9 Symmetry Violations and Quark Flavour Physics
565
9.5.6 Elucidation of CP Violation in K 0 Decays (II):
Discovery of Direct CP Violation in e(ε /ε)
9.5.6.1 Significance of the Double Ratio R
The real part of ε /ε is connected with the amplitude ratios η 00 and η +− of CPviolating K L decays to CP-conserving K S decays. A measurement of decay rates
with the required precision of 10 −3 is only possible by measuring the ratio of rates
in the same beam in the same time interval. From the Wu–Yang triangle relations
(9.90) η 00 = ε − 2ε and η +− = ε + ε , we obtain
ε
ε
=
1
6
1 −
η 00
η +−
2
.
(9.160)
A measurement of the double ratio
R =
|η 00 | 2
|η +− | 2 =
Γ (K L → 2π 0 )/Γ (K L → π + π − )
Γ (K S → 2π 0 )/Γ (K S → π + π − )
(9.161)
to a precision of about 0.3% is therefore required to distinguish between the two
remaining models, the KM milliweak model and the superweak model. Since the
KM model predicts values of e(ε /ε) in the range between 0.2 × 10 −3 and
3 × 10 −3 , the precision required for detecting a signal of direct CP violation
depends on the actual value. If the largest prediction is realized in nature, a precision
of δR = 5 × 10 −3 would be sufficient for a three-standard-deviation observation.
If, however, the lowest value is realized, a precision of δR = 0.4 × 10 −3 would
be needed, corresponding to samples of several million events for each of the four
decay modes.
9.5.6.2 The NA31 Experiment: First Evidence for Direct CP Violation
The first observation of direct CP violation was made by a collaboration of
physicists at CERN in 1988 [191]. The experiment, called “North Area No. 31”, or
NA31, was based on the concurrent detection of 2π 0 and π + π − decays. Collinear
beams of K L and K S were employed alternately. The beam layout and the apparatus
were described in Sect. 9.5.4.4. The K 0 → 2π 0 → 4γ decays were reconstructed
and separated from the background primarily due to K L → 3π 0 → 6γ decays
as described in Sect. 9.5.4.2. This background is uniformly distributed in a twodimensional scatter plot of photon-pair masses, while the 2π 0 signal peaks at a point
S where both photon pairs have the π 0 mass, with a 2 MeV resolution. Signal and
background events were counted in equal-area χ 2 contours around S. Figure 9.14
shows the χ 2 distribution of events in the K S beam and in the K L beam. The signal
region was taken as χ 2 < 9. Background in the K L data was subtracted by linear
565
9.5.6 Elucidation of CP Violation in K 0 Decays (II):
Discovery of Direct CP Violation in e(ε /ε)
9.5.6.1 Significance of the Double Ratio R
The real part of ε /ε is connected with the amplitude ratios η 00 and η +− of CPviolating K L decays to CP-conserving K S decays. A measurement of decay rates
with the required precision of 10 −3 is only possible by measuring the ratio of rates
in the same beam in the same time interval. From the Wu–Yang triangle relations
(9.90) η 00 = ε − 2ε and η +− = ε + ε , we obtain
ε
ε
=
1
6
1 −
η 00
η +−
2
.
(9.160)
A measurement of the double ratio
R =
|η 00 | 2
|η +− | 2 =
Γ (K L → 2π 0 )/Γ (K L → π + π − )
Γ (K S → 2π 0 )/Γ (K S → π + π − )
(9.161)
to a precision of about 0.3% is therefore required to distinguish between the two
remaining models, the KM milliweak model and the superweak model. Since the
KM model predicts values of e(ε /ε) in the range between 0.2 × 10 −3 and
3 × 10 −3 , the precision required for detecting a signal of direct CP violation
depends on the actual value. If the largest prediction is realized in nature, a precision
of δR = 5 × 10 −3 would be sufficient for a three-standard-deviation observation.
If, however, the lowest value is realized, a precision of δR = 0.4 × 10 −3 would
be needed, corresponding to samples of several million events for each of the four
decay modes.
9.5.6.2 The NA31 Experiment: First Evidence for Direct CP Violation
The first observation of direct CP violation was made by a collaboration of
physicists at CERN in 1988 [191]. The experiment, called “North Area No. 31”, or
NA31, was based on the concurrent detection of 2π 0 and π + π − decays. Collinear
beams of K L and K S were employed alternately. The beam layout and the apparatus
were described in Sect. 9.5.4.4. The K 0 → 2π 0 → 4γ decays were reconstructed
and separated from the background primarily due to K L → 3π 0 → 6γ decays
as described in Sect. 9.5.4.2. This background is uniformly distributed in a twodimensional scatter plot of photon-pair masses, while the 2π 0 signal peaks at a point
S where both photon pairs have the π 0 mass, with a 2 MeV resolution. Signal and
background events were counted in equal-area χ 2 contours around S. Figure 9.14
shows the χ 2 distribution of events in the K S beam and in the K L beam. The signal
region was taken as χ 2 < 9. Background in the K L data was subtracted by linear