Long-lived sterile neutrinos from an axionlike particle at Belle II

Axionlike particles (ALPs) can be produced in meson decays via tree-level quark-flavor-violating couplings, and decay to a pair of sterile neutrinos if also coupled to them. Such light sterile neutrinos are necessarily long-lived and may give rise to striking signatures of displaced vertices (DVs) at terrestrial experiments. In this work, we study the prospect of the ongoing Belle II experiment for detecting the sterile neutrinos from the ALP, leveraging the $\mathcal{O}(10^{10})$ $B$-mesons projected to be produced at the experiment with an integrated luminosity of 50 ab$^{-1}$. We propose search strategies for one or two DVs, and perform Monte-Carlo simulations in order to estimate the sensitivity reach of Belle II to active-sterile-neutrino mixing $|V_{eN}|^2$ as functions of the sterile-neutrino mass. Signatures include a selected list of sterile-neutrino final states, for which we estimate an $\mathcal{O}(1)$ or lower background level. Our results show that the proposed search strategies can probe values of $|V_{eN}|^2$ up to about two orders of magnitude beyond the existing bounds, for ALP mass over 4 GeV and sterile-neutrino mass above the $D$-meson threshold. Compared to the one-DV search, the two-DV one, despite its weaker sensitivities as a result of double exponential suppression of the sterile-neutrino decay positions, possesses the advantage of possible full reconstruction of the signal event allowing for pinning down the masses of the sterile neutrino and the ALP, if a discovery is made.