A question about mass eigenstates

[ndung200790]

I am very confuse about mass eigenstate. In some books they say'' If neutrinos are massless then lepton mixing is unobservable.Any Cabibbo-like rotation still leaves us with neutrino mass eigenstates''.
I do not understand that statement.Why the mixing of some states gives a state being mass eigenstate?
Please forgive me if it is bad question,I have to self-study physics in Vietnamese society.

 

[mfb]

Without neutrino masses, every superposition of neutrino states is a mass eigenstate, and therefore remains this superposition. In particular, every flavor eigenstate is a mass eigenstate, and does not mix.

With neutrino masses, the mass eigenstates can be different from flavor eigenstates. You can get 3 different mass eigenstates, and their flavor composition is given by the PMNS matrix (similar to the CKM matrix, just for neutrinos).