9 Symmetry Violations and Quark Flavour Physics
613
section and thus on |V cd | 2 , as well as on the semileptonic (muonic) branching
ratio of the produced charm mesons, ¯
B μ . The method was first used by the
CDHS group [141] but has also been applied by CCFR [142] and by CHARM
II [143]. Averaging the results is complicated, also because ¯
B μ is an effective
quantity which depends on the specific neutrino beam characteristics. One finds
¯
B μ |V cd | 2 = (0.463 ± 0.034) × 10 −2 [144] and using the average value of
¯
B μ = 0.087 ± 0.005 one obtains [133]
|V cd | = 0.230 ± 0.011 .
Similar to |V us |, |V cd | can also be extracted from semileptonic (D → ππν) and
leptonic (D + → μ + ν) charm decays. Also here, QCD lattice calculations are
used to determine the relevant form factors f
Dπ
+ (q 2 = 0) and f D [138]. Using
the average of the branching fraction measurements from BABAR, Belle, BES
III and CLEO-c for D → ππν [134] results into [133]
|V cd | = 0.2140 ± 0.0029 ± 0.0093,
where the first uncertainty is experimental and the second stems from the
theoretical uncertainty of the form factor calculation. The measurements of the
leptonic branching ratio D + → μ + ν by BES III and a CLEO-c results into [134]
|V cd | = 0.2164 ± 0.0050 ± 0.0015 ,
where also here the first error is experimental while the second describes the
uncertainty of the form factor calculation. For the average of the three different
determinations of |V cd | the Particle Data Group [133] quotes a value of
|V cd | = 0.218 ± 0.004 .
4. |V cs |. Measurements of semileptonic decays of D mesons to kaons D → Kν
as well as the measurement of leptonic decays of D s mesons, D +
s → μ + ν,
together with the corresponding form factors from lattice calculations allow the
determination of |V cs |. Branching fraction measurements have been performed
by Belle, BABAR, CLEO-c and BES III, and are averaged in [134]. From the
semileptonic measurements one obtains |V cs | = 0.967 ± 0.025 where the error
is dominated by the theoretical uncertainty of the form factor calculations. The
average of the leptonic measurements results into |V cs | = 1.006 ± 0.019 where
the dominating uncertainty is experimental. For the average of both values the
Particle Data Group [133] reports a values of
|V cs | = 0.997 ± 0.017.
613
section and thus on |V cd | 2 , as well as on the semileptonic (muonic) branching
ratio of the produced charm mesons, ¯
B μ . The method was first used by the
CDHS group [141] but has also been applied by CCFR [142] and by CHARM
II [143]. Averaging the results is complicated, also because ¯
B μ is an effective
quantity which depends on the specific neutrino beam characteristics. One finds
¯
B μ |V cd | 2 = (0.463 ± 0.034) × 10 −2 [144] and using the average value of
¯
B μ = 0.087 ± 0.005 one obtains [133]
|V cd | = 0.230 ± 0.011 .
Similar to |V us |, |V cd | can also be extracted from semileptonic (D → ππν) and
leptonic (D + → μ + ν) charm decays. Also here, QCD lattice calculations are
used to determine the relevant form factors f
Dπ
+ (q 2 = 0) and f D [138]. Using
the average of the branching fraction measurements from BABAR, Belle, BES
III and CLEO-c for D → ππν [134] results into [133]
|V cd | = 0.2140 ± 0.0029 ± 0.0093,
where the first uncertainty is experimental and the second stems from the
theoretical uncertainty of the form factor calculation. The measurements of the
leptonic branching ratio D + → μ + ν by BES III and a CLEO-c results into [134]
|V cd | = 0.2164 ± 0.0050 ± 0.0015 ,
where also here the first error is experimental while the second describes the
uncertainty of the form factor calculation. For the average of the three different
determinations of |V cd | the Particle Data Group [133] quotes a value of
|V cd | = 0.218 ± 0.004 .
4. |V cs |. Measurements of semileptonic decays of D mesons to kaons D → Kν
as well as the measurement of leptonic decays of D s mesons, D +
s → μ + ν,
together with the corresponding form factors from lattice calculations allow the
determination of |V cs |. Branching fraction measurements have been performed
by Belle, BABAR, CLEO-c and BES III, and are averaged in [134]. From the
semileptonic measurements one obtains |V cs | = 0.967 ± 0.025 where the error
is dominated by the theoretical uncertainty of the form factor calculations. The
average of the leptonic measurements results into |V cs | = 1.006 ± 0.019 where
the dominating uncertainty is experimental. For the average of both values the
Particle Data Group [133] reports a values of
|V cs | = 0.997 ± 0.017.