Dynamical Dark Matter, MATHUSLA, and the lifetime frontier

MATHUSLA is a proposed surface detector at CERN that would be able to observe the decays of nonhadronic electrically neutral long-lived particles (LLPs) with almost no background or trigger limitations. This would allow MATHUSLA to probe sub-GeV to TeV masses and lifetimes up to $c\tau \sim {10}^7\mathrm{m}$. MATHUSLA can play an important role in probing dark-matter scenarios involving extended hidden sectors, where additional dark states often manifest as LLPs. A prime example of such a scenario is furnished by the Dynamical Dark Matter (DDM) framework, which intrinsically gives rise to large ensembles of dark states exhibiting a broad range of masses and lifetimes. In this paper, we examine the extent to which MATHUSLA can probe the DDM parameter space, and we demonstrate that MATHUSLA may be capable of providing direct confirmation of certain unique aspects of the DDM framework which might be difficult to probe in other ways.

Figure 1

The reach of MATHUSLA within the DDM parameter space for the benchmark values $m_0=100\mathrm{MeV}$ and $\delta =1.5$. Black curves indicate contours of ${\sigma }_{\varphi }^{\min }{\mathrm{BR}}_{\chi \chi }$, while blue, red, and green curves indicate contours of $n_{\min }$, $n_{\max }-n_{\min }$, and $n_{\mathrm{cs}}$, respectively. Likewise, the orange shading indicates the region of DDM parameter space in which at least one of the ensemble constituents ${\chi }_n$ has a characteristic decay length $\beta \gamma c{\tau }_{\min }<1\mathrm{m}$. As discussed in the text, the region with $m_0/\mathrm{\Delta }m\gtrsim 0.1$, $7.5\lesssim y\lesssim 8.8$, and $\xi \gtrsim -0.3$ is a particular “sweet spot” within which multiple light states within the DDM ensemble comprise the present-day dark matter while numerous heavier states within the same ensemble can lead to an observable signal at MATHUSLA.

Figure 2

Same as Fig. 1, except that we have now shifted $m_0$ from 100 MeV to 100 keV. This allows MATHUSLA to be sensitive to DDM ensembles with smaller values of $y$, leading to an even more compelling “sweet spot” with $m_0/\mathrm{\Delta }m\gtrsim 0.01$, $4.3\lesssim y\lesssim 5.0$, and $\xi \gtrsim -0.2$.