The V puzzle: An update

Abstract

We discuss the impact of the recent untagged analysis of B 0 → D * lν l decays by the Belle Collaboration on the extraction of the CKM element |V cb | and provide updated SM predictions for the b → cτ ν observables R(D * ), Pτ , and F D * L . The value of |V cb | that we find is about 2σ 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. I. INTRODUCTIONThe values of the Cabibbo-Kobayashi-Maskawa matrix element |V cb | determined from inclusive and exclusive semileptonic B decays have differed at the level of about 3σ for quite some time. The situation around 2016 is well summarized by the latest HFLAV world average [1],1) which combines many experimental results by BaBar, Belle and previous experiments on B → D * ν with the only unquenched lattice calculation of the form factor at zero-recoil (where the D * is produced at rest in the B rest frame) available at the time [2]. The B → D ν channel tended to be considerably less precise. Eq. (1) should be compared with the most recent inclusive determination [3], |V cb | = (42.00 ± 0.64) 10 −3 (B → X c ν), (2)based on a fit to the moments of various kinematic distributions in the Heavy Quark Expansion. This 3σ discrepancy has become known as the V cb puzzle.The last few years have seen a series of new theoretical and experimental results, each bringing a new piece to the puzzle. First, progress in the lattice QCD calculations of the form factors of B → D ν [4, 5] at small recoil (high q 2 ) improved significantly the exclusive determination based on that channel: a combined fit [6] to experimental [7,8] and lattice data for the q 2 distribution gives 1 |V cb | = (40.49 ± 0.97) 10 −3 (B → D ν) , (3) in good agreement with both (1) and (2). *

Global fit to b → cτν transitions

“…The slightly larger significance with respect to the value quoted by HFLAV is due to our different SM prediction and has three aspects: slightly smaller central value and uncertainty for R D * , as well as the inclusion of the correlation between the SM predictions for R D and R D * . Regarding the central value, note also the ∼ 1σ lower central value of the SM prediction for R D * in [136] compared to [17] after taking into account new data for B → D * ν.…”

Theory determination of $$\varvec{\bar{B}\rightarrow D^{(*)}\ell ^-\bar{\nu }}$$ form factors at $$\varvec{\mathcal {O}(1/m_c^2)}$$

“…• No such parametrization dependence is found when employing the recent untagged Belle results [4], but the value of |V cb | extracted from the combined 2017/2018 Belle data remains ∼ 2σ smaller than the one from inclusive decays [20].…”

Constraints on New Physics from B Mesons

“…At present, unfortunately, a precise determination of the CKM matrix solely through treelevel decays is not possible. While the element |V us | is known to very good accuracy, the tensions between inclusive and exclusive determinations of |V ub | [1] and to a lesser extent also |V cb | [2] persist and lead to a significant uncertainty in the determination of the length of the side R b of the unitarity triangle. Therefore, in order to obtain a precise result for the full Unitarity Triangle (UT), one still needs to rely on the measurement of sin 2β from the time-dependent CP asymmetry in B → J/ψK S .…”