564
K. Kleinknecht and U. Uwer
We use this value in the following sections.
Mass Difference m Combining the values from the CERN–Heidelberg experiments [173–175] with those from Fermilab E731 and E773 [176, 179], from
CPLEAR [181, 198, 199] and from the most precise single measurement by kTeV
[180], we obtain
m = (0.5286 ± 0.0011) × 10
10 s
−1 .
(9.154)
Superweak Phase From the two parameters given above, we obtain the phase of ε
in the superweak model,
Φ SW = arctan
2 m
Γ S
= (43.4 ± 0.1)
◦ .
(9.155)
Moduli of the Amplitudes η +− and η 00 New measurements of η +− from the
ratio of π + π − decays and semileptonic decays yield precise values of η +− . We
combine these with previous results and obtain [160–162].
|η +− | = (2.230 ± 0.006) × 10
−3 .
(9.156)
Absolute measurements of the amplitude η 00 are much less precise. A recent average
including the CPLEAR result is
|η 00 | = (2.23 ± 0.11) × 10
−3 .
(9.157)
Phase +− In all measurements, this phase is extracted from an interference term
with a beat frequency m. Taking the results from NA31 [184], E731 [176], E773
[179], and kTeV [180], together with the pre-1975 data and the result from CPLEAR
[181], we obtain the world average
Φ +− = (43.3 ± 0.4)
◦
(9.158)
using the values for m and τ S above. This result is in excellent agreement with
the value of Φ SW = (43.4 ± 0.1) ◦ . Since the interference experiments were
evaluated without assuming CPT invariance, this constitutes a stringent test of CPT
invariance. The difference is Φ +− − Φ SW = −(0.1 ± 0.4) ◦ . At the same time, this
result can again be used to constrain the component of ε orthogonal to ε:
ε
ε
= −(1.7 ± 7.0) × 10
−3 .
(9.159)
Therefore, at this level of 10 −2 relative to the amplitude for CP violation by mixing,
ε, there is no evidence for a direct CP violation amplitude ε orthogonal to ε. Our
interest now shifts to the component of ε parallel to ε, i.e. e(ε /ε).
K. Kleinknecht and U. Uwer
We use this value in the following sections.
Mass Difference m Combining the values from the CERN–Heidelberg experiments [173–175] with those from Fermilab E731 and E773 [176, 179], from
CPLEAR [181, 198, 199] and from the most precise single measurement by kTeV
[180], we obtain
m = (0.5286 ± 0.0011) × 10
10 s
−1 .
(9.154)
Superweak Phase From the two parameters given above, we obtain the phase of ε
in the superweak model,
Φ SW = arctan
2 m
Γ S
= (43.4 ± 0.1)
◦ .
(9.155)
Moduli of the Amplitudes η +− and η 00 New measurements of η +− from the
ratio of π + π − decays and semileptonic decays yield precise values of η +− . We
combine these with previous results and obtain [160–162].
|η +− | = (2.230 ± 0.006) × 10
−3 .
(9.156)
Absolute measurements of the amplitude η 00 are much less precise. A recent average
including the CPLEAR result is
|η 00 | = (2.23 ± 0.11) × 10
−3 .
(9.157)
Phase +− In all measurements, this phase is extracted from an interference term
with a beat frequency m. Taking the results from NA31 [184], E731 [176], E773
[179], and kTeV [180], together with the pre-1975 data and the result from CPLEAR
[181], we obtain the world average
Φ +− = (43.3 ± 0.4)
◦
(9.158)
using the values for m and τ S above. This result is in excellent agreement with
the value of Φ SW = (43.4 ± 0.1) ◦ . Since the interference experiments were
evaluated without assuming CPT invariance, this constitutes a stringent test of CPT
invariance. The difference is Φ +− − Φ SW = −(0.1 ± 0.4) ◦ . At the same time, this
result can again be used to constrain the component of ε orthogonal to ε:
ε
ε
= −(1.7 ± 7.0) × 10
−3 .
(9.159)
Therefore, at this level of 10 −2 relative to the amplitude for CP violation by mixing,
ε, there is no evidence for a direct CP violation amplitude ε orthogonal to ε. Our
interest now shifts to the component of ε parallel to ε, i.e. e(ε /ε).