Correlating $B\to K^{(\ast)} \nu\bar{\nu}$ and flavor anomalies in SMEFT

Abstract

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 $10^{-4}$.