Axion-like particles solve the $B\to Kν\barν$ and $B\to πK$ puzzles

Abstract

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$σ$. An older puzzle persists in measurements of the branching ratios and CP asymmetries of $B \to πK $ 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 $π^0$. In the minimal model, the ALP has couplings to the photon, top quark and a heavy sterile neutrino $ν_N$. The ALP contributes to the $B \to π^0 K$ decays by mixing with the $π^0$. 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 $K^+ \to π^+ + \mathrm{inv}$ and $K_L \to π^0 + \mathrm{inv}$. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and $b \to s e^+ e^-$.