Eta Decay and Muonic Puzzles

TL;DR

This paper investigates a light scalar boson as a solution to muonic puzzles, refining its allowed mass range to 160 keV–3.5 MeV by incorporating strong interaction effects via the Nambu-Jona-Lasinio model, guiding future experimental searches.

Contribution

It improves previous constraints on the scalar boson mass by including strong interaction physics, providing a more precise target range for experimental verification.

Findings

Allowed scalar boson mass range is 160 keV to 3.5 MeV.

Inclusion of strong interaction effects narrows the parameter space.

Reanalysis of electron beam dump experiments constrains the scalar boson properties.

Abstract

New physics motivated by muonic puzzles (proton radius and muon $g-2$ discrepancies) is studied. Using a light scalar boson $\phi$, assuming Yukawa interactions, accounts for these muonic puzzles simultaneously. Our previous work limits the existence of such a scalar boson's mass $m_\phi$ 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 $\phi$ in computing the decay rate. Doing this involves including the strong interaction physics, involving quarks, necessary to compute the $\eta\pi\phi$ 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 $\eta\pi\phi$ vertex function to reanalyze the electron beam dump experiments. The result is that the allowed range of $m_\phi$ 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.