103
4.2. Discrete transformations: P, C and T
We have approached charge conjugation following the historical route,
which is to say via the electromagnetic interaction. But we can ask whether
(true) C is a good symmetry of other interactions, for example the weak
interaction. Consider applying C to the reaction (4.82), so that it becomes
π
−
→ μ
− + ¯
ν μ .
(4.103)
If C was a good symmetry, the (parity-violating) longitudinal polarization
of the μ
− in (4.103) should be the same as that of the μ
+ in (4.82). But
in fact it is the opposite, the μ
− spin being aligned along the direction of
its momentum. So C, like P, is violated in weak interactions. It is a good
symmetry in electromagnetic and strong interactions.
4.2.3 CP
It has probably occurred to the reader that, although C and P are each
violated in the decays (4.82) and (4.103), the combined transformation CP
might be a good symmetry: particles are changed to antiparticles, the sense
of longitudinal polarization is reversed, and the corresponding decays occur.
Indeed, the rates for these two decays are the same, and CP is conserved.
For a while, after 1956, it was hoped that CP would prove to be always
conserved, so as to avoid a ‘lopsided’ distinction between right and left, and
between matter and antimatter. But before long Christenson et al. (1964)
reported evidence for CP violation in the decays of neutral K-mesons, a result
soon confirmed by other experiments.
As we mentioned in section 1.2.2, it was the difficulty of incorporating CP
violation into the 2-generation electroweak theory that led Kobayashi and
Maskawa (1973) to propose a third generation of quarks, which allowed a CP
violating parameter to be included quite naturally. CP violation in K-decays
is a small effect (of order one part in 10
3 ), but in 1980 Carter and Sanda (1980)
showed that considerably larger effects, up to 20%, could be expected in rare
decays of neutral B mesons, according to the framework of Kobayashi and
Maskawa (KM). Some 20 years later, the ‘B factories’ at the asymmetric e
− e
+
colliders PEPII and KEKB began producing B mesons by the many millions,
¯
and intensive study of CP violation in the B
0 (db) ¯ − B
0 ( ¯
db) systems followed
at the BaBar and Belle detectors. Remarkably, all observations to date are
consistent with the original KM parametrization. We shall return to this
topic when we discuss weak interactions in volume 2, specifically in chapter
21. Meanwhile we refer to Bettini (2008), chapter 8, for an introductory
overview.
It is worth pausing here to note the significance of CP violation. First
of all, it implies that there is an absolute distinction between matter and
antimatter and, as a consequence, between left and right: these are not merely
a matter of convention. For example, the rate for the process
B
0
→ K
+ π
−
(4.104)
4.2. Discrete transformations: P, C and T
We have approached charge conjugation following the historical route,
which is to say via the electromagnetic interaction. But we can ask whether
(true) C is a good symmetry of other interactions, for example the weak
interaction. Consider applying C to the reaction (4.82), so that it becomes
π
−
→ μ
− + ¯
ν μ .
(4.103)
If C was a good symmetry, the (parity-violating) longitudinal polarization
of the μ
− in (4.103) should be the same as that of the μ
+ in (4.82). But
in fact it is the opposite, the μ
− spin being aligned along the direction of
its momentum. So C, like P, is violated in weak interactions. It is a good
symmetry in electromagnetic and strong interactions.
4.2.3 CP
It has probably occurred to the reader that, although C and P are each
violated in the decays (4.82) and (4.103), the combined transformation CP
might be a good symmetry: particles are changed to antiparticles, the sense
of longitudinal polarization is reversed, and the corresponding decays occur.
Indeed, the rates for these two decays are the same, and CP is conserved.
For a while, after 1956, it was hoped that CP would prove to be always
conserved, so as to avoid a ‘lopsided’ distinction between right and left, and
between matter and antimatter. But before long Christenson et al. (1964)
reported evidence for CP violation in the decays of neutral K-mesons, a result
soon confirmed by other experiments.
As we mentioned in section 1.2.2, it was the difficulty of incorporating CP
violation into the 2-generation electroweak theory that led Kobayashi and
Maskawa (1973) to propose a third generation of quarks, which allowed a CP
violating parameter to be included quite naturally. CP violation in K-decays
is a small effect (of order one part in 10
3 ), but in 1980 Carter and Sanda (1980)
showed that considerably larger effects, up to 20%, could be expected in rare
decays of neutral B mesons, according to the framework of Kobayashi and
Maskawa (KM). Some 20 years later, the ‘B factories’ at the asymmetric e
− e
+
colliders PEPII and KEKB began producing B mesons by the many millions,
¯
and intensive study of CP violation in the B
0 (db) ¯ − B
0 ( ¯
db) systems followed
at the BaBar and Belle detectors. Remarkably, all observations to date are
consistent with the original KM parametrization. We shall return to this
topic when we discuss weak interactions in volume 2, specifically in chapter
21. Meanwhile we refer to Bettini (2008), chapter 8, for an introductory
overview.
It is worth pausing here to note the significance of CP violation. First
of all, it implies that there is an absolute distinction between matter and
antimatter and, as a consequence, between left and right: these are not merely
a matter of convention. For example, the rate for the process
B
0
→ K
+ π
−
(4.104)