Decoding the $B\to K\nu \nu$ excess at Belle II: kinematics, operators, and masses

An excess in the branching fraction for $B^{+}\to K^{+}\nu \nu$ recently measured at Belle II may be a hint of new physics. We perform thorough likelihood analyses for different new physics scenarios such as $B\to KX$ with a new invisible particle $X$, or $B\to K\chi \chi$ through a scalar, vector, or tensor current with $\chi$ being a new invisible particle or a neutrino. We find that vector-current 3-body decay with $m_X\simeq 0.6$ GeV - which may be dark matter - is most favored, while 2-body decay with $m_X\simeq 2$ GeV is also competitive. The best-fit branching fractions for the scalar and tensor cases are a few times larger than for the 2-body and vector cases. Past BaBar measurements provide further discrimination, although the best-fit parameters stay similar.