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 $\mathcal{B}(B^0\to K^{\ast 0}\nu \bar{\nu })$, the upper bound of the ratio $\mathcal{B}(B^0\to K^{\ast 0}\nu \bar{\nu })/\mathcal{B}(B^{+}\to K^{+}\nu \bar{\nu })$ 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 $B^0\to K^{\ast 0}\nu \bar{\nu }$ 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 $10^{-4}$.

22 pages, 2 figures, 3 tables, final version accepted in EPJC

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