# Some words on neutrino physics?

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1. Dec 1, 2013

### amitbashyal

Hi everyone, I am doing a final project on the title " fundamentals of neutrino physics". I wanted to raise some issues with neutrino which makes it the possible way to the physics beyond standard model. I am myself doing some research on these topics but at some points the math bugs me out. Anyway, i have some questions which answers themselves confounded me due to the complicated math. Some pf them are:
1. Why wouldnt there be a mirror image of a neutrino? Is it because they are chargeless? They are still in the lepton family but unlike electrons, muons and tau, they are not right handed. I know this is the major source of cp violation but still I couldn't find a better explanation. In fact I looked up at what means left handedness and right handedness. According to a site called quantum-diary ( i guess), that depends upon the perception. The same electron might be left handed or right handed depending upon the frame of reference. I got that but this really bugged me out. What property of neutrino keeps it from having mirror image?
2. I looked at the issue of whether the neutrinos are dirac fermions or majarona fermions. But i couldnt get why would neutrino be majarona?
3. This question is really stupid but somehow I saw a lot of topics on theta 13 but no one seemed to describe it properly. They are explained using variables like A and B. Can anybody explain what it really means in simplest term? Like are there theta12, theta23, theta21 mixing angles? And if so, is theta 12 equal to theta21 ( i had a thought that since mixing angles depend upon the square of mass difference between two types of neutrinos, they should be equal.)
4. And one last thing, what makes neutrino a good candidate for dark matter, its negligible interaction with matter and EM force? Since neutrinos are nearly massless, does our current calculations, like the total neutrinos produced from stars in milky way galaxy all this time will equal the mass of dark matter that slows down our galaxy? I think it is extremely impossible given the low interaction of neutrinos with mass?

It is a lot of questions to ask in a single thread but any kind of insight on any of these topics will be highly appreciated. And its not a hw problem. They are the topics i came across when i was doing my research on this topic.

Thanks a lot.

2. Dec 1, 2013

### michael879

1) right handed neutrinos MAY exist, but only left handed leptons interact weakly, and neutrinos have no electric or color charge. So if they do exist, they would only interact gravitationally and we would never really be able to see them

2) majorana mass terms are only possible for chargeless fermions, since the term violates charge conservation. Since neutrinos are massless both Dirac and majorana mass terms are possible and it's not yet clear which kind of lepton they are. A particularly interesting minimal extension to the SM involves both Dirac and majorana mass terms which interfere with each other via the seesaw mechanism. This results in very massive right handed neutrinos
(Dark matter candidate) and nearly massless left handed neutrinos

3. Dec 1, 2013

### michael879

4) left handed neutrinos are ruled out as dark matter candidates by both the limit on total neutrinos in the universe and the observation of dark matter being "cold". Like I said though, right handed neutrinos are still a viable candidate

4. Dec 1, 2013

### Bill_K

There are two closely related concepts: helicity and chirality. "Handedness" usually refers to chirality. Helicity is the projection of the spin on the direction of motion. Chirality is the eigenvalue of γ5. For a massless particle, helicity and chirality coincide, and are a constant of the motion. For a particle with mass, they are less satisfactory and differ. Chirality is no longer a constant of the motion, and helicity depends on the rest frame.

Left-handed fermions are the ones that participate in the weak interaction. If the neutrino has mass, then it also has a right-handed component (same particle, not a "mirror image" particle). The right-handed component has no weak or EM interaction, and hence is referred to as "sterile".

It's better to talk about Dirac and Majorana masses, because a fermion can have both at the same time. Dirac mass couples left- and right-handed components, $m \overline{\nu_L} \nu_R$ while Majorana mass couples to the conjugate: $M \overline{{\nu_R}^c} \nu_R$.

See the beginning of this paper, which I quote a few things from. The neutrino flavor states are related to the neutrino mass eigenstates by a unitary matrix called the PMNS matrix. This matricx is parametrized by three angles θ12, θ13, θ23 and one phase δ. There are no other θ's. Oscillations are determined by the θ's. CP violation is not determined by the θ's, rather by the phase angle δ.

Last edited: Dec 1, 2013
5. Dec 1, 2013

### RGevo

Hello, on my phone as per usual so my answers will be short.

For the standard model, the left handed leptons sit in doublet. This is to do with the gauge symmetries of the standard model. If the standard model was different, the particle content and it's behaviour would be different.

The mixing angles are how flavour and mass basis are not aligned. The among of alignment is not predicted by the Standard model. For 3 generations, this alignment can be found mathematically written in terms of 3 mixing angles between the generations. So 13 = 31.

Fermion masses are Dirac in the sm, the marriage of left and right handed fermions. If neutrinos have mass, where is the right handed neutrino coming from?