# ${\it V}_{\it cb}$ 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.

# $\vert {\it V}_{\it cb}\vert$ ${\times }$ $\boldsymbol F$(1) (from ${{\boldsymbol B}^{0}}$ $\rightarrow$ ${{\boldsymbol D}^{*-}}{{\boldsymbol \ell}^{+}}{{\boldsymbol \nu}}$ ) INSPIRE search

VALUE DOCUMENT ID TECN  COMMENT
$\bf{ 0.03561 \pm0.00043}$ OUR EVALUATION  with $\rho {}^{2}=1.205$ $\pm0.026$ and a correlation 0.338. The fitted $\chi {}^{2}$ is 30.2 for 23 degrees of freedom.
$\bf{ 0.0355 \pm0.0008}$ OUR AVERAGE  Error includes scale factor of 1.7.
$0.03483$ $\pm0.00015$ $\pm0.00056$ 1
 2019
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0359$ $\pm0.0002$ $\pm0.0012$ 2
 2009 A
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0392$ $\pm0.0018$ $\pm0.0023$ 3
 2004 D
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$0.0431$ $\pm0.0013$ $\pm0.0018$ 4
 2003
CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0355$ $\pm0.0014$ ${}^{+0.0023}_{-0.0024}$ 5
 2001 H
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.0371$ $\pm0.0010$ $\pm0.0020$ 6
 2000 Q
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.0319$ $\pm0.0018$ $\pm0.0019$ 7
 1997
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.0346$ $\pm0.0002$ $\pm0.0010$ 8
 2010
BELL Rep. by WAHEED 2019
$0.0359$ $\pm0.0006$ $\pm0.0014$ 9
 2008 AT
BABR Repl. by AUBERT 2009A
$0.0344$ $\pm0.0003$ $\pm0.0011$ 10
 2008 R
BABR Repl. by AUBERT 2009A
$0.0355$ $\pm0.0003$ $\pm0.0016$ 11
 2005 E
BABR Repl. by AUBERT 2008R
$0.0377$ $\pm0.0011$ $\pm0.0019$ 12
 2004 D
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$0.0354$ $\pm0.0019$ $\pm0.0018$ 13
 2002 F
BELL Repl. by DUNGEL 2010
$0.0431$ $\pm0.0013$ $\pm0.0018$ 14
 2002
CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.0328$ $\pm0.0019$ $\pm0.0022$
 1997 G
OPAL Repl. by ABBIENDI 2000Q
$0.0350$ $\pm0.0019$ $\pm0.0023$ 15
 1996 P
DLPH Repl. by ABREU 2001H
$0.0351$ $\pm0.0019$ $\pm0.0020$ 16
 1995
$0.0314$ $\pm0.0023$ $\pm0.0025$
 1995 N
ALEP Repl. by BUSKULIC 1997
1  Uses fully reconstructed ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ events (${{\mathit \ell}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$) and ${{\mathit \eta}_{{EW}}}$ = 1.0066.
2  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 $\rho {}^{2}$ = $1.22$ $\pm0.02$ $\pm0.07$.
3  Measurement using fully reconstructed ${{\mathit D}^{*}}$ sample with a $\rho {}^{2}$ = $1.32$ $\pm0.15$ $\pm0.33$.
4  Average of the ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(2010)}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{*}{(2007)}}$) ${{\mathit \ell}^{+}}{{\mathit \nu}}$ modes with $\rho {}^{2}$ = $1.61$ $\pm0.09$ $\pm0.21$ and $\mathit f_{+−}$ = $0.521$ $\pm0.012$.
5  ABREU 2001H measured using about 5000 partial reconstructed ${{\mathit D}^{*}}$ sample with a $\rho {}^{2}=1.34$ $\pm0.14$ ${}^{+0.24}_{-0.22}$.
6  ABBIENDI 2000Q: measured using both inclusively and exclusively reconstructed ${{\mathit D}^{*\pm}}$ samples with a $\rho {}^{2}=1.21$ $\pm0.12$ $\pm0.20$. The statistical and systematic correlations between $\vert {\it V}_{\it cb}\vert {\times }\mathit F$(1) and $\rho {}^{2}$ are $0.90$ and $0.54$ respectively.
7  BUSKULIC 1997 : measured using exclusively reconstructed ${{\mathit D}^{*\pm}}$ with a $\mathit a{}^{2}=0.31$ $\pm0.17$ $\pm0.08$. The statistical correlation is $0.92$.
8  Uses fully reconstructed ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ events (${{\mathit \ell}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$).
9  Measured using the dependence of ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$ decay differential rate and the form factor description by CAPRINI 1998 with $\rho {}^{2}$ = $1.16$ $\pm0.06$ $\pm0.08$.
10  Measured using fully reconstructed ${{\mathit D}^{*}}$ sample and a simultaneous fit to the Caprini-Lellouch-Neubert form factor parameters: $\rho {}^{2}$ = $1.191$ $\pm0.048$ $\pm0.028$, $\mathit R_{1}$(1) = $1.429$ $\pm0.061$ $\pm0.044$, and $\mathit R_{2}$(1) = $0.827$ $\pm0.038$ $\pm0.022$.
11  Measurement using fully reconstructed ${{\mathit D}^{*}}$ sample with a $\rho {}^{2}$ = $1.29$ $\pm0.03$ $\pm0.27$.
12  Combines with previous partial reconstructed ${{\mathit D}^{*}}$ measurement with a $\rho {}^{2}$ = $1.39$ $\pm0.10$ $\pm0.33$.
13  Measured using exclusive ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(892)}^{-}}{{\mathit e}^{+}}{{\mathit \nu}}$ decays with $\rho {}^{2}$= $1.35$ $\pm0.17$ $\pm0.19$ and a correlation of $0.91$.
14  BRIERE 2002 result is based on the same analysis and data sample reported in ADAM 2003 .
15  ABREU 1996P: measured using both inclusively and exclusively reconstructed ${{\mathit D}^{*\pm}}$ samples.
16  BARISH 1995 : 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. They report their experiment's uncertainties $\pm{}0.0019$ $\pm0.0018$ $\pm0.0008$, where the first error is statistical, the second is systematic, and the third is the uncertainty in the lifetimes. We combine the last two in quadrature.

$\vert {\it V}_{\it cb}\vert$ ${\times }$ $\mathit F$(1) (from ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ )
References:
 WAHEED 2019
PR D100 052007 Measurement of the CKM matrix element $|V_{cb}|$ from $B^0\to D^{*-}\ell^ {+} \nu_\ell$ at Belle
 DUNGEL 2010
PR D82 112007 Measurement of the Form Factors of the Decay ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$ and Determination of the CKM Matrix Element $\vert {\it V}_{\it cb}\vert$
 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
 AUBERT 2008AT
PRL 100 231803 Measurement of the Decay ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$
 AUBERT 2008R
PR D77 032002 Determination of the Form Factors for the Decay ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ and of the CKM Matrix Element $\vert \mathit V_{cb}\vert$
 AUBERT 2005E
PR D71 051502 Measurement of the ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$ Decay Rate and $\vert {\it V}_{\it cb}\vert$
 ABDALLAH 2004D
EPJ C33 213 Measurement of $\vert \mathit V_{cb}\vert$ using the Semileptonic Decay ${{\overline{\mathit B}}_{{d}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$
PR D67 032001 Determination of the ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit \ell}}{{\overline{\mathit \nu}}}$ Decay Width and |$\mathit V_{cb}$|
 ABE 2002F
PL B526 247 Determination of $\vert \mathit V_{CB}\vert$ using the Semileptonic Decay ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}}$
 BRIERE 2002
PRL 89 081803 Improved Measurement of |$\mathit V_{cb}$| using ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \ell}}{{\mathit \nu}}$ Decay
 ABREU 2001H
PL B510 55 Measurement of $\mathit V_{cb}$ from the Decay Process ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$
 ABBIENDI 2000Q
PL B482 15 Measurement of $\vert \mathit V_{cb}\vert$ using ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$ Decays
 ACKERSTAFF 1997G
PL B395 128 A Measurement of $\vert \mathit V_{cb}\vert$ using ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$ Decays
 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 ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$
 ABREU 1996P
ZPHY C71 539 Determination of $\vert \mathit V_{cb}\vert$ from the Semileptonic Decay ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$
 BARISH 1995
PR D51 1014 Measurements of the ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \ell}}{{\overline{\mathit \nu}}}$ Branching Fractions and |$\mathit V_{cb}$|
 BUSKULIC 1995N
PL B359 236 A Measurement of the $\vert \mathit V_{cb}\vert$ from ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$