Recently, the Belle II collaboration announced the first measurement of
B(B+βK+Ξ½Ξ½Λ), which is found to be about 2.7Ο
higher than the SM prediction. We decipher the data with two new physics
scenarios: the underlying bβsΞ½Ξ½Λ transition is, besides the SM
contribution, further affected by heavy new mediators that are much heavier
than the EW scale, or amended by an additional decay channel with undetected
light final states like dark matter or axion-like particles. These two
scenarios can be most conveniently analyzed in the SMEFT and the dark SMEFT
(DSMEFT) framework, respectively. We consider the flavour structures of the
resulting effective operators to be either generic or satisfy the minimal
flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In
the first scenario, once the MFV is assumed, only one SM-like low-energy
effective operator induced by the SMEFT dim-6 operators can account for the
Belle II excess, the parameter space of which is, however, excluded by the
Belle upper bound on B(B0βKβ0Ξ½Ξ½Λ). In the second
scenario, it is found that the Belle II excess can be accommodated by 22 of the
DSMEFT operators involving one or two scalar, fermionic, or vector dark matters
as well as ALPs. These operators also receive dominant constraints from the
B0βKβ0+inv and Bsββinv decays. In the MFV hypothesis, the number
of viable operators is reduced to 14, and the B+βΟ++inv and
K+βΟ++inv decays start to put further constraints. Within the parameter
space allowed by all the current experimental data, the q2 distributions
(and FLβ) of the BβK(β)+inv decays are studied for each viable
operator. In addition, we, for the first time, calculate systematically the
longitudinal polarization fraction FLβ of Kβ in the BβKβ+inv decays
within the DLEFT.Comment: 51 pages, 13 figures, comments welcome; v2: discussions on FLβ of
the BβKβ+inv decay in the DSMEFT added, errors in the BβV+inv decays for some operators involving two scalar or vector DM
fields fixed, the related discussions and figures 2, 6, 7, 11 and 12
corrected, main conclusion unchanged, a few comments and refs adde