Probing the flavor-specific scalar mediator for the muon $(g-2)$ deviation, the proton radius puzzle and the light dark matter production

Abstract: Flavor-specific scalar bosons exist in various Standard Model extensions and couple to a single generation of fermions via a global flavor symmetry breaking mechanism. Given this strategy, we propose a MeV flavor-specific scalar model in dimension-$5$ operator series, which explains the muon g-2 anomaly and proton radius puzzle by coupling with the muon and down-quark at the same time. The framework is consistent with the null result of high-intensity searches. Specifically, the supernova constraints for muon couplings become weakened by including the contribution of down-quark interaction. The parameter space for explaining muon $g-2$ discrepancy is available when $10\%$ energy deposition is required in the energy explosion process in the supernova, but this is ruled out by the $1\%$ energy deposition requirement. We also investigate the searches for mediator and dark matter and the resulting constraints on viable parameter space such as nuclear physics constraints, direct detection for light boosted dark matter, and possible CMB constraints. When compared to conventional dark matter production, light dark matter production has two additional modifications: bound state formation and early kinetic equilibrium decoupling. We are now looking into the implications of these effects on the relic density of light dark matter.