Vector-channel scattering of dark particles in a Sp(4) gauge theory

Abstract

We report new results obtained in our lattice studies of the $Sp(4)$ gauge theory coupled to two fundamental Dirac fermions. This theory provides a candidate for the dynamical origin of dark matter models within the strongly interacting massive particle paradigm. We employ Lüscher's formalism to analyse finite-volume energy levels and study the scattering amplitude of two pseudoscalar states in the spin-1 channel. We present our preliminary findings for a set of ensembles generated within a broad range of (Wilson) fermion masses.

Figures (3)

• Figure 1: Finite-volume energy spectra, $E_{\rm cm}/m_{\pi_D}$, normalisaed to the pNGB masses, in the vector channel (${\bf 10}$ of $Sp(4)$) in ensembles generated with three choices of lattice parameters: $(\beta,a\,m_0)=(6.9,0.92)$ (top), $(7.05,0.863)$ (middle), and $(7.05,0.867)$ (bottom). Different colours are for the different assignments of the total momentum of the system in lattice units, $\vec{d}=(L/2\pi)\vec{P}$, as shown in the legends. The filled down-pointing and up-pointing triangles denote ground state and first excited state energies in the $A_1$ channel, while the filled circles are for the ground state energies, extracted from single meson operators, in the other channels with $R'=T_1,~E,~B_1$. The solid and dashed lines represent the $2$- and $4$-pNGB thresholds, respectively.
• Figure 2: The infinite-volume phase shift, $\delta_1$, in the spin-1 channel for the heavy (upper panel) and light (lower) cases. Different colours are for the different assignments of the total momentum of the system in lattice units, $\vec{d}=(L/2\pi)\vec{P}$, as shown in the legends. The shaded bands are the fit results obtained using the effective range expansion at the leading order and the Breit-Wigner form, respectively, in the heavy and light cases.
• Figure 3: Cross sections for pNGB/DM scattering in the channels characterised by the ${\bf 10}$ and ${\bf 14}$ of $Sp(4)$) channels, assuming the pNGBs act as dark matter particles with mass $m_{\rm DM}=100$ MeV. Solid, dashed, and dot-dashed lines denote central values, while the shaded regions represent the statistical uncertainties. The result for the ${\bf 14}$ is taken from Ref. Dengler:2024maq.