Revisiting the production of ALPs at B-factories

In this paper, the production of Axion-Like Particles (ALPs) at $B$-factories via the process $e^+e^- \to \gamma a$ is revisited. To this purpose, the relevant cross-section is computed via an effective Lagrangian with simultaneous ALP couplings to $b$-quarks and photons. The interplay between resonant and non-resonant contributions is shown to be relevant for experiments operating at $\sqrt{s}=m_{\Upsilon(nS)}$, with $n=1,2,3$, while the non-resonant one dominates at $\Upsilon(4S)$. These effects imply that the experimental searches performed at different quarkonia resonances are sensitive to complementary combinations of ALP couplings. To illustrate these results, constraints from existing BaBar and Belle data on ALPs decaying into invisible final states are derived, and the prospects for the Belle-II experiment are discussed.