Axion-like particles solve the Bto Kνbarν and Bto π K puzzles

The recent measurement of the branching ratio of $B^+ \to K^+ + \mathrm{inv}$ (where "inv" denotes invisible states) by the Belle~II collaboration is enhanced relative to the standard model expectation by 2.7$\sigma$. An older puzzle persists in measurements of the branching ratios and CP asymmetries of $B \to \pi K $ decays. We address these two anomalies in flavor-changing neutral current $B$ decays, with a short-lived axion-like particle (ALP) with mass close to that of the $\pi^0$. In the minimal model, the ALP has couplings to the photon, top quark and a heavy sterile neutrino $\nu_N$. The ALP contributes to the $B \to \pi^0 K$ decays by mixing with the $\pi^0$. It contributes to $B^+ \to K^+ + \mathrm{inv}$ by its off-shell coupling to sterile neutrino pairs. We make predictions for all $B \to K^{(*)} + \mathrm{inv}$ modes and for the rare kaon decays $K^+ \to \pi^+ + \mathrm{inv}$ and $K_L \to \pi^0 + \mathrm{inv}$. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and $b \to s e^+ e^-$.