Eur. Phys. J. C (2024) 84: 1012
https://doi.org/10.1140/epjc/s10052-024-13425-x

Regular Article

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

Department of Physics, College of Physics & Optoelectronic Engineering, Jinan University, 510632, Guangzhou, People’s Republic of China

^c fanrongxu@jnu.edu.cn

Received: 11 July 2024
Accepted: 25 September 2024
Published online: 7 October 2024

Abstract

The recent measurement of $\mathcal{B}(B^{+}\to K^{+}\nu \overline{\nu })$ by Belle-II reveals a $2.8\sigma$ deviation from the Standard Model (SM) prediction. Combining this with a prior Belle measurement of $\mathcal{B}(B^0\to K_{}^{\ast 0}\nu \overline{\nu })$, the upper bound of the ratio $\mathcal{B}(B^0\to K_{}^{\ast 0}\nu \overline{\nu })/\mathcal{B}(B^{+}\to K^{+}\nu \overline{\nu })$ is notably smaller than the SM prediction. In this work, tensions are solved within the framework of Standard Model effective field theory (SMEFT). The flavor-changing-neutral-current (FCNC) and charged-current observables of either down-type ($b\to s\nu \overline{\nu }$, $b\to s{\ell }^{+}{\ell }^{-}$, and $b\to u_i\ell \overline{\nu }$) or up-type ($u_j\to u_i\nu \overline{\nu }$, $u_j\to u_i{\ell }^{+}{\ell }^{-}$, and $u_j\to s\ell \overline{\nu }$) processes, described by low-energy effective field theory (LEFT) operators, are interconnected by a minimal set of four SMEFT operators at the electroweak scale. 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 $\mathcal{B}(B\to K_{}^{(\ast )}\nu \overline{\nu })$. 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 $B^0\to K_{}^{\ast 0}\nu \overline{\nu }$ 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 ${10}^{-4}$.