Probing dark photons from a light scalar at Belle II

In the minimal $U(1)$ extension of the Standard Model (SM), a new gauge boson referred to as "dark photon" is predicted. The dark-photon mass can be generated from an additional Higgs mechanism associated with a dark scalar boson. At $B$-factories such as Belle II, large numbers of $B$-mesons are produced and can decay to a kaon plus the dark scalar via the latter's mixing with the SM Higgs boson. We evaluate the sensitivity of Belle II for the case in which the dark scalar decays exclusively into a pair of dark photons via the new $U(1)$ gauge coupling, and the dark photons are long lived owing to a small kinetic mixing $\epsilon$. We study the experimental signature in which each dark photon decays into a pair of charged leptons, pions, or kaons, resulting in a pair of displaced vertices, and argue that the search is essentially background-free. We perform detailed Monte-Carlo simulations to determine the expected number of signal events at Belle II with an integrated luminosity of 50 ab$^{-1}$, taking into account the efficiencies for both final-state-particle identification and displaced tracking. We find that for experimentally allowed values of the scalar mixing angle and kinematically allowed dark-photon and dark-scalar masses, the proposed search is uniquely sensitive to the medium-$\epsilon$ regime, which is currently mostly unexcluded by experiments.