Is the PMNS Matrix Unitary? Exploring Neutrino Eigenstates

[McLaren Rulez]

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.

 

[Parlyne]

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.

 

[Bill_K]

Because it's a transformation from one orthonormal basis to another, which is always unitary.

 

[McLaren Rulez]

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.