Why do we write that there are no right-handed neutrinos?

[Jason Wright]

I'm puzzled why, now that we know that neutrinos have mass, we still read that there are only left-handed neutrinos, as far as we know.

I understand that right-handed neutrinos do not interact by the weak force, so we would not detect them. My question is why we read that they might not / probably do not even exist.

With electrons, their mass couples their left- and right-handed chiral states, so they oscillate between the two. If they are Dirac particles, shouldn't neutrinos do the same?

Is it observationally permitted that the Universe is filled with right-handed neutrinos (either primordial or having oscillated from the left-handed chirality), or do are there constraints from, for instance, cosmic neutrino detectors or cosmology that rule this out?

 

[Orodruin]

I understand that right-handed neutrinos do not interact by the weak force, so we would not detect them. My question is why we read that they might not / probably do not even exist.

Where did you read this? It is difficult to answer your questions if we do not know what you have read.

The bottom line is, we don't know if they exist or not. We currently have no experimental evidence of their existence.

With electrons, their mass couples their left- and right-handed chiral states, so they oscillate between the two. If they are Dirac particles, shouldn't neutrinos do the same?

We currently do not know the origin of neutrino masses. They could be Dirac particles and get their mass from the Higgs vev and the corresponding Yukawa couplings just like the charged fermions, but we also have no evidence that this is the case either. We simply do not know and there are may different models for neutrino masses out there.

I would say that the main reason why high-energy physicists dislike Dirac neutrinos with just the addition of right-handed neutrinos and neutrino Yukawas to the Standard Model is that those Yukawas would have to be extremely small. Many already consider it a problem that the electron Yukawa is so much smaller than the top Yukawa and the neutrino Yukawas would be orders and orders of magnitude smaller still.

In addition, as soon as you introduce right-handed neutrinos (or, equivalently, Standard Model-singlet fermions) into your theory, something happens that does not happen for charged fermions. Not only is the Yukawa coupling between left- and right-handed neutrinos allowed, but since the right-handed neutrino is a Standard Model singlet a Majorana mass term for it would not be forbidden by gauge invariance and it becomes a free parameter with mass dimension in the Lagrangian for which you have no real handle on what scale it should be in. If you let the Yukawas have a size of order one and set a very high scale for the Majorana mass of the right-handed neutrinos (ca 10¹⁵ GeV), then you will naturally get very small Majorana masses for the left-handed neutrinos as a result. This is the very popular seesaw mechanism (more precisely, a type-I seesaw), which is one of the more widely considered models for describing the lightness of active neutrinos.

However, there are also other ways of introducing neutrino masses that do not require the introduction of right-handed neutrinos, for example the type-II seesaw mechanism.

Is it observationally permitted that the Universe is filled with right-handed neutrinos (either primordial or having oscillated from the left-handed chirality), or do are there constraints from, for instance, cosmic neutrino detectors or cosmology that rule this out?

There are some models where right-handed neutrinos are dark matter candidates (or rather, the neutrinos that are dominantly right-handed, there would be a small mixing angle to the light neutrinos). You typically cannot oscillate from light neutrinos to heavy right-handed neutrinos in most situations (because kinematics would be well determined enough to tell whether you have a heavy neutrino or a light one). It is difficult to say more without a more specific model in mind.

 

[Jason Wright]

Where did you read this? It is difficult to answer your questions if we do not know what you have read.

An example:
Quantum Field Theory for the Gifted Amateur, Lancaster & Blundell, p. 330, sidenote 11: "Neutrinos only exist as left-handed particles. They are (at least approximately) massless…"

The bottom line is, we don't know if they exist or not. We currently have no experimental evidence of their existence.

I understand this; my question might have been better phrased as: given that we know neutrinos have mass, how could right-handed neutrinos not exist? I think you do answer this below (type-II seesaw as an example), which I am grateful for. Your answer also helps me appreciate that the statement in Lancaster & Blundell is probably just a didactic oversimplification that I should not take to be strictly true but "true enough" in the context of the lesson in that chapter.

We currently do not know the origin of neutrino masses. They could be Dirac particles and get their mass from the Higgs vev and the corresponding Yukawa couplings just like the charged fermions, but we also have no evidence that this is the case either. We simply do not know and there are may different models for neutrino masses out there.

I would say that the main reason why high-energy physicists dislike Dirac neutrinos with just the addition of right-handed neutrinos and neutrino Yukawas to the Standard Model is that those Yukawas would have to be extremely small. Many already consider it a problem that the electron Yukawa is so much smaller than the top Yukawa and the neutrino Yukawas would be orders and orders of magnitude smaller still.

In addition, as soon as you introduce right-handed neutrinos (or, equivalently, Standard Model-singlet fermions) into your theory, something happens that does not happen for charged fermions. Not only is the Yukawa coupling between left- and right-handed neutrinos allowed, but since the right-handed neutrino is a Standard Model singlet a Majorana mass term for it would not be forbidden by gauge invariance and it becomes a free parameter with mass dimension in the Lagrangian for which you have no real handle on what scale it should be in. If you let the Yukawas have a size of order one and set a very high scale for the Majorana mass of the right-handed neutrinos (ca 10¹⁵ GeV), then you will naturally get very small Majorana masses for the left-handed neutrinos as a result. This is the very popular seesaw mechanism (more precisely, a type-I seesaw), which is one of the more widely considered models for describing the lightness of active neutrinos.

However, there are also other ways of introducing neutrino masses that do not require the introduction of right-handed neutrinos, for example the type-II seesaw mechanism.

I think this answers part of the question I had, which is that there are ways to explain neutrino masses that lack right-handed neutrinos

There are some models where right-handed neutrinos are dark matter candidates (or rather, the neutrinos that are dominantly right-handed, there would be a small mixing angle to the light neutrinos). You typically cannot oscillate from light neutrinos to heavy right-handed neutrinos in most situations (because kinematics would be well determined enough to tell whether you have a heavy neutrino or a light one). It is difficult to say more without a more specific model in mind.

Ah, this is helpful. I'll dive in more deeply to exactly why right-handed neutrinos would not be expected to have the same masses as left-handed ones (because unlike electrons, they lack charge, I gather?) and that should help me fully answer my question.

Thank you!

 

[Orodruin]

An example:
Quantum Field Theory for the Gifted Amateur, Lancaster & Blundell, p. 330, sidenote 11: "Neutrinos only exist as left-handed particles. They are (at least approximately) massless…"

I do not have access to this text. In general, I would expect any text that makes such a statement to be talking about the Standard Model, not about "reality". The Standard Model does not include right-handed neutrinos.

I'll dive in more deeply to exactly why right-handed neutrinos would not be expected to have the same masses as left-handed ones (because unlike electrons, they lack charge, I gather?) and that should help me fully answer my question.

The point is that you can have Dirac neutrinos if you introduce right-handed neutrinos. However, that also allows a Majorana mass for the right-handed neutrinos that break lepton number. In essence, a neutral Dirac fermion can be written as two Majorana fermions with the same mass. When you introduce the right-handed Majorana mass you break the symmetry between those two Majorana fermions and you are left with two Majorana fermions with different masses.

 

[Jason Wright]

Thanks.

I found this:

https://warwick.ac.uk/fac/sci/physi...neutrinolectures/lec_neutrinomass_writeup.pdf

which also helps a lot. They key I was missing is that popular stories about the "sterile" neutrino are often actually talking about right-handed neutrinos—I had not made the connection before. Understanding that, things make much more sense.

Thanks again for your help.

 

[Orodruin]

Right-handed neutrino, singlet fermion, sterile neutrino. I am not sure the proverb exists in English, but in my native tongue we say that a "beloved child has many names". Many times they refer to particular realisations (e.g., particular ranges for the mass parameters), but in essence they are all the same. A singlet Weyl fermion added to the Standard Model.

 

[Jason Wright]

Right-handed neutrino, singlet fermion, sterile neutrino. I am not sure the proverb exists in English, but in my native tongue we say that a "beloved child has many names". Many times they refer to particular realisations (e.g., particular ranges for the mass parameters), but in essence they are all the same. A singlet Weyl fermion added to the Standard Model.

Great! OK, last question for now: most of the treatments I see for this restrict the discussion to the electron neutrino. But there are 3 families of neutrino. Would the right-handed neutrino in most treatments of the problem be a right-handed electron neutrino, or a new, fourth type of neutrino altogether? This paper:

https://arxiv.org/pdf/1803.10661.pdf

refers to a "3+1" model, with one additional "sterile" neutrino state for the other 3 to mix into, suggesting that even though there are 3 left-handed neutrinos, we only think about there being one right-handed neutrino. Is that right? Or are they just assuming that only one of the 3 right-handed neutrinos is relevant to the physics, the other two having masses too large to matter?

 

[Orodruin]

Since it does not interact it does not have flavour in the same way. The flavoured neutrinos are defined by how they interact and a sterile neutrino by definition does not interact.

Also, this is one of the cases where it is customary to call it a ”sterile neutrino” rather than a ”right-handed” one because it is quite light. Even if they are technically the same with different mass regimes, ”right-handed” typically suggests pretty heavy additional singlet fermions.

You can introduce as many right-handed neutrinos as you want (but it has to be corroborated by experiments in the end!). The 3+1 is usually thought of to be a toy model of sorts and the phenomenology is not that different if you introduce more.

 

[Jason Wright]

Since it does not interact it does not have flavour in the same way. The flavoured neutrinos are defined by how they interact and a sterile neutrino by definition does not interact.

Also, this is one of the cases where it is customary to call it a ”sterile neutrino” rather than a ”right-handed” one because it is quite light. Even if they are technically the same with different mass regimes, ”right-handed” typically suggests pretty heavy additional singlet fermions.

You can introduce as many right-handed neutrinos as you want (but it has to be corroborated by experiments in the end!). The 3+1 is usually thought of to be a toy model of sorts and the phenomenology is not that different if you introduce more.

Ah! That makes sense!

Thanks for all of your help; this really helps me connect the language in the popular science articles to that in the papers they link to.