Exploring muonphilic ALPs at muon colliders

Axion-like particles (ALPs) are new particles that extend beyond the standard model (SM) and are highly motivated. When considering ALPs within an effective field theory framework, their couplings with SM particles can be studied independently. It is a daunting task to search for GeV-scale ALPs coupled to muons in collider experiments because their coupling is proportional to the muon mass. However, a recent study by Altmannshofer, Dror, and Gori (2022) highlighted the importance of a four-point interaction, $W$-$\mu$-$\nu_{\mu}$-$a$, as well as interactions from the chiral anomaly which couplings are not dependent on the muon mass. These interactions provide a new opportunity to explore muonphilic ALPs ($\mu$ALPs) at the GeV scale. We have explored various $\mu$ALPs production channels at muon colliders with $\mu$ALPs decaying into a pair of muons. Especially, we found a pair of neutrinos accompanied by a $\mu$ALP is a most effective channel to search for $\mu$ALPs in the electrowek violating (EWV) scenario. In contract, a photon plus a $\mu$ALP becomes a better channel to search for $\mu$ALPs in the electroweak preserving (EWP) scenario because there is no $W$-$\mu$-$\nu_{\mu}$-$a$ interaction in this situation. Most importantly, we found that the future bounds for $\mu$ALPs in EWV scenario are much stronger than the ones in EWP scenario and the existing bounds for exploring $\mu$ALPs with $1$ GeV $\leq m_a\lesssim M_W$.