Probing Muonphilic Force Carriers and Dark Matter at Kaon Factories

Rare kaon decays are excellent probes of light, new weakly coupled particles. If such particles X couple preferentially to muons, they can be produced in K →μ ν X decays. We evaluate the future sensitivity for this process at NA62 assuming X decays either invisibly or to dimuons. Our main physics target is the parameter space that resolves the (g -2 )_μ anomaly, where X is a gauged L_μ-L_τ vector or a muonphilic scalar. The same parameter space can also accommodate dark matter freeze-out or reduce the tension between cosmological and local measurements of H₀ if the new force decays to dark matter or neutrinos, respectively. We show that for invisible X decays, a dedicated single muon trigger analysis at NA62 could probe much of the remaining (g -2 )_μ favored parameter space. Alternatively, if X decays to muons, NA62 can perform a dimuon resonance search in K →3 μ ν events and greatly improve existing coverage for this process. Independently of its sensitivity to new particles, we find that NA62 is also sensitive to the standard model predicted rate for K →3 μ ν , which has never been measured.