# Neutrino Oscillation & Helicity: Exploring Contradictions

• spidey
In summary: This is the source of the so-called "chiral violation" which is the basis of the mass-less neutrino hypothesis.
spidey
All neutrinos are left handed and all anti neutrinos are right handed.so,it should be lorentz invariant and travel at speed of light. if it travels at c,then it is massless. but, neutrino oscillation requires mass? why there is contradiction?

A massive neutrino will generally have a helicity h=-v/c. This is so close to 1 that there is as yet no experimental spin measurement accurate enough to measure the difference.

spidey said:
All neutrinos are left handed and all anti neutrinos are right handed.so,it should be lorentz invariant and travel at speed of light. if it travels at c,then it is massless. but, neutrino oscillation requires mass? why there is contradiction?
You don't even really need helicity to get a "contradiction". Neutrino oscillation can happen only of neutrinos of different flavors have different masses. If a neutrino is created by the Sun in an electronic flavor, it has a given energy and a given momentum. How can it be measured on Earth with a different mass if energy and momentum are conserved ?

I mean to say that the issue of symmetries in neutrino oscillation can not be thought of academically without proper treatment of (elementary) quantum effects. The answer is indeed what Clem points out : the problem is academic because the symmetry violations are so tiny, they merely stem from the Heisenberg's inequalities. I don't mean to say it is trivial either, such a proper treatment is rather tedious.

Neutrino mass, mixing, and flavor change
C. Amsler et al., Physics Letters B667, 1 (2008)

spidey said:
All neutrinos are left handed and all anti neutrinos are right handed.so,it should be lorentz invariant and travel at speed of light. if it travels at c,then it is massless. but, neutrino oscillation requires mass? why there is contradiction?

Well, you hit the nail on the head. All neutrinos are left handed (and anti-neutrinos right handed) only in the approximation mass=0. Now that we know they have mass, this rule simply isn't true any more (that is, it's possible to define a reference frame where neutrinos are right-handed).

thanks for the replies mates..so not all neutrinos are left handed..there is a reference frame where it will be right handed..

humanino said:
You don't even really need helicity to get a "contradiction". Neutrino oscillation can happen only of neutrinos of different flavors have different masses.

Neutrino mass, mixing, and flavor change
C. Amsler et al., Physics Letters B667, 1 (2008)

Thanks Humanino..but i don't understand the technical paper, very difficult to follow with my limited knowledge..

The usual terminology as I understand it is to call particles that enter the weak interaction with V-A (The sign is different in some formalisms.) are called "left handed" so that all leptons are left handed, even if they do not have pure alignment.

I think there is a confusion between helicity and chirality. The weak interaction couples to the left-handed chiral component of the neutrino. If the neutrino were massless, that would also be the left-handed polarization state of the neutrino.

Since the neutrino has mass, one can boost to a frame where the polarization becomes right-handed, but there is still a left-handed chiral component, so it still feels the weak force.

## 1. What is a neutrino?

A neutrino is a tiny, subatomic particle that has no electric charge and interacts very weakly with other particles. It is one of the building blocks of the universe and is produced in various processes, such as nuclear reactions and radioactive decay.

## 2. What is neutrino oscillation?

Neutrino oscillation, also known as neutrino mixing, is the phenomenon where neutrinos change from one type to another as they travel through space. This is due to the fact that neutrinos have mass and their three different types, or flavors, are a combination of their mass states.

## 3. What is helicity?

Helicity is a physical property of particles that describes the direction of their spin relative to their momentum. It can be either left-handed or right-handed, depending on whether the spin is in the same direction or opposite direction as the momentum.

## 4. How do neutrino oscillation and helicity relate to each other?

Neutrino oscillation and helicity are related in the sense that neutrinos with a specific helicity can only change to another type of neutrino with the same helicity. This is because of the conservation of angular momentum, where the helicity of a particle must remain constant during interactions.

## 5. What contradictions are being explored in the study of neutrino oscillation and helicity?

The main contradiction being explored in this field is the fact that neutrinos have mass, which was not initially predicted in the Standard Model of particle physics. This contradicts the idea that neutrinos were massless and has led to further research and experiments to better understand the nature of these elusive particles.

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