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Register a new userThe $V_{cb}$ puzzle: an update
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We discuss the impact of the recent untagged analysis of ${B}^0rightarrow D^{*}lbar{ u}_l$ decays by the Belle Collaboration on the extraction of the CKM element $|V_{cb}|$ and provide updated SM predictions for the $bto ctau u$ observables $R(D^*)$, $P_tau$, and $F_L^{D^*}$. The value of $|V_{cb}|$ that we find is about $2sigma$ from the one from inclusive semileptonic $B$ decays, and is very sensitive to the slope of the form factor at zero recoil which should soon become available from lattice calculations.
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We discuss the recent progress in the study of semileptonic kaon and pion decays, including new experimental results, improved electroweak radiative corrections, form factor calculations and isospin-breaking effects. As a result, we obtain $|V_{us}|=0.22309(40)(39)(3)$ from kaon semileptonic decays and $|V_{us}/V_{ud}|=0.22908(66)(41)(40)(2)(1)$ from the ratio between the kaon and pion semileptonic decay rates. We report an apparent violation of the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity at a $3.2sim 5.6sigma$ level, and a discrepancy at a $2.2sigma$ level between the value of $|V_{us}/V_{ud}|$ determined from the vector and axial charged weak interactions. Prospects for future improvements in those comparative precision tests involving $|V_{ud}|$, $|V_{us}|$ and their implications for physics beyond the Standard Model are described.
We perform the simultaneous $|V_{ub}|$ and $|V_{cb}|$ extractions with only the exclusive $Lambda_b$ decays of $Lambda_bto (p,Lambda_c^+)mubar u_mu$, $Lambda_bto ppi^-$ and $Lambda_bto Lambda_c^+ (pi^-, D^-)$. We obtain that $|V_{ub}|=(3.7pm 0.3)times 10^{-3}$ and $|V_{cb}|=(45.9pm 2.7)times 10^{-3}$. Our value of $|V_{ub}|$ is larger than that of $(3.27pm 0.15pm 0.16pm 0.06)times 10^{-3}$, previously extracted by the LHC Collaboration from the exclusive $Lambda_b$ decays also, but nearly identical to $(3.72pm 0.19)times 10^{-3}$ from the exclusive $B$ decays. On the other hand, our extracted result of $|V_{cb}|$ favors the value of $(42.2pm 0.8)times 10^{-3}$ from the inclusive $B$ decays.
In this addendum to $B_s$ mixing observables and $|V_{td}/V_{ts}|$ from sum rules cite{King:2019lal} we study the impact of the recent improvements in the theoretical precision of $B$ meson mixing onto CKM unitarity fits. Our key results are the most precise determination of the angle $gamma = left(63.4pm0.9right)^circ$ in the unitarity triangle and a new value for the CKM element $|V_{cb}|=(41.6pm0.7)cdot10^{-3}$.
The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $vert V_{cb}vert$ is extracted from exclusive semileptonic $B to D^{(*)}$ decays adopting a novel unitarity-based approach which allows to determine in a full non-perturbative way the relevant hadronic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B to D^{(*)}$ FFs at small recoil, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence. Thus, we address the extraction of $vert V_{cb}vert$ from the experimental data on the semileptonic $B to D^{(*)} ell u_ell$, obtaining $vert V_{cb}vert = (40.7 pm 1.2 ) cdot 10^{-3}$ from $B to D$ and $vert V_{cb}vert = (40.6 pm 1.6 ) cdot 10^{-3}$ from $B to D^*$. Our results, though still based on preliminary lattice data for the $B to D^*$ form factors, are consistent within $sim 1$ standard deviation with the most recent inclusive determination $vert V_{cb} vert_{incl} = (42.00 pm 0.65) cdot 10^{-3}$. We investigate also the issue of Lepton Flavor Universality thanks to new theoretical estimates of the ratios $R(D^{(*)})$, namely $R(D) = 0.289(8)$ and $R(D^{*}) = 0.249(21)$. Our findings differ respectively by $sim 1.6sigma$ and $sim1.8sigma$ from the latest experimental determinations.
We point out that the recently increased value of the angle $gamma$ in the Unitarity Triangle (UT), determined in tree-level decays to be $gamma=(74.0^{+5.0}_{-5.8})^circ$ by the LHCb collaboration, combined with the most recent value of $|V_{cb}|$ implies an enhancement of $Delta M_{d}$ over the data in the ballpark of $30%$. This is roughly by a factor of two larger than the enhancement of $Delta M_{s}$ that is independent of $gamma$. This disparity of enhancements is problematic for models with Constrained Minimal Flavour Violation (CMFV) and also for $U(2)^3$ models. In view of the prospects of measuring $gamma$ with the precision of $pm 1^circ$ by Belle II and LHCb in the coming years, we propose to use the angles $gamma$ and $beta$ together with $|V_{cb}|$ and $|V_{us}|$ as the fundamental parameters of the CKM matrix until $|V_{ub}|$ from tree-level decays will be known precisely. Displaying $Delta M_{s,d}$ as functions of $gamma$ clearly demonstrates the tension between the value of $gamma$ from tree-level decays, free from new physics (NP) contributions, and $Delta M_{s,d}$ calculated in CMFV and $U(2)^3$ models and thus exhibits the presence of NP contributions to $Delta M_{s,d}$ beyond these frameworks. We calculate the values of $|V_{ub}|$ and $|V_{td}|$ as functions of $gamma$ and $|V_{cb}|$ and discuss the implications of our results for $varepsilon_K$ and rare $K$ and $B$ decays. We also briefly discuss a future strategy in which $beta$, possibly affected by NP, is replaced by $|V_{ub}|$.
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