Disentangling left and right-handed neutrino effects in $B\to K^{(\ast )}\nu \nu$

The first observation of $\mathcal{B}(B^{+}\to K^{+}\nu \nu )$ by the Belle II experiment lies almost $3\sigma$ away from the Standard Model expectation. In this letter we study this result in the SMEFT, extended by a light right-handed neutrino. We explore the correlations between the measured decay rate and other observables, such as $\mathcal{B}(B\to K^{\ast }\nu \nu )$ and $F_L(B\to K^{\ast }\nu \nu )$, showing that they could disentangle among scenarios involving left-handed neutrinos and those with the right-handed ones. Furthermore, we find that the high-$p_T$ tails of Drell-Yan processes studied at LHC provide important constraints that help us exclude some of the scenarios consistent with the Belle II result.