Singlet Mesons in Dark $Sp(4)$ Theories

TL;DR

This paper presents preliminary lattice results on the meson spectrum in $Sp(4)$ gauge theory with two fundamental fermions, exploring implications for composite dark matter models and revealing a specific mass hierarchy pattern.

Contribution

It provides the first lattice measurements of the $ ext{eta'}$ meson mass and the $ ext{pi}^0$ disconnected contributions in $Sp(4)$ theories, relevant for BSM dark matter models.

Findings

The $ ext{eta'}$ is slightly heavier than the $ ext{pi}$ and lighter than the $ ho$.

Disconnected contributions to $ ext{pi}^0$ are small.

The $ ext{pi} ext{pi}$ scattering length suggests phenomenological relevance for dark matter models.

Abstract

We explore some aspects of $Sp(4)$ gauge theory with two fundamental fermions in the context of composite Goldstone Dark Matter. We present preliminary lattice results for the mass of the pseudoscalar iso-singlet meson $\eta'$ using unimproved Wilson fermions and the standard plaquette action. We find that the $\eta'$ is slightly heavier than the pseudoscalar non-singlets $\pi$ and lighter than the vector mesons $\rho$ for multiple ensembles with $m_\pi/m_\rho \geq 0.77$. This pattern is potentially relevant for Beyond the Standard Model physics model building. Furthermore, we show that for $N_f=1+1$ flavours the disconnected contributions to the unflavoured pseudoscalar $\pi^0$ are small. We supplement this measurement by a calculation of the $\pi\pi$ scattering length $a_0$ which shows that the ensemble studied might be phenomenologically relevant for Dark Matter models such as the Strongly Interacting Massive Particles paradigm.