Volume 430 -
The 39th International Symposium on Lattice Field Theory (LATTICE2022) -
Particle physics beyond the Standard Model

Dark Isosinglet Mesons in $Sp(4)$ gauge theory

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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.

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