${\it V}_{\it cb}$ MEASUREMENTS

For the discussion of ${\it V}_{\it cb}$ measurements, which is not repeated here, see the review on ``Determination of $\vert {\it V}_{\it cb}\vert $ and $\vert {\it V}_{\it ub}\vert $.''
The CKM matrix element $\vert {\it V}_{\it cb}\vert $ can be determined by studying the rate of the semileptonic decay ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}}{}^{(*)}$ ${{\mathit \ell}}{{\mathit \nu}}$ as a function of the recoil kinematics of ${{\mathit D}}{}^{(*)}$ mesons. Taking advantage of theoretical constraints on the normalization and a linear $\omega ~$dependence of the form factors ($\mathit F(\omega $), $\mathit G(\omega $)) provided by Heavy Quark Effective Theory (HQET), the $\vert {\it V}_{\it cb}\vert {\times }\mathit F(\omega $) and $\rho {}^{2}$ ($\mathit a{}^{2}$) can be simultaneously extracted from data, where $\omega $ is the scalar product of the two-meson four velocities, $\mathit F$(1) is the form factor at zero recoil ($\omega $=1) and $\rho {}^{2}$ is the slope, sometimes denoted as $\mathit a{}^{2}$. Using the theoretical input of $\mathit F$(1), a value of $\vert {\it V}_{\it cb}\vert $ can be obtained.
``OUR EVALUATION'' is an average using rescaled values of the data listed below. The average and rescaling were performed by the Heavy Flavor Averaging Group (HFLAV) and are described at https://hflav.web.cern.ch/. The averaging/rescaling procedure takes into account correlations between the measurements.

$\vert {\it V}_{\it cb}\vert $ ${\times }$ $\boldsymbol G$(1) (from ${{\boldsymbol B}}$ $\rightarrow$ ${{\boldsymbol D}^{-}}{{\boldsymbol \ell}^{+}}{{\boldsymbol \nu}}$ ) INSPIRE search

VALUE

DOCUMENT ID

TECN

COMMENT

$\bf{ 0.04157 \pm0.00100}$

OUR EVALUATION with $\rho {}^{2}=1.128$ $\pm0.033$ and a correlation 0.751. The fitted $\chi {}^{2}$ is 4.7 for 8 degrees of freedom.

$\bf{ 0.0422 \pm0.0010}$

OUR AVERAGE

$0.04229$ $\pm0.00137$

GLATTAUER

2016

BELL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.0423$ $\pm0.0019$ $\pm0.0014$

AUBERT

2010

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.0431$ $\pm0.0008$ $\pm0.0023$

AUBERT

2009

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.0416$ $\pm0.0047$ $\pm0.0037$

⁴

BARTELT

1999

CLE2

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.0278$ $\pm0.0068$ $\pm0.0065$

⁵

BUSKULIC

1997

ALEP

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$

• • • We do not use the following data for averages, fits, limits, etc. • • •

$0.0411$ $\pm0.0044$ $\pm0.0052$

⁶

ABE

2002

BELL

Repl. by GLATTAUER 2016

$0.0337$ $\pm0.0044$ ${}^{+0.0072}_{-0.0049}$

⁷

ATHANAS

1997

CLE2

Repl. by BARTELT 1999

¹ Obtained from a fit to the combined partially reconstructed ${{\mathit B}}$ $\rightarrow$ ${{\overline{\mathit D}}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ sample while tagged by the other fully reconstructed ${{\mathit B}}$ meson in the event. Also reports fitted $\rho {}^{2}$ = $1.09$ $\pm0.05$.

² Obtained from a fit to the combined ${{\mathit B}}$ $\rightarrow$ ${{\overline{\mathit D}}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ sample in which a hadronic decay of the second ${{\mathit B}}$ meson is fully reconstructed and $\rho {}^{2}$ = $1.20$ $\pm0.09$ $\pm0.04$.

³ Obtained from a global fit to ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ events, with reconstructed ${{\mathit D}^{0}}{{\mathit \ell}}$ and ${{\mathit D}^{+}}{{\mathit \ell}}$ final states and $\rho {}^{2}$ = $1.20$ $\pm0.04$ $\pm0.07$.

⁴ BARTELT 1999 : measured using both exclusive reconstructed ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ samples.

⁵ BUSKULIC 1997 : measured using exclusively reconstructed ${{\mathit D}^{\pm}}$ with a $\mathit a{}^{2}=-0.05$ $\pm0.53$ $\pm0.38$. The statistical correlation is $0.99$.

⁶ Using the missing energy and momentum to extract kinematic information about the undetected neutrino in the ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ decay.

⁷ ATHANAS 1997 : measured using both exclusive reconstructed ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ samples with a $\rho {}^{2}=0.59$ $\pm0.22$ $\pm0.12{}^{+0.59}_{-0}$. They report their experiment's uncertainties $\pm{}0.0044$ $\pm0.0048$ ${}^{+0.0053}_{-0.0012}$, where the first error is statistical, the second is systematic, and the third is the uncertainty due to the form factor model variations. We combine the last two in quadrature.

References:

GLATTAUER

2016

PR D93 032006

Measurement of the Decay ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ in Fully Reconstructed Events and Determination of the Cabibbo-Kobayashi-Maskawa Matrix Element $\vert {\it V}_{\it cb}\vert $

AUBERT

2010

PRL 104 011802

Measurement of $\vert {\it V}_{\it cb}\vert $ and the Form-Factor Slope in ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$ Decays in Events Tagged by a Fully Reconstructed ${{\mathit B}}$ Meson

AUBERT

2009A

PR D79 012002

Measurements of the Semileptonic Decays ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \ell}}{{\overline{\mathit \nu}}}$ and ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \ell}}{{\overline{\mathit \nu}}}$ using a Global Fit to ${{\mathit D}}{{\mathit X}}{{\mathit \ell}}{{\overline{\mathit \nu}}}$ Final States

ABE

2002E

PL B526 258

Measurement of B( ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$ ) and Determination of $\vert \mathit V_{cb}\vert $

BARTELT

1999

PRL 82 3746

Measurement of the ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \ell}}{{\mathit \nu}}$ Branching Fractions and Form Factor

ATHANAS

1997

PRL 79 2208

Measurement of the ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \ell}}{{\overline{\mathit \nu}}}$ Partial Width and Form Factor Parameters

BUSKULIC

1997

PL B395 373

Measurement of $\vert \mathit V_{cb}\vert $, Form Factors and Branching Fractions in the Decays ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$ and ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$