The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

TL;DR

This paper explores the implications of assuming exclusive determinations of CKM elements on rare K and B decays within the Standard Model, revealing new tensions and increased room for new physics, especially in meson mixing and decay processes.

Contribution

It presents a novel analysis assuming exclusive CKM values, contrasting with traditional global fit approaches, and uncovers significant tensions and potential signals of new physics.

Findings

3.1σ tension in ΔMs independent of γ

Tensions in ΔMd range from 4.0σ to 1.1σ for γ between 60° and 75°

2.7σ anomaly in B_s→μ+μ− from exclusive CKM assumption

Abstract

The most common predictions for rare $K$ and $B$ decay branching ratios in the Standard Model are based on the CKM elements $|V_{cb}|$ and $|V_{ub}|$ resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route. We assume that the future true values of $|V_{cb}|$ and $|V_{ub}|$ will be both from exclusive determinations and set them equal to the most recent ones from FLAG. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using the HPQCD $B^0_{s,d}-\bar B^0_{s,d}$ hadronic matrix elements a $3.1\sigma$ tension in $\Delta M_s$ independently of $\gamma$ is found. For $60^\circ\le\gamma\le 75^\circ$ the tension in $\Delta M_d$ between $4.0\sigma$ and $1.1\sigma$ is found and in the case of $\epsilon_K$ between $5.2\sigma$ and $2.1\sigma$. Moreover, the room for new physics in $K^+\to\pi^+\nu\bar\nu$, $K_L\to\pi^0\nu\bar\nu$ and $B\to K(K^*)\nu\bar\nu$ decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which $|V_{cb}|$ in the former scenario is replaced by the most recent inclusive $|V_{cb}|$ and present the dependence of all observables considered by us in both scenarios as functions of $\gamma$. We also compare the determination of $|V_{cb}|$ from $\Delta M_s$, $\Delta M_d$, $\epsilon_K$ and $S_{\psi K_S}$ using $B^0_{s,d}-\bar B^0_{s,d}$ hadronic matrix elements from LQCD with $2+1+1$ flavours, $2+1$ flavours and their average. Only for the $2+1+1$ case values for $\beta$ and $\gamma$ exist for which the same value of $|V_{cb}|$ is found: $|V_{cb}|=42.6(4)\times 10^{-3}$. This in turn implies a $2.7\sigma$ anomaly in $B_s\to\mu^+\mu^-$.