Do neutrinos really have a massless state?

Question

I have read these questions:

Do neutrinos change speed in neutrino oscillations?

Neutrinos always travel at same speed?

Neutrinos always travel at same speed?

Where are all the slow neutrinos?

Neutrino Oscillations and Conservation of Momentum

There are a lot of questions on this site about neutrino speed and mass, but none of them answer my question.

The neutrino is the lightest known massive particle, and for a while its rest mass (or if it is massless) was a debate. Today we do know that the neutrino does have a rest mass.

A neutrino (/nuːˈtriːnoʊ/ or /njuːˈtriːnoʊ/) (denoted by the Greek letter ν) is a fermion (an elementary particle with spin of 1 / 2 ) that interacts only via the weak subatomic force and gravity.[2][3] The neutrino is so named because it is electrically neutral and because its rest mass is so small (-ino) that it was long thought to be zero. The mass of the neutrino is much smaller than that of the other known elementary particles.[1]

https://en.wikipedia.org/wiki/Neutrino

I have read this question:

Which is the lightest thing in this universe? Is that a photon or neutrino?

Where rob says:

There are three flavors of neutrino and they all have different masses. Therefore at least two of them are massive; whether the lightest neutrino is massless is an open question.

This information is from several years ago, there might be new information (I did not find any) on this.

So it could be that the neutrino is oscillating between flavors in flight, and these flavors are superpositions of massive and massless states, and this could mean too that it is oscillating between the speed of light and a slower speed, but because of this, it can never slow down (on average when measured over a long distance) from the vicinity of the speed of light.

Question:

1. Do neutrinos really have a massless state?

Answer 1

The oscillation of neutrinos is closely related to the concept of superposition of quantum states.

There are three distinct 'flavors' of neutrinos: electron, muon and tau. When a neutrino is produced in a particle reaction, it's almost always produced with a specific flavour.

Neutrinos however may also have three different masses (one of them possibly being $0$). What is important to understand, that the properties of mass and flavour are not independent - you don't have, for example three electron neutrinos with diferent masses. Rather, each flavor of neutrinos is a different mixture (superpositino) of neutrinos with different masses. Any mixture of flavors can be interpreted as some mixture of masses, and vice versa.

When you have a nautrino from, for example, the Sun, it's usually produced as an electron neutrino, which is a specific superposition of mass states. Each component travels with a different speed (one possibly with the speed of light), but differences aren't big enough to separate them on the distance Sun-Earth. Ratheer, and as they travel they experience relative change in phase, from the equation $$ |\psi_i\rangle \rightarrow e^{-i(E_it-\vec p_i\vec x)/\hbar}|\psi_i\rangle$$ When they are all ultrarelativistic and traveling vith the speed very close to the speed of light, we have $$ t \approx |\vec x|/c$$ $$ E_i = \sqrt{|\vec p_i|^2c^2+ (m_ic^2)^2} \approx |\vec p_i|c + \frac{m_i^2c^3}{2|\vec p_i|}$$ $$ E_i t - |\vec p_i||\vec x| \approx \frac{m_i^2c^2|\vec x|}{2|\vec p_i|} \approx \frac{m_i^2c^3|\vec x|}{2 E_i} $$ The differences in masses cause differences in phases. As the different components of the neutrino gain different phases, they become a different mixture, a different flavor. That's why a neutrino that was produced as an electron neutrino after some time may be detected as a muon neutrino or a tau neutrino.

If you do wait long enough the neutrinos with different masses will get separated. At that point they no longer interfere with each other, and they won't oscillate - instead, a neutrino of a fixed mass has fixed chances of being detected as having one of the three flavors, and these chances do not change.

Answer 2

Neutrinos are relatively hard to slow down due to their size, every time they come in contact with anything they slow down, however due to their size it is relatively rare, this is when they can be detected, finding them after they hit something however is a different story.