· Oscillations · 2 min read
What Is the PMNS Matrix?
The PMNS matrix is the mathematical object that links the three neutrino flavour states to the three mass states, encoding the mixing angles and the CP phase that govern oscillation.
The PMNS matrix is the table of numbers that connects the three neutrino flavours — electron, muon and tau — to the three states of definite mass. Each flavour a neutrino is created in is a specific blend of mass states, and the PMNS matrix records exactly how much of each mass state goes into each flavour. Without this mixing, neutrino oscillation could not happen.
Where does the name come from?
The matrix is named after Bruno Pontecorvo, Ziro Maki, Masami Nakagawa and Shoichi Sakata. Bruno Pontecorvo first proposed that neutrinos might transform between states in the late 1950s, while Maki, Nakagawa and Sakata set out the flavour-mixing framework in 1962. The combined initials give us PMNS, sometimes shortened to the MNS matrix.
What is inside the matrix?
The PMNS matrix is a 3-by-3 array, but its physical content is captured by just four numbers. Three of these are mixing angles, written as theta-12, theta-23 and theta-13. The fourth is a phase, delta, which can introduce a difference between how neutrinos and antineutrinos behave. That phase is the source of charge-parity, or CP, violation in the lepton sector. If neutrinos are their own antiparticles, two further Majorana phases appear, though these do not affect oscillation.
Why does the PMNS matrix matter?
Because it governs oscillation, the PMNS matrix turns abstract quantum mechanics into measurable predictions. Reactor, accelerator and atmospheric experiments each probe different combinations of its angles, and together they pin down the values listed in the global fits. You can find the current best estimates on the parameters page. The matrix is the neutrino counterpart of the CKM matrix that describes quark mixing, but the neutrino angles turn out to be far larger, which is one of the open puzzles of particle physics.
The PMNS matrix is not a fixed law handed down in advance. Its entries are quantities we measure, refine and occasionally revise as experiments improve. Each new result sharpens the picture of how the three known neutrinos relate to one another.
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References
- 1.S. Navas et al. (Particle Data Group), Review of Particle Physics, Phys. Rev. D (2024). DOI: 10.1103/PhysRevD.110.030001.