548
K. Kleinknecht and U. Uwer
2. For an initially pure K 0 state, the interference term changes sign.
3. For an incoherent mixture of K 0 (intensity N K ) and K 0 (intensity N K ), the
interference term is multiplied by the “dilution factor”
N K − N K
N K + N
K
.
(9.115)
Measurement of the interference term under these conditions is called the vacuum
interference method.
4. For the coherent mixture behind a regenerator, a S = a L = 1, and we obtain
R 2 (τ ) = | 2 e −Γ S τ + |η| 2 e −Γ L τ + 2|||η| e −(Γ L +Γ S )(τ/2) cos
m τ + Φ − arg η
.
(9.116)
9.5.3.2 Semileptonic Decays
Interference phenomena and CP violation can also be observed in the decay of a
coherent mixture of K 0 and K 0 mesons into semileptonic final states. In particular
the time-dependent charge asymmetry δ(τ ) = (N + − N − )/(N + + N − ) shows an
oscillatory behavior, where N + denotes decays into π + e − ν final states and N − into
π − e + ν. Assuming CPT invariance, we obtain
δ(τ ) = 2
1 − |x| 2
|1 − x| 2
e ε + |V | e
−(1/2)(Γ S −Γ L )τ cos ( τ + Φ V )
.
(9.117)
where x is the ratio of amplitudes with S = −Q and = x is consistent
with zero, in agreement with the = Q rule.
For an initially pure K L beam (R = 0), the asymmetry is independent of the
decay time:
δ L = 2 e ε
1 − |x| 2
|1 − x| 2 .
(9.118)
For an initial incoherent mixture of K 0 (N K ) and K 0 (N K ) the quantity |R| has to
be replaced by (N K − N K )/(N K + N K ), i.e. by the same dilution factor as for 2π
interference in a short-lived beam.
For the coherent mixture created by a regenerator, R is given by the regeneration
amplitude , and Φ R by the regeneration phase Φ .
K. Kleinknecht and U. Uwer
2. For an initially pure K 0 state, the interference term changes sign.
3. For an incoherent mixture of K 0 (intensity N K ) and K 0 (intensity N K ), the
interference term is multiplied by the “dilution factor”
N K − N K
N K + N
K
.
(9.115)
Measurement of the interference term under these conditions is called the vacuum
interference method.
4. For the coherent mixture behind a regenerator, a S = a L = 1, and we obtain
R 2 (τ ) = | 2 e −Γ S τ + |η| 2 e −Γ L τ + 2|||η| e −(Γ L +Γ S )(τ/2) cos
m τ + Φ − arg η
.
(9.116)
9.5.3.2 Semileptonic Decays
Interference phenomena and CP violation can also be observed in the decay of a
coherent mixture of K 0 and K 0 mesons into semileptonic final states. In particular
the time-dependent charge asymmetry δ(τ ) = (N + − N − )/(N + + N − ) shows an
oscillatory behavior, where N + denotes decays into π + e − ν final states and N − into
π − e + ν. Assuming CPT invariance, we obtain
δ(τ ) = 2
1 − |x| 2
|1 − x| 2
e ε + |V | e
−(1/2)(Γ S −Γ L )τ cos ( τ + Φ V )
.
(9.117)
where x is the ratio of amplitudes with S = −Q and = x is consistent
with zero, in agreement with the = Q rule.
For an initially pure K L beam (R = 0), the asymmetry is independent of the
decay time:
δ L = 2 e ε
1 − |x| 2
|1 − x| 2 .
(9.118)
For an initial incoherent mixture of K 0 (N K ) and K 0 (N K ) the quantity |R| has to
be replaced by (N K − N K )/(N K + N K ), i.e. by the same dilution factor as for 2π
interference in a short-lived beam.
For the coherent mixture created by a regenerator, R is given by the regeneration
amplitude , and Φ R by the regeneration phase Φ .