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

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 $B_{s,d}^0-{\bar{B}}_{s,d}^0$ 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 $B\to K(K^{\ast })\nu \bar{\nu }$ 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 $B_{s,d}^0-{\bar{B}}_{s,d}^0$ 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 $B_s\to {\mu }^{+}{\mu }^{-}$.

20 pages, 8 Figures, V2: new references and uncertainties in Fig. 8 added. Conclusions unchanged. V3: Determination of $\gamma$ and $|V_{cb}|$ significantly improved. Equation (19) and numerous references to Lattice QCD calculations added. Conclusions strengthened

References in corpus (13)

• Updated NNLO QCD predictions for the weak radiative B-meson decays
• Bs mixing observables and Vtd/Vts from sum rules
• Three loop calculations and inclusive $V_{cb}$
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Heavy-Quark Expansion for ${\bar{B}}_s\to D_s^{(\ast )}$ Form Factors and Unitarity Bounds beyond the $SU(3{)}_F$ Limit
• Standard-model prediction of ${\epsilon }_K$ with manifest CKM unitarity
• Neutral $B$ meson mixings and $B$ meson decay constants with static heavy and domain-wall light quarks
• $|V_{cb}|$ and $R(D^{(\ast )})$ using lattice QCD and unitarity
• B-meson decay constants from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
• The $\bar{B}\to \pi$ form factors from QCD and their impact on $|V_{ub}|$
• Impact of $B\to K\nu \bar{\nu }$ measurements on beyond the Standard Model theories
• Searching for New Physics with $\overline{\mathcal{B}}(B_{s,d}\to \mu \bar{\mu })/\Delta M_{s,d}$
• Loopy Determinations of $V_{ub}$ and $V_{cb}$

Cited by in corpus (12)

• 50 Years of Quantum Chromodynamics
• Revisiting $B\to K^{(\ast )}\nu \bar{\nu }$ decays in the Standard Model and beyond
• Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD
• Standard Model Predictions for Rare K and B Decays without New Physics Infection
• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
• New Physics in $B_q^0-{\bar{B}}_q^0$ Mixing: Present Challenges, Prospects, and Implications for $B_q^0\to {\mu }^{+}{\mu }^{-}$
• The Rumble in the Meson: a leptoquark versus a $Z^{\prime }$ to fit $b\to s{\mu }^{+}{\mu }^{-}$ anomalies including 2022 LHCb $R_{K^{(\ast )}}$ measurements
• 331 Model Predictions for Rare $B$ and $K$ Decays, and $\Delta F=2$ Processes: an Update
• Flavonstrahlung in the $B_3-L_2$ $Z^{\prime }$ Model at Current and Future Colliders
• $B\to K^{(\ast )}\nu \bar{\nu }$ in covariant confined quark model
• Kaon physics overview
• Rare decays at LHCb