Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

Vcb and Vub CKM Matrix Elements
OMITTED FROM SUMMARY TABLE

See the related review(s):Semileptonic B Hadron Decays, Determination of Vcb andVubVcb MEASUREMENTS
For the discussion of Vcb measurements, which is not repeated here, seethe review on “Determination of Vcb and Vub .”The CKM matrix element Vcb can be determined by studying the rate of
the semileptonic decay B → D (∗) ℓ ν as a function of the recoil kinematics of D (∗) mesons. Taking advantage of theoretical constraints on thenormalization and a linear ω dependence of the form factors (F (ω), G (ω))
provided by Heavy Quark Effective Theory (HQET), the Vcb ×F (ω) andρ2 can be simultaneously extracted from data, where ω is the scalar product of the two-meson four velocities, F (1) is the form factor at zero recoil(ω=1) and ρ2 is the slope. Using the theoretical input of F (1), a value of
Vcb can be obtained.

Vcb × F (1) (from B 0 → D ∗− ℓ+ ν)
VALUE (units 10−2 )DOCUMENT ID

TECNCOMMENT

3.534± 0.037 OUR EVALUATION(Produced by HFLAV) with ρ2 =1.139 ± 0.020 and a2correlation 0.268. The fitted χ is 63.2 for 27 degrees of freedom.
3.60 ± 0.06 OUR AVERAGE Error includes scale factor of 1.5. See the ideogram below.
1 ADACHI
3.676± 0.028 ± 0.086
23J BELL e + e − → Υ(4S)2
3.64 ± 0.09
PRIM
23 BELL e + e − → Υ(4S)33.506± 0.015 ± 0.056
WAHEED
21 BELL e + e − → Υ(4S)
4 AUBERT
3.59 ± 0.02 ± 0.1209A BABR e + e − → Υ(4S)
53.92 ± 0.18 ± 0.23
ABDALLAH
04D DLPH e + e − → Z 064.31 ± 0.13 ± 0.18
ADAM
03 CLE2 e + e − → Υ(4S)+ 0.23
7 ABREU
3.55 ± 0.14 −01H DLPH e + e − → Z
0.24
8 ABBIENDI
3.71 ± 0.10 ± 0.20
00Q OPAL e + e − → Z
93.19 ± 0.18 ± 0.19
BUSKULIC
97 ALEP e + e − → Z• • • We do not use the following data for averages, fits, limits, etc. • • •3 WAHEED
3.483± 0.015 ± 0.056
19 BELL Repl. by WAHEED 21103.46 ± 0.02 ± 0.10
DUNGEL10 BELL Rep. by WAHEED 1911 AUBERT
3.59 ± 0.06 ± 0.14
08AT BABR Repl. by AUBERT 09A
12 AUBERT
3.44 ± 0.03 ± 0.11
08R BABR Repl. by AUBERT 09A
13 AUBERT
3.55 ± 0.03 ± 0.16
05E BABR Repl. by AUBERT 08R143.77 ± 0.11 ± 0.19
ABDALLAH
04D DLPH e + e − → Z 015
3.54 ± 0.19 ± 0.18
ABE02F BELL Repl. by DUNGEL 1016 BRIERE
4.31 ± 0.13 ± 0.18
02 CLE2 e + e − → Υ(4S)
3.28 ± 0.19 ± 0.22

https://pdg.lbl.gov

ACKERSTAFF 97G OPAL Repl. by ABBIENDI 00Q

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

17 ABREU
18 BARISH

3.50 ± 0.19 ± 0.23
3.51 ± 0.19 ± 0.20
3.14 ± 0.23 ± 0.25

BUSKULIC

96P DLPH Repl. by ABREU 01H
95 CLE2 Repl. by ADAM 03
95N ALEP Repl. by BUSKULIC 97

WEIGHTED AVERAGE
3.60±0.06 (Error scaled by 1.5)
Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not necessarily the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.

χ
ADACHIPRIM
WAHEED
AUBERTABDALLAH
ADAM
ABREU
ABBIENDI
BUSKULIC

0.7
0.2
2.6
0.0
1.2
10.3
0.0
0.2
2.4
17.7
(Confidence Level = 0.024)

2.5

3

3.5

4

4.5

523J
23
2109A
04D0301H
00Q
972BELL
BELL
BELL
BABR
DLPH
CLE2DLPH
OPAL
ALEP

5.5Vcb × F (1) (from B 0 → D ∗− ℓ+ ν)
1 Measured from differential shapes of exclusive B → D ∗ ℓ− ν (ℓ = e or µ) decays. UsingℓCNL form factor parametrization and the zero-recoil lattice QCD point F(1) = 0.906 ±0.013 ADACHI 23J finds Vcb CNL = (40.57 ± 0.31 ± 0.95 ± 0.58)×10−3 where the last
uncertainty is due to the prediction of F(1). Also reports a measurement of Vcb BGL= (40.13 ± 0.27 ± 0.93 ± 0.58) × 10−3 using BGL form factors parametrization.
2 Measured from differential shapes of exclusive B → D ∗ ℓ− ν decays with hadronic tagℓside reconstruction and extracting the CNL and BGL form factor parameters. PRIM 23finds Vcb CNL = (40.2 ± 0.9) × 10−3 with the zero-recoil lattice QCD point F(1) =0.906 ± 0.013. PRIM 23 provides also a measurement of Vcb BGL = (40.7 ± 1.0) ×10−3 .
3 WAHEED 21 uses fully reconstructed D ∗− ℓ+ ν events (ℓ = e or µ) and ηEW = 1.0066.
4 Obtained from a global fit to B → D (∗) ℓ ν events, with reconstructed D 0 ℓ and D + ℓℓ
final states and ρ2 = 1.22 ± 0.02 ± 0.07.
5 Measurement using fully reconstructed D ∗ sample with a ρ2 = 1.32 ± 0.15 ± 0.33.
6 Average of the B 0 → D ∗ (2010)− ℓ+ ν and B + → D ∗ (2007)) ℓ+ ν modes with ρ2 =1.61 ± 0.09 ± 0.21 and f+− = 0.521 ± 0.012.
7 ABREU 01H measured using about 5000 partial reconstructed D ∗ sample with a+ 0.24 .
ρ2 =1.34 ± 0.14 −0.22
8 ABBIENDI 00Q: measured using both inclusively and exclusively reconstructed D ∗±samples with a ρ2 =1.21 ± 0.12 ± 0.20. The statistical and systematic correlations
between Vcb ×F(1) and ρ2 are 0.90 and 0.54 respectively.

https://pdg.lbl.gov

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

9 BUSKULIC 97: measured using exclusively reconstructed D ∗± with a a2 =0.31 ± 0.17 ±0.08. The statistical correlation is 0.92.
10 Uses fully reconstructed D ∗− ℓ+ ν events (ℓ = e or µ).
11 Measured using the dependence of B − → D ∗0 e − ν decay differential rate and thee
form factor description by CAPRINI 98 with ρ2 = 1.16 ± 0.06 ± 0.08.
12 Measured using fully reconstructed D ∗ sample and a simultaneous fit to the CapriniLellouch-Neubert form factor parameters: ρ2 = 1.191 ± 0.048 ± 0.028, R1 (1) = 1.429 ±0.061 ± 0.044, and R2 (1) = 0.827 ± 0.038 ± 0.022.
13 Measurement using fully reconstructed D ∗ sample with a ρ2 = 1.29 ± 0.03 ± 0.27.
14 Combines with previous partial reconstructed D ∗ measurement with a ρ2 = 1.39 ± 0.10 ±0.33.
15 Measured using exclusive B 0 → D ∗ (892)− e + ν decays with ρ2 = 1.35 ± 0.17 ± 0.19
and a correlation of 0.91.
16 BRIERE 02 result is based on the same analysis and data sample reported in ADAM 03.
17 ABREU 96P: measured using both inclusively and exclusively reconstructed D ∗± samples.
18 BARISH 95: measured using both exclusive reconstructed B 0 → D ∗− ℓ+ ν and B + →D ∗0 ℓ+ ν samples. They report their experiment’s uncertainties ±0.0019 ± 0.0018 ±0.0008, where the first error is statistical, the second is systematic, and the third is theuncertainty in the lifetimes. We combine the last two in quadrature.

Vcb × G (1) (from B → D − ℓ+ ν)
VALUE (units 10−2 )DOCUMENT ID

TECNCOMMENT

4.121± 0.100 OUR EVALUATION(Produced by HFLAV) with ρ2 =1.128 ± 0.033 and acorrelation 0.747. The fitted χ2 is 4.8 for 8 degrees of freedom.
4.22 ± 0.10 OUR AVERAGE
1 GLATTAUER 16 BELL e + e − → Υ(4S)4.229± 0.137
2 AUBERT
4.23 ± 0.19 ± 0.14
10 BABR e + e − → Υ(4S)3
4.31 ± 0.08 ± 0.23
AUBERT
09A BABR e + e − → Υ(4S)
4 BARTELT
4.16 ± 0.47 ± 0.37
99 CLE2 e + e − → Υ(4S)52.78 ± 0.68 ± 0.65
BUSKULIC
97 ALEP e + e − → Z• • • We do not use the following data for averages, fits, limits, etc. • • •6 ABE
4.11 ± 0.44 ± 0.52
02E BELL Repl. by GLATTAUER 16+ 0.72
3.37 ± 0.44 −0.49

7 ATHANAS97

CLE2Repl. by BARTELT 99

1 Obtained from a fit to the combined partially reconstructed B → D ℓ ν sample whileℓtagged by the other fully reconstructed B meson in the event. Also reports fitted ρ2 =1.09 ± 0.05.
2 Obtained from a fit to the combined B → D ℓ+ ν sample in which a hadronic decay ofℓthe second B meson is fully reconstructed and ρ2 = 1.20 ± 0.09 ± 0.04.
3 Obtained from a global fit to B → D (∗) ℓ ν events, with reconstructed D 0 ℓ and D + ℓℓ
final states and ρ2 = 1.20 ± 0.04 ± 0.07.
4 BARTELT 99: measured using both exclusive reconstructed B 0 → D − ℓ+ ν and B + →D 0 ℓ+ ν samples.
5 BUSKULIC 97: measured using exclusively reconstructed D ± with a a2 =− 0.05 ± 0.53 ±0.38. The statistical correlation is 0.99.
6 Using the missing energy and momentum to extract kinematic information about theundetected neutrino in the B 0 → D − ℓ+ ν decay.
7 ATHANAS 97: measured using both exclusive reconstructed B 0 → D − ℓ+ ν and B + →D 0 ℓ+ ν samples with a ρ2 =0.59 ± 0.22 ± 0.12+ 0.59 . They report their experiment’s−0+ 0.0053 , where the first error is statistical, the second
uncertainties ±0.0044 ± 0.0048 −0.0012
is systematic, and the third is the uncertainty due to the form factor model variations.
We combine the last two in quadrature.

https://pdg.lbl.gov

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)+Vcb (from D ∗−s µ νµ )VALUE (units 10−3 )DOCUMENT ID

TECNCOMMENT

1 AAIJ41.4± 0.6
0.6±± 0.9± 1.2
20E LHCB p p at 7, 8 TeV
1 Measured from an inclusive sample of D − µ+ candidates using CNL parameterization ofsthe form factor. AAIJ 20E provides also measurement of Vcb = (42.3 ± 0.8 ± 0.9 ±1.2) × 10−3 using BGL parameterization of the form factor. The third uncertainty isdue to the external inputs used in the measurement.

Vub MEASUREMENTS
For the discussion of Vub measurements, which is not repeated here, see
the review on ”Determination of Vcb and Vub .”The CKM matrix element Vub can be determined by studying the rateof the charmless semileptonic decay b → u ℓ ν. The relevant branchingratio measurements based on exclusive and inclusive decays can be foundin the B Listings, and are not repeated here.

Vcb and Vub CKM Matrix Elements REFERENCES
ADACHIPRIM
WAHEEDAAIJ
WAHEED
GLATTAUER
AUBERT
DUNGEL
AUBERT
AUBERT
AUBERT
AUBERTABDALLAH
ADAM
ABE
ABE
BRIEREABREU
ABBIENDI
BARTELTCAPRINI
ACKERSTAFF
ATHANAS
BUSKULICABREU
BARISHBUSKULIC

23J
232120E
1916101009A
08AT
08R
05E
04D0302E02F
0201H00Q
999897G979796P9595N

PR D108 092013
PR D108 012002
PR D103 079901
PR D101 072004
PR D100 052007
PR D93 032006
PRL 104 011802
PR D82 112007
PR D79 012002
PRL 100 231803
PR D77 032002
PR D71 051502
EPJ C33 213
PR D67 032001
PL B526 258
PL B526 247
PRL 89 081803
PL B510 55
PL B482 15
PRL 82 3746
NP B530 153
PL B395 128
PRL 79 2208
PL B395 373
ZPHY C71 539
PR D51 1014
PL B359 236

https://pdg.lbl.gov

I. Adachi et al.
M.T. Prim et al.
E. Waheed et al.
R. Aaij et al.
E. Waheed et al.
R. Glattauer et al.
B. Aubert et al.
W. Dungel et al.
B. Aubert et al.
B. Aubert et al.
B. Aubert et al.
B. Aubert et al.
J. Abdallah et al.
N.E. Adam et al.
K. Abe et al.
K. Abe et al.
R. Briere et al.
P. Abreu et al.
G. Abbiendi et al.
J. Bartelt et al.
I. Caprini, L. Lellouch, M. Neubert
K. Ackerstaff et al.
M. Athanas et al.
D. Buskulic et al.
P. Abreu et al.
B.C. Barish et al.
D. Buskulic et al.

Page 4(BELLE II Collab.)(BELLE Collab.)(BELLE Collab.)(LHCb Collab.)(BELLE Collab.)(BELLE Collab.)(BABAR Collab.)(BELLE Collab.)(BABAR Collab.)(BABAR Collab.)(BABAR Collab.)(BABAR Collab.)(DELPHI Collab.)(CLEO Collab.)(BELLE Collab.)(BELLE Collab.)(CLEO Collab.)(DELPHI Collab.)(OPAL Collab.)(CLEO Collab.)(BCIP, CERN)(OPAL Collab.)(CLEO Collab.)(ALEPH Collab.)(DELPHI Collab.)(CLEO Collab.)(ALEPH Collab.)

Created: 7/25/2024 17:21