9 Symmetry Violations and Quark Flavour Physics
615
To consider different theoretical treatments the authors assign an additional
quadratic error of ±0.17 × 10 −3 .
The determination of |V ub | from exclusive decays, such as B → ππν decays,
suffers experimentally from very small signal yields and requires the theoretical
determination of the corresponding form factors. Lattice form factor calculations
are available for the high q 2 regions. So called light-cone QCD sum rules (LCSR)
are applicable for the low q 2 region. A simultaneous fit to experimental B →
ππν data and lattice results as function of q 2 together with additional constraints
from LCSR results into
|V ub | = (3.67 ± 0.09 ± 0.12) × 10
−3 [134].
The inclusive and exclusive determinations of |V ub | are largely independent and
the large discrepancy between both methods remains a puzzle. Inflating the errors
to account for this discrepancy [145] quotes an average of
|V ub | = (3.94 ± 0.36) × 10
−3
The LHCb experiment has used the ratio of the two baryonic decays Λ b →
pμ − ¯
ν and Λ b → Λ c μ − ¯
ν to extract the ratio |V ub /V cb | = 0.083 ± 0.006 [146].
The q 2 -dependent form factor ratio had to be taken into account to consider the
different kinematical ranges of the two decays. Using the above average for |V cb |
one obtains
|V ub | = (3.50 ± 0.26) × 10
−3 .
7. |V tb |. An experimental determination of |V tb | without assuming unitarity is
possible using the production of single-top quarks. Single-top quark production
cross-sections have been measured by the Tevatron experiments CDF and D0,
and at LHC by ATLAS and CMS. Using these measurements [133] quotes the
value
|V tb | = 1.019 ± 0.025 .
8. |V td | and |V ts |. The two CKM elements |V td | and |V ts | are expected to be very
tiny and tree-level decays of the top-quark to a d-quark or s-quark will be
very difficult to measure. However, both elements are accessible through the
measurements of the mixing frequency of B 0 and B 0
s mesons (see Sect. 9.6).
Using the most recent lattice QCD results for the hadronic factors, f B d
ˆ
B B d =
(219 ±14) MeV and f B s
ˆ
B B s = (270 ±16) MeV [138], together with the world
averages for the mixing frequencies Δm d and Δm s results into [133]
|V td | = (8.1 ± 0.5) × 10
−3 and
|V ts | = (39.4 ± 2.3) × 10
−3 ,
615
To consider different theoretical treatments the authors assign an additional
quadratic error of ±0.17 × 10 −3 .
The determination of |V ub | from exclusive decays, such as B → ππν decays,
suffers experimentally from very small signal yields and requires the theoretical
determination of the corresponding form factors. Lattice form factor calculations
are available for the high q 2 regions. So called light-cone QCD sum rules (LCSR)
are applicable for the low q 2 region. A simultaneous fit to experimental B →
ππν data and lattice results as function of q 2 together with additional constraints
from LCSR results into
|V ub | = (3.67 ± 0.09 ± 0.12) × 10
−3 [134].
The inclusive and exclusive determinations of |V ub | are largely independent and
the large discrepancy between both methods remains a puzzle. Inflating the errors
to account for this discrepancy [145] quotes an average of
|V ub | = (3.94 ± 0.36) × 10
−3
The LHCb experiment has used the ratio of the two baryonic decays Λ b →
pμ − ¯
ν and Λ b → Λ c μ − ¯
ν to extract the ratio |V ub /V cb | = 0.083 ± 0.006 [146].
The q 2 -dependent form factor ratio had to be taken into account to consider the
different kinematical ranges of the two decays. Using the above average for |V cb |
one obtains
|V ub | = (3.50 ± 0.26) × 10
−3 .
7. |V tb |. An experimental determination of |V tb | without assuming unitarity is
possible using the production of single-top quarks. Single-top quark production
cross-sections have been measured by the Tevatron experiments CDF and D0,
and at LHC by ATLAS and CMS. Using these measurements [133] quotes the
value
|V tb | = 1.019 ± 0.025 .
8. |V td | and |V ts |. The two CKM elements |V td | and |V ts | are expected to be very
tiny and tree-level decays of the top-quark to a d-quark or s-quark will be
very difficult to measure. However, both elements are accessible through the
measurements of the mixing frequency of B 0 and B 0
s mesons (see Sect. 9.6).
Using the most recent lattice QCD results for the hadronic factors, f B d
ˆ
B B d =
(219 ±14) MeV and f B s
ˆ
B B s = (270 ±16) MeV [138], together with the world
averages for the mixing frequencies Δm d and Δm s results into [133]
|V td | = (8.1 ± 0.5) × 10
−3 and
|V ts | = (39.4 ± 2.3) × 10
−3 ,