A Bayesian Framework for Dark Photon Searches at LDMX

Abstract

Despite decades of experimental searches, dark matter, a hypothetical form of matter with highly suppressed electromagnetic interactions, has yet to be detected. The absence of any detection in the 10 GeV–TeV mass range has motivated searches in lower mass ranges, reaching sub-GeV levels. Due to the Lee-Weinberg bound, a thermal-relic dark matter particle at this mass scale requires a new force mediator to bring the annihilation cross-section into agreement with the observed relic density. This force mediator is dubbed the dark photon, and several experiments designed to produce and detect it have been built or are currently under construction. The main objective of this thesis is to develop a Bayesian framework for inferring the coupling strength and mass of the dark photon using data from the upcoming Light Dark Matter eXperiment (LDMX), a fixed target experiment where dark photons are expected to be produced in electron-tungsten collisions. The framework is validated on MadGraph5- simulated data sets to quantify LDMX’s (Phase II) detection capabilities and parameterinference power. This task is accomplished using dynamic nested sampling, designed for estimating posteriors and calculating marginal likelihoods. The secondary objective is to investigate whether the degeneracy between the dark photon mass and interaction model can be resolved through a combined analysis of the recoil-electron’s transverse momentum |pT | and total energy E. The degeneracy is explored by comparing Bayes factors computed from the marginal likelihoods of the different models. The framework recovers the dark photon mass and coupling accurately for benchmarks corresponding to thermal relic targets for complex scalar dark matter with R ≡ mA′/mχ = 2.5, while identifying benchmarks with R = 2.2, producing fewer expected signal events, as being below detection threshold. Using two-dimensional (E, |pT |) kinematics, the Bayes factor comparison breaks the mass-model degeneracy between the interaction model groups ([KM, C, A] and [M, E]), with maximum Bayes factors of lnK = 591. One-dimensional analysis of E and |pT | alone still separates the model groups, though less decisively, with maximum Bayes factors of lnK ≈ 42 for E alone and lnK ≈ 22 for |pT | alone. The introduction of a relic-target prior on gf further separates KM from [C, A], at the cost of additional assumptions.