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

Abstract

The determination of $|V_{cb}|$ from exclusive semileptonic $B\to D^{\ast }\ell \nu$ 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.

7 pages, section on toy MC added, published version

References in corpus (8)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Combined analysis of semileptonic $B$ decays to $D$ and $D^{\ast }$: $R(D^{(\ast )})$, $|V_{cb}|$, and new physics
• $R(D^{\ast })$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
• Extraction of $|V_{cb}|$ from $B\to D^{(\ast )}\ell {\nu }_{\ell }$ and the Standard Model predictions of $R(D^{(\ast )})$
• A fresh look at the determination of |V_cb| from B-> D^* l nu
• Model-Independent Extraction of $|V_{cb}|$ from $\bar{B}\to D^{\ast }\ell \overline{\nu }$
• Tensions and correlations in $|V_{cb}|$ determinations
• Precise determination of the CKM matrix element $\left|V_{cb}\right|$ with ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with hadronic tagging at Belle

Cited by in corpus (10)

• Lepton-flavour non-universality of $\bar{B}\to D^{\ast }\ell \bar{\nu }$ angular distributions in and beyond the Standard Model
• Measurement of Differential Distributions of $B\to D^{\ast }\ell {\bar{\nu }}_{\ell }$ and Implications on $|V_{cb}|$
• Constrained second-order power corrections in HQET: $R(D^{(\ast )})$, $|V_{cb}|$, and new physics
• $B\to D^{\ast }\ell {\nu }_{\ell }$ semileptonic form factors from lattice QCD with Möbius domain-wall quarks
• Revisiting fits to $B^0\to D^{\ast -}{\ell }^{+}{\nu }_{\ell }$ to measure $|V_{cb}|$ with novel methods and preliminary LQCD data at non-zero recoil
• Discriminating $B\to D^{\ast }\ell \nu$ form factors via polarization observables and asymmetries
• Determination of $|V_{cb}|$ using ${\overline{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with Belle II
• New physics contributions to moments of inclusive $b\to c$ semileptonic decays
• Relations between $b\to c\tau \nu$ Decay Modes in Scalar Models
• On magnitudes of some CKM matrix elements