On the dark matter origin of an LDMX signal

Fixed target experiments where beam electrons are focused upon a thin target have shown great potential for probing new physics, including the sub-GeV dark matter (DM) paradigm. However, a signal in future experiments such as the light dark matter experiment (LDMX) would require an independent validation to assert its DM origin. To this end, we propose to combine LDMX and next generation DM direct detection (DD) data in a four-step analysis strategy, which we here illustrate with Monte Carlo simulations. In the first step, the hypothetical LDMX signal (i.e. an excess in the final state electron energy and transverse momentum distributions) is $\textit{recorded}$. In the second step, a DM DD experiment operates with increasing exposure to test the DM origin of the LDMX signal. Here, LDMX and DD data are simulated. In the third step, a posterior probability density function (pdf) for the DM model parameters is extracted from the DD data, and used to $\textit{predict}$ the electron recoil energy and transverse momentum distributions at LDMX. In the last step, $\textit{predicted}$ and $\textit{recorded}$ electron recoil energy and transverse momentum distributions are compared in a chi-square test. We present the results of this comparison in terms of a threshold exposure that a DD experiment has to operate with to assert whether $\textit{predicted}$ and $\textit{recorded}$ distributions $\textit{can}$ be statistically dependent. We find that this threshold exposure grows with the DM particle mass, $m_\chi$. It varies from 0.012 kg-year for a DM mass of $m_\chi=4$ MeV to 1 kg-year for $m_\chi=25$ MeV, which is or will soon be within reach.