335
21.2. CP violation in B meson oscillations
This method has been applied by both BaBar and Belle to determine γ.
Their most recently published results are
BaBar (Aubert et al. 2010) : γ = 68 ± 14 ± 4 ± 3
◦
(21.25)
Belle (Poluektov et al. 2010) : γ
(21.26)
= 78.4
+10.8
± 3 ± 8.9
◦
−11.6
where the last uncertainty is due to the D-decay modelling (which ignores,
for example, rescattering among the three final state particles). Both these
experiments use decays B
±
→ DK
± , B
±
→ D
∗ K
± with D
∗
→ Dπ
0 and D
∗
→
Dγ; BaBar in addition uses the decays D
0
→ K S K
+ K
− .
We now turn to the other main method of detecting CP violation, through
the interference between decays of (for example) B
0 and B ¯ 0 mesons that have
been produced in a coherent state by mixing. For this we need to set up the
formalism describing time-dependent mixing.
21.2 CP violation in B meson oscillations
¯
B
0 -B
0 oscillations have been studied by the BaBar and Belle collaborations at
the PEP2 and KEKB asymmetric e
+ e
− colliders. These machines operate at
a centre of mass energy equal to the mass of the Υ(4S) resonance state, which
¯
is some 20 MeV above the threshold for B
0 B
0 production. If produced in a
−
symmetric e
+ e collider (with equal and opposite momenta for the e
+ and
e
− ), the produced B mesons would move very slowly, v/c ∼ 0.06, covering a
distance of only some 30 μm before decaying (cτ for B mesons is about 460
μm). This would make it impossible to resolve the decay vertices of the two
¯
Bs, as is required in order to observe B
0 -B
0 oscillations, since the accuracy of
the decay vertex reconstruction is roughly 100 μm. Oddone (1989) suggested
making e
+ e
− collisions with asymmetric energy colliding beams, so that the
B mesons now move with the motion of the centre of mass, which can be
considerable. For example, at PEP2 (e
− 9 GeV, e
+ 3.1 GeV) β cm ∼ 0.5
and γ cm ∼ 1.15, so that the distance travelled in the (asymmetric) lab frame
during the lifetime of an average B meson is ∼ 250 μm, which is measurable.
At KEKB (e
− 8 GeV, e
− 3.5 GeV), β cm γ cm ∼ 0.425.
Since the Υ(4S) state has J = 1, the decay Υ → BB leaves the B mesons in
a p wave state, which is forbidden for two identical spinless bosons; therefore
B ¯ 0
one must be a B
0 and the other a , but we do not know which is which until
one has been identified (‘tagged’) in some way. The flavour of the tagged B
may be determined, for example, by the charge of the lepton emitted in the
semi-leptonic decays B
0
→ D
− e
+ ν e , B ¯ 0 → D
+ e
− ν ¯ e . We shall not describe the
evolution of the BB coherent state following production; interested readers
may consult Cohen et al. (2009) for an instructive discussion, which also
covers neutrino oscillations. We shall be interested in the time dependence of
the state of the meson which partners the tagged meson, once the correlated
21.2. CP violation in B meson oscillations
This method has been applied by both BaBar and Belle to determine γ.
Their most recently published results are
BaBar (Aubert et al. 2010) : γ = 68 ± 14 ± 4 ± 3
◦
(21.25)
Belle (Poluektov et al. 2010) : γ
(21.26)
= 78.4
+10.8
± 3 ± 8.9
◦
−11.6
where the last uncertainty is due to the D-decay modelling (which ignores,
for example, rescattering among the three final state particles). Both these
experiments use decays B
±
→ DK
± , B
±
→ D
∗ K
± with D
∗
→ Dπ
0 and D
∗
→
Dγ; BaBar in addition uses the decays D
0
→ K S K
+ K
− .
We now turn to the other main method of detecting CP violation, through
the interference between decays of (for example) B
0 and B ¯ 0 mesons that have
been produced in a coherent state by mixing. For this we need to set up the
formalism describing time-dependent mixing.
21.2 CP violation in B meson oscillations
¯
B
0 -B
0 oscillations have been studied by the BaBar and Belle collaborations at
the PEP2 and KEKB asymmetric e
+ e
− colliders. These machines operate at
a centre of mass energy equal to the mass of the Υ(4S) resonance state, which
¯
is some 20 MeV above the threshold for B
0 B
0 production. If produced in a
−
symmetric e
+ e collider (with equal and opposite momenta for the e
+ and
e
− ), the produced B mesons would move very slowly, v/c ∼ 0.06, covering a
distance of only some 30 μm before decaying (cτ for B mesons is about 460
μm). This would make it impossible to resolve the decay vertices of the two
¯
Bs, as is required in order to observe B
0 -B
0 oscillations, since the accuracy of
the decay vertex reconstruction is roughly 100 μm. Oddone (1989) suggested
making e
+ e
− collisions with asymmetric energy colliding beams, so that the
B mesons now move with the motion of the centre of mass, which can be
considerable. For example, at PEP2 (e
− 9 GeV, e
+ 3.1 GeV) β cm ∼ 0.5
and γ cm ∼ 1.15, so that the distance travelled in the (asymmetric) lab frame
during the lifetime of an average B meson is ∼ 250 μm, which is measurable.
At KEKB (e
− 8 GeV, e
− 3.5 GeV), β cm γ cm ∼ 0.425.
Since the Υ(4S) state has J = 1, the decay Υ → BB leaves the B mesons in
a p wave state, which is forbidden for two identical spinless bosons; therefore
B ¯ 0
one must be a B
0 and the other a , but we do not know which is which until
one has been identified (‘tagged’) in some way. The flavour of the tagged B
may be determined, for example, by the charge of the lepton emitted in the
semi-leptonic decays B
0
→ D
− e
+ ν e , B ¯ 0 → D
+ e
− ν ¯ e . We shall not describe the
evolution of the BB coherent state following production; interested readers
may consult Cohen et al. (2009) for an instructive discussion, which also
covers neutrino oscillations. We shall be interested in the time dependence of
the state of the meson which partners the tagged meson, once the correlated