Neutral particle oscillations were first investigated in 1954 by Murray Gell-mann and Abraham Pais.
[1] For example, a neutron cannot transmute into an antineutron as that would violate the conservation of baryon number.
But in those hypothetical extensions of the Standard Model which include interactions that do not strictly conserve baryon number, neutron–antineutron oscillations are predicted to occur.
[2][3][4] Such oscillations can be classified into two types: In those cases where the particles decay to some final product, then the system is not purely oscillatory, and an interference between oscillation and decay is observed.
After the striking evidence for parity violation provided by Wu et al. in 1957, it was assumed that CP (charge conjugation-parity) is the quantity which is conserved.
[6] However, in 1964 Cronin and Fitch reported CP violation in the neutral Kaon system.
In 2001, CP violation in the B0 ⇄ B0 system was confirmed by the BaBar and the Belle experiments.
[12][13] Also known as the Davis experiment, it used a huge tank of perchloroethylene in Homestake mine (it was deep underground to eliminate background from cosmic rays), South Dakota.
Because the neutrino interacts very weakly, only about one argon atom was collected every two days.
In 1968, Bruno Pontecorvo showed that if neutrinos are not considered massless, then νe (produced in the sun) can transform into some other neutrino species (νμ or ντ), to which Homestake detector was insensitive.
since the exponential term is just a phase factor: It does not produce an observable new state.
, is diagonal: It can be shown, that oscillation between states will occur if and only if off-diagonal terms of the Hamiltonian are not zero.
), that is then under time evolution we get[17] which unlike the previous case, is distinctly different from
Hence, the necessary conditions for oscillation are: If the particle(s) under consideration undergoes decay, then the Hamiltonian describing the system is no longer Hermitian.
[19] Since any matrix can be written as a sum of its Hermitian and anti-Hermitian parts,
is an anti-Unitary operator[20] and satisfies the relation hence and similarly for the diagonal elements of
(8) The suffixes stand for Heavy and Light respectively (by convention) and this implies that
), and certain other conditions are met, then CP violation can be observed as a result of this phenomenon.
Depending on the condition, CP violation can be classified into three types:[19][21] Consider the processes where
(11) Hence, the particle-antiparticle oscillation becomes a CP violating process as the particle and its antiparticle (say,
Usually, an alternative classification of CP violation is made:[21] Considering a strong coupling between two flavor eigenstates of neutrinos (for example, νe–νμ, νμ–ντ, etc.)
and a very weak coupling between the third (that is, the third does not affect the interaction between the other two), equation (6) gives the probability of a neutrino of type
One important inference is that neutrinos have a finite mass, although very small.
are independent, and the expression for probability in equation (13) is not sensitive to the sign of
(as sine squared is independent of the sign of its argument), it is not possible to determine the neutrino mass spectrum uniquely from the phenomenon of flavor oscillation.
We can draw the following inferences: The 1964 paper by Christenson et al.[7] provided experimental evidence of CP violation in the neutral Kaon system.
This implied that the long lived Kaon cannot be purely the CP eigenstate
In other words, direct CP violation is observed in the asymmetry between the two modes of decay.
Quoting David J. Griffiths:[22] The neutral Kaon system adds a subtle twist to the old question, 'What is a particle?'
But whether you choose to analyze the process in terms of states of linear or circular polarization is largely a matter of taste.