Singlet Mesons in Dark $Sp(4)$ Theories

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 ${\eta }^{\prime }$ using unimproved Wilson fermions and the standard plaquette action. We find that the ${\eta }^{\prime }$ is slightly heavier than the pseudoscalar non-singlets $\pi$ and lighter than the vector mesons $\rho$ for multiple ensembles with $m_{\pi }/m_{\rho }\ge 0.77$. 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.

Comments: 8 pages, 2 figures, Proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany