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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 matrix〔The PMNS matrix is not unitary in the seesaw model.〕 which contains information on the mismatch of quantum states of neutrinos when they propagate freely and when they take part in the weak interactions. It is important in the understanding 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.〔 reproduced and translated in 〕 ==The PMNS matrix== The Standard Model of particle physics contains three generations or "flavors" of neutrinos, νe, νμ, and ντ labeled according to the charged leptons with which they partner 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, ν1, ν2, and ν3, which diagonalize the neutrino's free-particle Hamiltonian. Observations of neutrino oscillation have experimentally determined that for neutrinos, like the quarks, these two eigenbases are not the same - they are "rotated" relative to each other. Each flavor state can thus be written as a superposition of mass eigenstates, and vice-versa. The PMNS matrix, with components ''Uai'' corresponding to the amplitude of mass eigenstate ''i'' in flavor ''a'', parameterizes the unitary transformation between the two bases: : The vector on the left represents a generic neutrino state expressed in the flavor basis, and on the right is the PMNS matrix multiplied by a vector representing the same neutrino state in the mass basis. A neutrino of a given flavor ''α'' is thus a "mixed" state of neutrinos with different mass: if one could measure directly that neutrino's mass, it would be found to have mass ''m''i with probability |''U''''αi''|2. The PMNS matrix for antineutrinos is identical to the matrix for neutrinos under CPT symmetry. Due to the difficulties of detecting neutrinos, it is much more difficult to determine the individual coefficients than in the equivalent matrix for the quarks (the CKM matrix). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pontecorvo–Maki–Nakagawa–Sakata matrix」の詳細全文を読む スポンサード リンク
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