Meson spectrum in SU(N) gauge theories with quarks in higher representations: A check of Casimir scaling hypothesis

TL;DR

This paper investigates the meson spectrum in SU(N) gauge theories with various quark representations, providing evidence that meson masses follow Casimir scaling and align with Regge trajectories, thus enhancing understanding of confinement.

Contribution

It offers the first lattice QCD evidence supporting Casimir scaling for meson masses across different quark representations in SU(N) gauge theories.

Findings

Meson masses are compatible with Casimir scaling hypothesis.

Large-N meson spectrum exhibits Regge trajectories.

Results support the orientifold equivalence at large N.

Abstract

Gauge theories with gauge group $SU(N)$ and quarks belonging to arbitrary representations of $SU(N)$ form a rich landscape of QCD-like theories, whose study can shed new light on the properties of confinement. Four cases are particularly worth of interest: quarks in the fundamental representation, quarks in the 2-indice (anti)symmetric representation and quarks in the adjoint representation. The last three corresponding QCD-like theories are equivalent at large-$N$ for bosonic observables: It is the orientifold equivalence. The behavior of the lightest vector meson mass versus $N$ has been studied in quenched lattice QCD in the chiral limit in these theories. We show that the observed behaviors are compatible with a string tension proportional to the quadratic Casimir of $SU(N)$ in the quark color representation, $\textit{i.e.}$ with the Casimir scaling hypothesis. The large-$N$ limit of some excited meson masses computed in quenched lattice QCD with quarks in the fundamental representation is also shown to be compatible with QCD string's well-known signature: Regge trajectories.