Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

Abstract

We review the current status of the long-term programme of numerical investigation of Sp(2N) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the Sp(2N) Yang–Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on Sp(4), and summarise the numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. We also describe our approach to open access.

Scattering of dark pions in an Sp(4)-gauge theory

“…In this paper, we used lattice field theory to study scattering properties of a specific realisation of SIMP DM. Together with studies on the mass spectrum [4,6,20,21], these non-perturbative results can be used to determine low energy constants in an effective description with chiral perturbation theory [4,6]. The natural next step is the determination of the phase shift in the isospin-1 channel including the 3 → 2 process as well as further derived quantities [17].…”

The deconfinement phase transition in $Sp(2N)$ gauge theories and the density of states method

“…For a recent review on this see Ref. [1] and references therein. Due to the non-perturbative nature of these theories, the lattice is the natural first-principles method to study their properties.…”

Chimera baryon spectrum in the Sp(4) completion of composite Higgs models

“…Our collaboration has been developing an extensive programme of lattice studies [8][9][10][11][12][13][14] focused on the 𝑆 𝑝(4) gauge theory coupled to 𝑁 𝑓 = 2 Dirac fermions in the fundamental, ( 𝑓 ), and 𝑛 𝑓 = 3 Dirac fermions in the two-index antisymmetric, (𝑎𝑠), representations of the gauge group [15]. In the ( 𝑓 ) sector, the 𝑆𝑈 (4)/𝑆 𝑝(4) coset, due to the pseudoreality [16], provides candidates for the SM Higgs doublet with only one additional Goldstone mode.…”