Initially it was thought that although
parity was violated,
CP (charge parity) symmetry was conserved. In order to understand the discovery of
CP violation, it is necessary to understand the mixing of neutral kaons; this phenomenon does not require CP violation, but it is the context in which CP violation was first observed.
Neutral kaon mixing s, since these interactions do not conserve strangeness. The strange quark in the anti- turns into a down quark by successively absorbing two
W-bosons of opposite charge. The down antiquark in the anti- turns into a strange antiquark by emitting them. Since neutral kaons carry strangeness, they cannot be their own antiparticles. There must be then two different neutral kaons, differing by two units of strangeness. The question was then how to establish the presence of these two mesons. The solution used a phenomenon called
neutral particle oscillations, by which these two kinds of mesons can turn from one into another through the weak interactions, which cause them to decay into pions (see the adjacent figure). These oscillations were first investigated by
Murray Gell-Mann and
Abraham Pais together. They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write : \psi(t) = U(t)\psi(0) = {\rm e}^{iHt} \begin{pmatrix}a \\ b\end{pmatrix}, \qquad H =\begin{pmatrix}M & \Delta\\ \Delta & M\end{pmatrix} , where
ψ is a
quantum state of the system specified by the amplitudes of being in each of the two
basis states (which are
a and
b at time
t = 0). The diagonal elements (
M) of the
Hamiltonian are due to strong interaction physics, which conserves strangeness. The two diagonal elements must be equal, since the particle and antiparticle have equal masses in the absence of the weak interactions. The off-diagonal elements, which mix opposite strangeness particles, are due to weak interactions;
CP symmetry requires them to be real. The consequence of the matrix
H being real is that the probabilities of the two states will forever oscillate back and forth. However, if any part of the matrix were imaginary, as is forbidden by CP symmetry, then part of the combination will diminish over time. The diminishing part can be either one component (
a) or the other (
b), or a mixture of the two.
Mixing The eigenstates are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can call
K1, which is the difference of the two states of opposite strangeness, and
K2, which is the sum. The two are eigenstates of
CP with opposite eigenvalues;
K1 has
CP = +1, and
K2 has
CP = −1 Since the two-pion final state also has
CP = +1, only the
K1 can decay this way. The
K2 must decay into three pions. Since the mass of
K2 is just a little larger than the sum of the masses of three pions, this decay proceeds very slowly, about 600 times slower than the decay of
K1 into two pions. These two different modes of decay were observed by
Leon Lederman and his coworkers in 1956, establishing the existence of the two weak eigenstates (states with definite
lifetimes under decays via the weak force) of the neutral kaons. These two weak eigenstates are called the (K-long, τ) and (K-short, θ). CP symmetry, which was assumed at the time, implies that =
K1 and =
K2.
Oscillation An initially pure beam of will turn into its antiparticle, , while propagating, which will turn back into the original particle, , and so on. This is called particle oscillation. On observing the weak decay
into leptons, it was found that a always decayed into a positron, whereas the antiparticle decayed into the electron. The earlier analysis yielded a relation between the rate of electron and positron production from sources of pure and its antiparticle . Analysis of the time dependence of this
semileptonic decay showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the and . Since this is due to weak interactions it is very small, 10−15 times the mass of each state, namely .
Regeneration A beam of neutral kaons decays in flight so that the short-lived disappears, leaving a beam of pure long-lived . If this beam is shot into matter, then the and its antiparticle interact differently with the nuclei. The undergoes quasi-
elastic scattering with
nucleons, whereas its antiparticle can create
hyperons.
Quantum coherence between the two particles is lost due to the different interactions that the two components separately engage in. The emerging beam then contains different linear superpositions of the and . Such a superposition is a mixture of and ; the is regenerated by passing a neutral kaon beam through matter. Regeneration was observed by
Oreste Piccioni and his collaborators at
Lawrence Berkeley National Laboratory. Soon thereafter, Robert Adair and his coworkers reported excess regeneration, thus opening a new chapter in this history.
CP violation While trying to verify Adair's results, J. Christenson,
James Cronin,
Val Fitch and
Rene Turlay of
Princeton University found decays of into two pions (
CP = +1) in an
experiment performed in 1964 at the
Alternating Gradient Synchrotron at the
Brookhaven laboratory. As explained in
an earlier section, this required the assumed initial and final states to have different values of
CP, and hence immediately suggested CP violation. Alternative explanations such as nonlinear quantum mechanics and a new unobserved particle (
hyperphoton) were soon ruled out, leaving CP violation as the only possibility. Cronin and Fitch received the Nobel Prize in Physics for this discovery in 1980. It turns out that although the and are weak eigenstates (because they have definite
lifetimes for decay by way of the weak force), they are not quite
CP eigenstates. Instead, for small ε (and up to normalization), : =
K2 + ε
K1 and similarly for . Thus occasionally the decays as a
K1 with
CP = +1, and likewise the can decay with
CP = −1. This is known as
indirect CP violation, CP violation due to mixing of and its antiparticle. There is also a
direct CP violation effect, in which the CP violation occurs during the decay itself. Both are present, because both mixing and decay arise from the same interaction with the
W boson and thus have CP violation predicted by the
CKM matrix. Direct CP violation was discovered in the kaon decays in the early 2000s by the
NA48 and
KTeV experiments at CERN and Fermilab. == See also ==