# ${\it V}_{\it cb}$ 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
$0.04229$ $\pm0.00137$ 1
 2016
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0423$ $\pm0.0019$ $\pm0.0014$ 2
 2010
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0431$ $\pm0.0008$ $\pm0.0023$ 3
 2009 A
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0416$ $\pm0.0047$ $\pm0.0037$ 4
 1999
CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0278$ $\pm0.0068$ $\pm0.0065$ 5
 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
 2002 E
BELL Repl. by GLATTAUER 2016
$0.0337$ $\pm0.0044$ ${}^{+0.0072}_{-0.0049}$ 7
 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 ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$