# N = 5, 6, 7, 8: Nested hypothesis tests and truncation dependence of $|V_{cb}|$

## TL;DR

This paper introduces a nested hypothesis testing method to optimize the BGL form factor parametrization for determining |V_{cb}| from B meson decays, revealing tensions with heavy quark symmetry that impact the consistency of exclusive and inclusive decay measurements.

## Contribution

It proposes a novel nested hypothesis test approach to select the optimal number of parameters in BGL fits for |V_{cb}|, improving the robustness of the analysis.

## Key findings

- Six BGL parameters are optimal for fitting Belle data.
- Fits with more parameters align |V_{cb}| with inclusive decay results.
- Tensions with heavy quark symmetry remain in certain fits.

## 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.