Is the PMNS Matrix Always Unitary in Neutrino Physics?

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Discussion Overview

The discussion centers on the unitarity of the PMNS matrix in neutrino physics, specifically addressing whether this property is an assumption or can be proven. Participants explore the implications of mixing different neutrino states and the mathematical foundations of the matrix.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the PMNS matrix is always unitary and seeks clarification on the motivation behind this assumption or proof.
  • Another participant asserts that if only three neutrino states mix, the mixing matrix must be a 3x3 unitary matrix, as non-unitarity would alter the kinetic terms in the Lagrangian.
  • A different participant states that the transformation from one orthonormal basis to another is inherently unitary, implying that the PMNS matrix should be unitary.
  • One participant expresses a lack of familiarity with the kinetic Lagrangian but acknowledges the explanation provided.

Areas of Agreement / Disagreement

There is no consensus on whether the PMNS matrix is always unitary, as participants present differing views on the implications of mixing additional neutrino states.

Contextual Notes

The discussion does not resolve the assumptions regarding the number of neutrino states or the implications of including sterile neutrinos in the mixing matrix.

McLaren Rulez
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Hi,

Okay, I thought I had created this thread but looks like I didn't hit submit or something. Anyway, my question is, why is the PMNS matrix which is used to go between the mass eigenstates and flavour eigenstates of neutrinos unitary? Is it an assumption (if so, what is the motivation behind it) and if not, how can it be proved?

Thank you.
 
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If there are only three neutrino states that mix, the mixing matrix must be a 3x3 unitary matrix, as anything else would change the form of the kinetic terms in the Lagrangian. If, however, other (presumably sterile) neutrinos mix in, the 3x3 matrix will not be unitary; but, the larger matrix that describes the full mixing will be.
 
Because it's a transformation from one orthonormal basis to another, which is always unitary.
 
Bill_K said:
Because it's a transformation from one orthonormal basis to another, which is always unitary.

Thank you! That makes sense. Parlyne, I am unfamiliar with the kinetic lagrangian; nevertheless, thank you for replying.
 

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