The recent measurement of $\mathcal{ B}(B^+\to K^+\nu\bar{ \nu})$ by Belle-II reveals a $2.8~\sigma$ deviation from the Standard Model (SM) prediction. Combining this with a prior Belle measurement of $\mathcal{ B}(B^{ 0}\to K^{ \ast0}\nu\bar{ \nu})$, the upper bound of the ratio $\mathcal{ B}(B^{ 0}\to K^{ \ast0}\nu\bar{ \nu})/\mathcal{ B}(B^+\to K^+\nu\bar{ \nu})$ is notably smaller than the SM prediction. In this work, tensions are solved within the framework of Standard Model Effective Field Theory (SMEFT). Flavor observables, described by Low-Energy Effective Field Theory (LEFT) operators, are interconnected by SMEFT at the electroweak scale. Utilizing a set of only four SMEFT operators, the FCNC process $b\to s\nu\bar{ \nu}$ is correlated with $b\to s\ell^+\ell^-$, $b\to u_i\ell\bar{ \nu}$, $u_j\to s\ell\bar{ \nu}$, $u_j\to u_i\nu\bar{ \nu}$, and $u_j\to u_i\ell^+\ell^-$. Subsequently, we obtain the latest ranges of Wilson coefficients for these four operators through a global fit that accommodates flavor anomalies such as $R_{ K^{ (\ast)}}$, $R_{ D^{ (\ast)}}$, and $\mathcal{ B}(B\to K^{ (\ast)}\nu\bar{ \nu})$. Our findings reveal that predictions for $\mathcal{ B}(B^+\to \tau^+\nu_\tau)$ and $\mathcal{ B}(D_s^+\to \tau^+\nu_\tau)$ align well with measured values from Belle and BESIII, based on the fitted coefficients. The predicted branching fraction for $B^0\to K^{ \ast0}\nu\bar{ \nu}$ is $(1.42\pm 0.74)\times 10^{ -5}$, closely approaching the current experimental upper limit. Anticipation surrounds the rare decay $B_s\to \tau^+ \tau^-$, expected in the near future with a branching fraction on the order of $10^{ -4}$.
Categories: hep-ph nucl-th