Eur. Phys. J. C (2024) 84: 1217
https://doi.org/10.1140/epjc/s10052-024-13534-7

Regular Article

Implications of $B\to K\nu \overline{\nu }$ under rank-one flavor violation hypothesis

¹ INFN, Sezione di Trieste, SISSA, Via Bonomea 265, 34136, Trieste, Italy
² Università degli Studi di Roma la Sapienza and INFN Section of Roma 1, Piazzale Aldo Moro 5, 00185, Rome, Italy
³ SISSA International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy
⁴ Dipartimento di Fisica e Astronomia ‘G. Galilei’, Università di Padova and INFN Sezione di Padova, Via F. Marzolo 8, 35131, Padua, Italy

^a claudio.toni@pd.infn.it

Received: 30 July 2024
Accepted: 24 October 2024
Published online: 25 November 2024

Abstract

We study the implications of the observed excess in $B^{+}\to K^{+}\nu \overline{\nu }$ under the assumption of Rank-One Flavour Violation, i.e. that New Physics couples to a single specific direction in flavour space. By varying this direction we perform analyses at the level of the low-energy EFT, the SMEFT, and with explicit mediators such as leptoquarks and colorless vectors ($Z^{\prime }$ and $V^{\prime }$). We study correlations with other flavour, electroweak and collider observables, finding that the most interesting ones are with $K\to \pi \nu \overline{\nu }$, $B_s\to {\mu }^{+}{\mu }^{-}$, meson mixing and the LHC searches in ${\tau }^{+}{\tau }^{-}$ high-energy tails. Among the various mediators, the scalar leptoquarks ${\tilde{R}}_2$ and $S_1$ offer the best fits of the Belle-II excess, while being consistent with the other bounds. On the other hand, colorless vectors are strongly constrained by meson mixing and resonance searches in $pp\to {\tau }^{+}{\tau }^{-}$. In all cases we find that a flavour alignment close to the third generation is generically preferred.