or the 2-index, antisymmetric or symmetric, representations. This study sets the stage for future precision calculations with dynamical fermions in the low mass region of lattice parameter space. Our results have potential phenomenological applications ranging from composite Higgs models, to top (partial) compositeness, to dark matter models with composite, strong-coupling dynamical origin. Having adopted the Wilson flow as a scale-setting procedure, we apply Wilson chiral perturbation theory to extract the continuum and massless limits for the observables of interest. The resulting measurements are used to perform a simplified extrapolation to the large-$N$ limit, hence drawing a preliminary connection with gauge theories with unitary groups. We conclude with a brief discussion of the Weinberg sum rules.