Implications of $B\to K\hat{I}½\bar{\hat{I}}½$ under Rank-One Flavor Violation hypothesis

Abstract

We study the implications of the observed excess in $B^{+}\to K^{+}\hat{I}½\bar{\hat{I}}½$ 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 $K\to \ddot{I}€\hat{I}½\bar{\hat{I}}½$, $B_s\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}$, meson mixing and the LHC searches in $\ddot{I}{„}^{+}\ddot{I}{„}^{-}$ 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 $pp\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$. In all cases we find that a flavour alignment close to the third generation is generically preferred.

v2: matches published version v1: 34 pages, 13 figures