Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions

TL;DR

This study explores the meson spectra and decay constants of the $Sp(4)$ gauge theory with quenched fundamental and antisymmetric fermions, providing first lattice results relevant for composite Higgs models.

Contribution

It presents the first lattice investigation of $Sp(4)$ gauge theories with two types of fermions, comparing their meson properties and analyzing symmetry breaking patterns.

Findings

Antisymmetric fermions lead to larger meson masses and decay constants than fundamental fermions.

The global symmetry $SU(4) imes SU(6)$ breaks to $Sp(4) imes SO(6)$ in the studied theories.

Results will aid future dynamical simulations and studies of large $N$ behavior in $Sp(2N)$ theories.

Abstract

We perform lattice studies of meson mass spectra and decay constants of the $Sp(4)$ gauge theory in the quenched approximation. We consider two species of (Dirac) fermions as matter field content, transforming in the 2-index antisymmetric and the fundamental representation of the gauge group, respectively. All matter fields are formulated as Wilson fermions. We extrapolate to the continuum and massless limits, and compare to each other the results obtained for the two species of mesons. In the case of two fundamental and three antisymmetric fermions, the long-distance dynamics is relevant for composite Higgs models. This is the first lattice study of this class of theories. The global $SU(4) \times SU(6)$ symmetry is broken to the $Sp(4) \times SO(6)$ subgroup, and the condensates align with the explicit mass terms present in the lattice formulation of the theory. The main results of our quenched calculations are that, with fermions in the 2-index antisymmetric representation of the group, the masses squared and decay constant squared of all the mesons we considered are larger than the corresponding quantities for the fundamental representation, by factors that vary between $\sim$1.2 and $\sim$2.7. We also present technical results that will be useful for future lattice investigations of dynamical simulations, of composite chimera baryons, and of the approach to large $N$ in the $Sp(2N)$ theories considered. We briefly discuss their high-temperature behaviour, where symmetry restoration and enhancement are expected.