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Register a new userEmerging $Delta M_{d}$-Anomaly from Tree-Level Determinations of $|V_{cb}|$ and the Angle $gamma$
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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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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 update the standard model (SM) predictions of $R(D^*)$ using the latest results on the decay distributions in $B to D^* ell u_{ell}$ ($ell = mu, e$) by Belle collaboration, while extracting $|V_{cb}|$ at the same time. Depending on the inputs used in the analysis, we define various fit scenarios. Although the central values of the predicted $R(D^*)$ in all the scenarios have reduced from its earlier predictions in 2017, the results are consistent with each other within the uncertainties. In this analysis, our prediction of $R(D^*)$ is consistent with the respective world average at $sim 3sigma$. We have also predicted several angular observables associated with $B to D^* tau u_{tau}$ decays. We note that the predicted $F_L(D^*)$ is consistent with the corresponding measurement at 2$sigma$. Utilizing these new results, we fit the Wilson coefficients appearing beyond the standard model of particle physics (BSM). To see the trend of SM predictions, we have utilized the recently published preliminary results on the form-factors at non-zero recoil by the lattice groups like Fermilab-MILC and JLQCD and predicted the observables in $B to D^* ell u_{ell}$, and $B to D^* tau u_{tau}$ 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 $|V_{cb}|=(41.6pm0.7)cdot10^{-3}$.
We extract $|V_{cb}|$ from the available data in the decay $B to D^{(*)}ell u_{ell}$. Our analysis uses the $q^2(w)$ binned differential decay rates in different subsamples of $Bto Dell u_ell$ ($ell = e, mu$), while for the decay $Bto D^*ell u_ell$, the unfolded binned differential decay rates of four kinematic variables including the $q^2$ bins have been used. In the CLN and BGL parameterizations of the form factors, the combined fit to all the available data along with their correlations yields $|V_{cb}| = (39.77 pm 0.89)times 10^{-3}$ and $(40.90 pm 0.94)times 10^{-3}$ respectively. In these fits, we have used the inputs from lattice and light cone sum rule (LCSR) along with the data. Using our fit results and the HQET relations (with the known corrections included) amongst the form factors, and parameterizing the unknown higher order corrections (in the ratios of HQET form factors) with a conservative estimate of the normalizing parameters, we obtain $R(D^{*}) = 0.259 pm 0.006$ (CLN) and $R(D^*) = 0.257 pm 0.005$ (BGL).
We reemphasize that the ratio $R_{smu} equiv overline{mathcal{B}}(B_stomubarmu)/Delta M_s$ is a measure of the tension of the Standard Model (SM) with latest measurements of $overline{mathcal{B}}(B_stomubarmu)$ that does not suffer from the persistent puzzle on the $|V_{cb}|$ determinations from inclusive versus exclusive $bto cellbar u$ decays and which affects the value of the CKM element $|V_{ts}|$ that is crucial for the SM predictions of both $overline{mathcal{B}}(B_stomubarmu)$ and $Delta M_s$, but cancels out in the ratio $R_{smu}$. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about $2sigma$ for $R_{smu}$ measurements with the SM independently of $|V_{ts}|$. We also discuss the ratio $R_{dmu}$ which could turn out, in particular in correlation with $R_{smu}$, to be useful for the search for New Physics, when the data on both ratios improves. Also $R_{dmu}$ is independent of $|V_{cb}|$ or more precisely $|V_{td}|$.
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