SU(2) Gauge Theory with Two Fundamental Flavours: a Minimal Template for Model Building

TL;DR

This study explores the spectrum of an SU(2) gauge theory with two flavors, providing insights relevant for models of composite Higgs and dark matter, with improved lattice data and non-perturbative renormalization.

Contribution

The paper offers an updated lattice analysis of SU(2) gauge theory with two flavors, including new data, lattice spacings, and non-perturbative renormalization, to inform beyond Standard Model physics.

Findings

Vector and axial resonance masses are above current LHC bounds.

Results suggest a compressed dark matter spectrum at large dark pion masses.

Spin-one resonances are significant for phenomenological models.

Abstract

We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are $m_V/F_{\rm{PS}}\sim 13.1(2.2)$ and $m_A/F_{\rm{PS}}\sim 14.5(3.6)$ (combining statistical and systematic errors). In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are $m_V > 3.2(5)$ TeV and $m_A > 3.6(9)$ TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.