Probing a muonic force with the periastron advance in binary pulsar systems

Pulsars, highly magnetized, rotating neutron stars, can have significant muon abundances in their dense cores, making them promising environments to probe ultralight mediators coupled to muons. The precise measurement of periastron advance in binary pulsar systems provides a sensitive probe of such long-range forces. In this work, we study the periastron advance constraints from binary pulsar systems on the ultralight muonic mediators. We compute the muon number fraction in neutron stars, by properly taking into account the suppression effect of the long-range muonic force. We find that the periastron advance constraints impose the most stringent constraints on ultralight muonic mediators in the mass range of $\simeq(10^{-17},\,2\times10^{-15})$ eV, probing muonic couplings as small as $\mathcal{O}(10^{-21})$, which surpass the limits from LIGO/Virgo gravitational wave measurements, by about an order of magnitude.