Meson spectroscopy in the Sp(4) gauge theory with three antisymmetric fermions

Abstract

We report the results of an extensive numerical study of the Sp(4) lattice gauge theory coupled to fermion matter content consisting of three (Dirac) flavors, transforming in the two-index antisymmetric representation of the gauge group. In the presence of (degenerate) fermion masses, the theory has an enhanced global SU(6) symmetry, broken explicitly and spontaneously to its SO(6) subgroup. This symmetry breaking pattern makes the theory interesting for applications in the context of composite Higgs models, as well as for the implementation of top partial compositeness. Alternatively, it can also provide a dynamical realization of the strongly interacting massive particle paradigm for the origin of dark matter. We adopt the standard plaquette gauge action, along with the Wilson-Dirac formulation for the fermions, and apply the (rational) hybrid Monte Carlo algorithm in our ensemble generation process. We monitor the autocorrelation and topology of the ensembles. We explore the bare parameter space, and identify the weak and strong coupling regimes, which are separated by a line of first-order bulk phase transitions. We measure two-point correlation functions between meson operators that transform as nontrivial representations of SO(6), and extract the ground-state masses, in all accessible spin and parity channels. We assess the size of finite volume effects, and restrict attention to measurements in which these systematic effects are negligibly small compared to the statistical uncertainties. The accuracy of our data enables us to extract the decay constants of the composite particles in the pseudoscalar, vector and axial-vector channels. In addition, we measure the mass of the first excited state for one of the channels, the vector meson, by performing a generalized eigenvalue problem analysis involving two different meson operators. Spectral quantities show a mass dependence that is compatible with the expectation that, at long distances, the theory undergoes confinement, accompanied by the spontaneous breaking of the approximate global symmetries acting on the matter fields. Finally, we discuss the continuum and massless extrapolations within the framework of Wilson chiral perturbation theory, after setting the physical scale using the gradient flow method, and compare the results to those of existing studies in the quenched approximation, as well as to the literature on closely related theories.Published by the American Physical Society2025