M³: a new muon missing momentum experiment to probe (g − 2)_μ and dark matter at Fermilab

New light, weakly-coupled particles are commonly invoked to address the persistent ∼ 4σ anomaly in (g−2)_μ and serve as mediators between dark and visible matter. If such particles couple predominantly to heavier generations and decay invisibly, much of their best-motivated parameter space is inaccessible with existing experimental techniques. In this paper, we present a new fixed-target, missing-momentum search strategy to probe invisibly decaying particles that couple preferentially to muons. In our setup, a relativistic muon beam impinges on a thick active target. The signal consists of events in which a muon loses a large fraction of its incident momentum inside the target without initiating any detectable electromagnetic or hadronic activity in downstream veto systems. We propose a two-phase experiment, M³ (Muon Missing Momentum), based at Fermilab. Phase 1 with ∼ 10¹⁰ muons on target can test the remaining parameter space for which light invisibly-decaying particles can resolve the (g − 2)_μ anomaly, while Phase 2 with ∼ 10¹³ muons on target can test much of the predictive parameter space over which sub-GeV dark matter achieves freeze-out via muon-philic forces, including gauged U(1)_Lμ−Lτ.