The $\nu_{R}$-philic scalar: its loop-induced interactions and Yukawa forces in LIGO observations

Right-handed neutrinos ($\nu_{R}$) are often considered as a portal to new hidden physics. It is tempting to consider a gauge singlet scalar $(\phi)$ that exclusively couples to $\nu_{R}$ via a $\nu_{R}\nu_{R}\phi$ term. Such a $\nu_{R}$-philic scalar does not interact with charged fermions at tree level but loop-induced effective interactions are inevitable, which are systematically investigated in this work. The magnitude of the loop-induced couplings coincidentally meets the current sensitivity of fifth-force searches. In particular, the loop-induced coupling to muons could be tested in the recent LIGO observations of neutron star mergers as there might be a sizable Yukawa force in the binary system mediated by the $\nu_{R}$-philic scalar.