Displaced or invisible? ALPs from $B$ decays at Belle II

At colliders, neutral long-lived particles can be detected through displaced decay products or as missing energy. Which search strategy is better depends on the particle's decay length just as on the detector properties. We investigate the complementarity of displaced and invisible signatures for the Belle II experiment. Focusing on axion-like particles $a$ produced from meson decays, we present a new search strategy for two-body decays $B^+ \to K^+ a, a\to E\!\!\!/$ with missing energy $E\!\!\!/$. With $50\,$ab$^{-1}$ of data, Belle II can probe light invisible resonances with branching ratio $\mathcal{B}(B^+\to K^+ a) \gtrsim 10^{-7}$ and decay length $c\tau_a \gtrsim 1\,$m. For axion-like particles, we expect the sensitivity of $B^+ \to K^+ E\!\!\!/$ to small couplings to improve by up to two orders of magnitude compared to previous searches at collider and fixed-target experiments. For sub-GeV particles, $B^+ \to K^+ E\!\!\!/$ at Belle II and searches at beam-dump experiments are most sensitive; for heavier particles, searches for displaced vertices at Belle II, long-lived particle experiments at the LHC, and future fixed-target experiments can probe the smallest couplings.