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Concept
Pontecorvo–Maki–Nakagawa–Sakata matrix
Summary
In particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary
mixing matrix which contains information on the mismatch of quantum states of neutrinos when they propagate freely and when they take part in weak interactions. It is a model of neutrino oscillation. This matrix was introduced in 1962 by Ziro Maki, Masami Nakagawa, and Shoichi Sakata,
to explain the neutrino oscillations predicted by Bruno Pontecorvo.
The Standard Model of particle physics contains three generations or "flavors" of neutrinos,
and
each labeled with a subscript showing the charged lepton that it partners with in the charged-current weak interaction. These three eigenstates of the weak interaction form a complete, orthonormal basis for the Standard Model neutrino. Similarly, one can construct an eigenbasis out of three neutrino states of definite mass, , , and , which diagonalize the neutrino's free-particle Hamiltonian. Observations of neutrino oscillation established experimentally that for neutrinos, as for quarks, these two eigenbases are different – they are 'rotated' relative to each other.
Consequently, each flavor eigenstate can be written as a combination of mass eigenstates, called a "superposition", and vice versa. The PMNS matrix, with components corresponding to the amplitude of mass eigenstate in terms of flavor "e", "μ", "τ"; parameterizes the unitary transformation between the two bases:
The vector on the left represents a generic neutrino expressed in the flavor-eigenstate basis, and on the right is the PMNS matrix multiplied by a vector representing that same neutrino in the mass-eigenstate basis. A neutrino of a given flavor is thus a "mixed" state of neutrinos with distinct mass: If one could measure directly that neutrino's mass, it would be found to have mass with probability .
The PMNS matrix for antineutrinos is identical to the matrix for neutrinos under CPT symmetry.
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