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

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.

49 pages, 11 figures, 20 tables; Version accepted for publication in PRD

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• Low-energy effective description of dark $Sp(4)$ theories
• Color dependence of the topological susceptibility in Yang-Mills theories
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• Phenomenology of unusual top partners in composite Higgs models
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• Sp(4) gauge theories and beyond the standard model physics
• Electroweak spin-1 resonances in Composite Higgs models
• Holography of Strongly Coupled Gauge Theories
• Composite two-Higgs doublet model from dilaton effective field theory
• SU(2) gauge theory with one and two adjoint fermions towards the continuum limit
• The multicomponent dark matter structure and its possible observed manifestations