Subatomic Physics

9.8. The Fall of CP Invariance 269
2. The state |K0 2
transitions from |K0 2 〉 to |K0 1
〉 is an eigenstate of the total Hamiltonian. In vacuum, no
〉 can occur. For the two wells, the absence of
such transitions is expressed by Eq. (9.65). The corresponding relation for
kaons follows from Eqs. (9.80) and (9.81) as
〈K 0 1 |H|K0 2 〉 =0. (9.88)
3. As stated by Eq. (9.84), K 0 2 cannot decay into two pions if CP is conserved.
In 1964, a Princeton group performed an experiment to set a lower limit on
the two-pion decay of K 0 2 .(32) Another experiment was simultaneously done by an
Illinois group. (33) Both gave the astounding result that decays into two pions do
occur; the branching ratio was found to be approximately
Int(K 0 L → π+ π − )
Int(K 0 L → all charged modes) ≈ 2 × 10−3 . (9.89)
We have switched notation here and denote the long-lived neutral kaon with K0 L
and the short-lived one with K0 S . The reason for the switch is Eq. (9.82), which
defines K0 1 and K0 2 to be eigenstates of CP. Equation (9.89) indicates, however,
that the long-lived kaon is not an eigenstate of CP. It is customary to retain the
for the eigenstates of CP and to denote the real particles with
notation K0 1 and K0 2
K0 S and K0 L .
The news of violation of CP traveled through the world ofphysicswithnearly
the speed of light, just as, seven years earlier, had the news of parity breakdown.
It was greeted with even more scepticism. To describe the reason for the disbelief,
we digress to describe the celebrated CPT theorem. The CPT theorem is easy to
understand but difficult to prove. In a somewhat sloppy way, it can be stated as
follows: the product of the three operations T , C, andPcommutes with practically
every conceivable Hamiltonian, or
[CPT,H]=0. (9.90)
In other words, our world and a time-reversed parity-reflected antiworld must behave
identically. The order of the three operators T , C, andP is irrelevant. (34) The
operation CPT is thus very different from the individual operations T , C, andP .
It is easy to construct a Lorentz-invariant Hamiltonian that violates, for instance,
32 J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett. 13, 138 (1964).
V. L. Fitch, Rev. Mod. Phys. 53, 367 (1981); Science 212, 939 (1981); J. W. Cronin, Rev. Mod.
Phys. 53, 373 (1981); Science 212, 1221 (1981).
33 A. Abashian, R. J. Abrams, D. W. Carpenter, G. P. Fisher, B. M. K. Nefkens, and J. H.
Smith, Phys. Rev. Lett. 13, 243 (1964).
34 Since the order of the operations T , C, andP does not matter, there exist 3! possibilities of
naming the theorem. Lüders and Zumino checked that their choice,TCP, agreed with the name of
a well-known gasoline additive. Despite this, we use the more standard order, namely CPT. [G.
Lüders, Physikalische Blätter 22, 421 (1966).]