Abstract
The determination of $|V_{cb}|$ from exclusive semileptonic $B\to D^*\ell\nu$ decays is sensitive to the choice of form factor parametrization. Larger $|V_{cb}|$ values are obtained fitting the BGL versus the CLN parametrization to recent Belle measurements. For the BGL parametrization, published fits use different numbers of parameters. We propose a method based on nested hypothesis tests to determine the optimal number of BGL parameters to fit the data, and find that six parameters are optimal to fit the Belle tagged and unfolded measurement. We further explore the differences between fits that use different numbers of parameters. The fits which yield $|V_{cb}|$ values in better agreement with determinations from inclusive semileptonic decays, tend to exhibit tensions with heavy quark symmetry expectations. These have to be resolved before the determinations of $|V_{cb}|$ from exclusive and inclusive decays can be considered understood.
Highlights
In 2017, the Belle Collaboration presented, for the first time, unfolded measurements of the differential decay distributions for B → DÃlνdecays [1], and another measurement appeared more recently [2]
Using a prescription based on a nested hypothesis test, we find that at least six parameters are required to describe the data from Ref. [1]
The N 1⁄4 5 and 6 fits we study in detail yield jVcbj values in better agreement with determinations from inclusive semileptonic decays, but they exhibit tensions with expectations from heavy quark symmetry
Summary
In 2017, the Belle Collaboration presented, for the first time, unfolded measurements of the differential decay distributions for B → DÃlνdecays [1], and another measurement appeared more recently [2]. The choice of form factor parametrizations can have a sizable impact on the extracted value of jVcbj This is because heavy quark symmetry gives the strongest constraints on the differential rate at zero recoil (maximal dilepton invariant mass, q2) [3,4,5,6,7,8,9,10], resulting in both continuum methods and lattice QCD giving the most precise information on the normalization of the rate at zero repcoffiffiiffilffi.ffiffiffiffiHffiffiffioffiffiffiwffiffiffieffi ver, phase space vanishes near maximal q2 as q2max − q2, so the measured q2 spectrum has to be fitted over some range to extract jVcbj. The N 1⁄4 5 and 6 fits we study in detail yield jVcbj values in better agreement with determinations from inclusive semileptonic decays, but they exhibit tensions with expectations from heavy quark symmetry
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