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In particle physics, neutral particle oscillation is the transmutation of a neutral particle with nonzero internal quantum numbers into its antiparticle. These oscillations and the associated mixing of particles gives insight into the realization of discrete parts of the Poincare group, ie, parity (P), charge conjugation (C) and time reversal invariance (T).
## The phenomenon

## Quantum mechanical model

_{AB} = |M_{AB}| e^{iα} and Γ_{AB} = |Γ_{AB}| e^{i(α+β)}.### CPT symmetry

^{-1} = H. The transformation properties above imply that $CPT|Arangle=|Brangle$. Then $langle\; A|H|Arangle=langle\; B|H|Brangle$, so a test of CPT symmetry is that the masses and the decay widths of the particle and the antiparticle are equal. This is a major class of experimental tests of CPT symmetry.

+frac12{|Gamma_{AB}> e^{i(beta+pi/2)}right|,
where the plus signs are for the state $|1rangle$ and minus, for $|2rangle$. A change in the phase convention, $|Branglerightarrow\; e^\{-itheta\}|Brangle$ changes the definition of the eigenstates, but not the eigenvalues. By appropriate choice of this phase, the angle φ can always be set equal to zero, so that the eigenstates are orthogonal.
### Oscillations, regeneration and CP violation

### CPT symmetry breaking

## See also

Neutral particles such as the kaon, neutron, bottom quark mesons or neutrinos have internal quantum numbers called flavour. This means that the particle and antiparticle are different. If both particle and antiparticle can decay into the same final state, then it is possible for the decay and its time reversed process to contribute to oscillations—

- A → F → B → F → A → ...

Such a process is actually connected to the mass renormalization of the states A and B in quantum field theory. However, under certain circumstances it can be tackled through a simpler quantum mechanics model which neglects these intermediate multi-particle quantum states and concentrates only on the states A and B.

Consider a state $|psi\; (t)rangle\; =a(t)|Arangle\; +b(t)|Brangle$. Its time evolution is governed by the Hamiltonian, H, through the action of the evolution operator $U(t)=e^\{iHt\}$ on $|psi\; (0)rangle$. The 2×2 matrix Hamiltonian can be written as

- $H\; =\; begin\{pmatrix\}H\_\{AA\}\; \&\; H\_\{AB\}H\_\{BA\}\; \&\; H\_\{BB\}end\{pmatrix\}\; =\; M-frac\; i2Gamma,$

A and B are both flavour eigenstates. Oscillations mix these states, and the mass eigenstates are the states which propagate without mixing, ie, the eigenvectors of H.

The action of the discrete spacetime symmetries are

- $C|Arangle=-|Brangle,\; P|Arangle=-|Arangle,\; mathrm\{and\}\; T|Arangle=+|Arangle.,$

Any 2×2 matrix can be written in the form $E\_0\; I+Emathbf\; ucdotmathbf\{sigma\}$, where I is the identity matrix, σ_{i} are the Pauli matrices and u is a unit vector. With CPT symmetry, the diagonal elements of H are equal, so

- $u\; =\; begin\{pmatrix\}sinphi\; cosphi\; 0end\{pmatrix\},qquad$

- $left|1,2rightrangle\; =\; frac1\{sqrt2\}\; (left|Arightranglepm\; e^\{iphi\}left|Brightrangle),$

- $E\_\{1,2\}\; =\; M\_\{AA\}-frac12Gamma\_\{AA\}pm\; e^\{ialpha\}left|$

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Last updated on Friday October 10, 2008 at 22:06:54 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 10, 2008 at 22:06:54 PDT (GMT -0700)

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