Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

11. The CKM quark-mixing matrix 183
11.2.5. |Vcb| :
The determination of |Vcb| from inclusive semileptonic B decays use
the semileptonic rate measurement together with the leptonic energy
and the hadronic invariant-mass spectra. Determinations from exclusive
B → D (∗) ℓ¯ν decays are based on the fact that in the mb,c ≫ ΛQCD limit
all form factors are given by a single Isgur-Wise function [49], which is
normalized at zero recoil. The Vcb and Vub minireview [48] quotes the
combination with a scaled error as
|Vcb| =(40.6 ± 1.3) × 10 −3 . (11.11)
11.2.6. |Vub| :
The determination of |Vub| from inclusive B → Xuℓ¯ν decay suffers from
large B → Xcℓ¯ν backgrounds. In most regions of phase space where the
charm background is kinematically forbidden the rate is determined by
nonperturbative shape functions. At leading order in ΛQCD/mb there is
only one such function, which is related to the photon energy spectrum
in B → Xsγ [50,51]. The large and pure BB samples at the B factories
permit the selection of B → Xuℓ¯ν decays in events where the other B is
fully reconstructed [56]. With this full-reconstruction tag method, one can
measure the four-momenta of both the leptonic and hadronic systems, and
access wider kinematic regions because of improved signal purity.
To extract |Vub| from exclusive channels, the form factors have to be
known. Unquenched lattice QCD calculations of the B → πℓ¯ν form factor
for q2 > 16 GeV2 are available [57,58]. The theoretical uncertainties in
the inclusive and exclusive determinations are different. The Vcb and Vub minireview [48] quotes the combination
|Vub| =(3.89 ± 0.44) × 10 −3 . (11.12)
11.2.7. |Vtd| and |Vts| :
These CKM elements cannot be measured from tree-level top quark
decays, so one has to use B–B oscillations or loop-mediated rare K
and B decays. The mass difference of the two neutral B meson mass
eigenstates is well measured, Δmd =(0.507 ± 0.005) ps−1 [60]. For the B0 s
system, CDF measured Δms =(17.77 ± 0.10 ± 0.07) ps−1 [61] with more
than 5σ significance. Using unquenched lattice QCD calculations [63] and
assuming |Vtb| = 1, we find
|Vtd| =(8.4 ± 0.6) × 10 −3 , |Vts| =(38.7 ± 2.1) × 10 −3 . (11.13)
Several uncertainties are reduced in the lattice QCD calculation of the
ratio Δmd/Δms, which gives a new and significantly improved constraint,
� �
�V �
td/Vts =0.211 ± 0.001 ± 0.005. (11.14)
11.2.8. |Vtb| :
The determination of |Vtb| from top decays uses the ratio of branching
fractions B(t → Wb)/B(t → Wq)=|Vtb| 2 /( �
q |Vtq| 2 )=|Vtb| 2 , where
q = b, s, d [69,70]. The direct determination of |Vtb| without assuming
unitarity has become possible from the single top quark production cross
section. The (2.76 +0.58
−0.47 ) pb [71] average cross section measured by DØ [72]
and CDF [73] implies
|Vtb| =0.88 ± 0.07 . (11.15)