PMNS matrix
Introduction
The Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix, also known as the lepton mixing matrix, is a unitary matrixUnitary Matrix that describes the likelihood of a neutrino produced in one flavor state to be observed in another flavor state. The PMNS matrix is a fundamental aspect of the Standard Model of Particle Physics, particularly in the field of neutrino oscillationsNeutrino Oscillations.
History and Naming
The PMNS matrix is named after Ziro Maki, Masami Nakagawa, and Shoichi Sakata, who introduced the matrix in 1962. They were building on the work of Z. M. Pontecorvo, who had earlier suggested that neutrinos might oscillate between different types. The matrix was introduced to explain the small neutrino masses observed in the experiments.
Mathematical Description
The PMNS matrix is a 3x3 unitary matrix, meaning that its inverse is equal to its conjugate transpose. It is typically written in terms of four parameters: three mixing angles (θ12, θ23, θ13) and a CP-violating phase δ. The matrix can be parametrized as follows:
U(PMNS) =
Physical Interpretation
The PMNS matrix describes the probability of one type of neutrino changing into another type as it propagates. This phenomenon is known as neutrino oscillation. The matrix elements are complex numbers, and their absolute squares give the probabilities of different flavor transitions.
Experimental Determination
The parameters of the PMNS matrix are determined experimentally from measurements of neutrino oscillations. The mixing angles and the CP-violating phase can be measured in neutrino oscillation experiments, such as those performed at Super-KamiokandeSuper-Kamiokande Experiment or the Sudbury Neutrino ObservatorySudbury Neutrino Observatory Experiment.
Implications for Particle Physics
The existence of the PMNS matrix and neutrino oscillations implies that neutrinos have mass, a fact not incorporated in the original Standard Model of particle physics. This has led to the development of extensions to the Standard Model, such as the seesaw mechanismSeesaw Mechanism, to explain the small but nonzero neutrino masses.