Tensions and correlations in $|V_{cb}|$ determinations

Recently several papers extracted $|V_{cb}|$ using the Belle measurement [A. Abdesselam et al. (Belle Collaboration), arXiv:1702.01521.] of the exclusive $\overline{B}\to D^{*}\ell \overline{\nu }$ unfolded differential decay rates, available for the first time. Depending on the theoretical inputs, some of the fits yield higher $|V_{cb}|$ values, compatible with those from inclusive semileptonic $B$ decays. Since these four fits use mostly the same data, if their correlations were close to 100%, the tension between them would be over $5\sigma$. We determine the correlations, find that the tension between the results is less than $3\sigma$, and explore what might lead to improving the consistency of the fits. We find that fits that yield the higher values of $|V_{cb}|$, also suggest large violations of heavy quark symmetry. These fits are also in tension with preliminary lattice QCD data on the form factors. Without additional experimental data or lattice QCD input, there are no set of assumptions under which the tension between exclusive and inclusive determinations of $|V_{cb}|$ can be considered resolved.

Figure 1

The form factor ratios $R_1(w)$ (left) and $R_2(w)$ (right) for the BGL (red long dashed), CLN (gray dashed), CLNnoR (orange dotted) fits, and noHQS (purple dot-dot-dashed). The BGL, CLNnoR, and noHQS fits for $R_1$ suggest a possibly large violation of heavy quark symmetry, in conflict with lattice QCD predictions. The blue lines show our estimated bounds, based on preliminary FNAL/MILC lattice results [29]. The black data point for $R_1(1)$ follows from the FNAL/MILC $B\to D\ell \overline{\nu }$ result and heavy quark symmetry (see details in the text).

Figure 2

$\mathrm{d}\mathrm{\Gamma }/\mathrm{d}w$ for the fit scenarios shown in Fig. 1.