This preview shows pages 1–3. Sign up to view the full content.
–1–
DETERMINATION OF
V
cb
AND
V
ub
Updated March 2010 by R. Kowalewski (Univ. of Victoria,
Canada) and T. Mannel (Univ. of Siegen, Germany)
INTRODUCTION
Precision determinations of

V
ub

and

V
cb

are central to
testing the CKM sector of the Standard Model, and com
plement the measurements of CP asymmetries in
B
decays.
The length of the side of the unitarity triangle opposite the
wellmeasured angle
β
is proportional to the ratio

V
ub

/

V
cb

,
making its determination a high priority of the heavy ﬂavor
physics program.
The semileptonic transitions
b
→
c±
ν
±
and
b
→
u±
ν
±
pro
vide two avenues for determining these CKM matrix elements,
namely through inclusive and exclusive Fnal states. The experi
mental and theoretical techniques underlying these two avenues
are independent, providing a crucial crosscheck on our under
standing. Recent measurements and calculations are reﬂected
in the values quoted in this article, which is an update on the
previous review [1].
The theory underlying the determination of

V
qb

is mature,
in particular for

V
cb

. The theoretical approaches all use the
fact that the mass
m
b
of the
b
quark is large compared to
the scale Λ
QCD
that determines lowenergy hadronic physics.
The basis for precise calculations is a systematic expansion
in powers of Λ
/m
b
,wh
e
r
eΛ
∼
500
−
700 MeV is a hadronic
scale of the order of Λ
QCD
, using e±ectiveFeldtheory methods
to separate nonperturbative from perturbative contributions.
The expansion in Λ
/m
b
and
α
s
works well enough to enable a
precision determination of

V
cb

and

V
ub

in semileptonic decays.
The large data samples available at the
B
factories have
opened up new possibilities experimentally. Analyses where one
B
meson from an Υ(4
S
) decay is fully reconstructed allow
a recoiling semileptonic
B
decay to be studied with higher
purity than was previously possible. Improved knowledge of
CITATION: K. Nakamura
et al.
(Particle Data Group), JPG
37
, 075021 (2010) (URL: http://pdg.lbl.gov)
July 30, 2010
14:34
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document–2–
B
→
X
c
±
ν
±
decays allows partial rates for
B
→
X
u
±
ν
±
transi
tions to be measured in regions previously considered inacces
sible, increasing the acceptance for
B
→
X
u
±
ν
±
transitions and
reducing theoretical uncertainties.
Experimental measurements of the exclusive
B
→
π±
ν
±
decay are quite precise. Further improvement in the theoretical
calculation of the form factor normalization is needed to fully
exploit these measurements.
Throughout this review the numerical results quoted are
based on the methods of the Heavy Flavor Averaging Group [2].
DETERMINATION OF

V
cb

Summary:
The determination of

V
cb

from
B
→
D
∗
±
ν
±
decays is currently at a relative precision of about 3%. The main
limitation is the knowledge of the form factor near the maximum
momentum transfer to the leptons. For the
B
→
D±
ν
±
channel
experimental measurements have recently been substantially
improved, allowing this channel to provide a meaningful cross
check on
B
→
D
∗
±
ν
±
.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Kutter

Click to edit the document details