Eta decay and muonic puzzles

Abstract

New physics motivated by muonic puzzles (proton radius and muon g−2 discrepancies) is studied. Using a light scalar boson ϕ, assuming Yukawa interactions, accounts for these muonic puzzles simultaneously. Our previous work limits the existence of such a scalar boson's mass mϕ from about 160 keV to 60 MeV. We improve this result by including the influence of all of the possible particles that couple to the ϕ in computing the decay rate. Doing this involves including the strong interaction physics, involving quarks, necessary to compute the ηπϕ vertex function. The Nambu-Jona-Lasinio model, which accounts for the spontaneous symmetry breaking that yields the constituent mass is employed to represent the relevant strong-interaction physics. We use the ηπϕ vertex function to reanalyze the electron beam dump experiments. The result is that the allowed range of mϕ lies between about 160 keV and 3.5 MeV. This narrow range represents an inviting target for ruling out or discovering this scalar boson. A possible UV completion of our phenomenological model is discussed.