# Neutrino Oscillation

## Main Question or Discussion Point

If we have a beta decay where a solar neutrino is produced:
a proton converts into a neutron ,emitting a W. the W decays into an anti electron and a neutrino.
So in the end of the chain we have a neutrino that will travel through space and oscillate.
Neutrino Oscillation happens because of Neutrino mixing. but what is the difference between them?
and how neutrino mixing happens exactly here? Is the neutrino required to emit a W Boson like quarks do?

I'm new to the concept of Neutrinos, I'm really trying to understand how neutrino mixing happens.

Related High Energy, Nuclear, Particle Physics News on Phys.org
Orodruin
Staff Emeritus
Homework Helper
Gold Member
Neutrino mixing happens much in the same way as quark mixing. The big difference being that the quarks we generally talk about are defined according to their mass eigenstates and the neutrino flavours are determined by the states that interact via a W with a particular charged lepton. The mixing is a mismatch between the mass and flavour eigenstates and the mixing matrix rotate them into eachother.

In other words, the electron neutrino is not a mass eigenstate, it is a linear combination of mass eigenstates.

Also note that the majority of the solar neutrinos are produced by the pp process, which is not a beta decay.

If we have a beta decay where a solar neutrino is produced:
a proton converts into a neutron ,emitting a W. the W decays into an anti electron and a neutrino.
So in the end of the chain we have a neutrino that will travel through space and oscillate.
Neutrino Oscillation happens because of Neutrino mixing. but what is the difference between them?
and how neutrino mixing happens exactly here?
In general, we detect particles by having them interact with other particles in our detectors.

When we observe particles using their weak interaction (which is always true for neutrinos), we observe their _flavor_. However, when particles propagate through space, they do so according to their _mass_ (velocity depends on it).

Surprisingly for our macro-world intuition, those things are not the same: electron neutrino has no definite mass (it's a "mix of three different states each with different mass"); and similarly, least massive neutrino (call it v1) has no definite flavor (it's a "mix of three different flavor states").

When, say, electron neutrino is produced, it CANT travel through space as pure electron neutrino. It's impossible. It travels through space as a "mix of three different states each with different mass". But different massive particles with the same momentum have different velocities. So these three waves travel with different velocities, and therefore interference happens: at different points along the trajectory, each component has different amplitude. That's "oscillation".

The same thing happens with other weakly-interacting particles, such as quarks:
When an up-type quark is produced via weak interaction, it travels through space as a "mix of three different states each with different mass". But quark masses are large, velocities are sufficiently different, and very soon after creation its different mass components drift apart along the trajectory so that their wavefunctions no longer overlap and no longer interfere. Thus you arrive at a more intuitively understandable picture: "its an u-quark with probability N%, c-quark with probability M%, or t-quark with probability (100-N-M)% (regardless of position on the trajectory)".

For neutrinos, masses are tiny and velocities are always very, very close to c and even closer to each other. Thus three mass components propagate almost on top of each other, very slowly drifting apart, with wavefunctions overlapping and interfering for a long time.