# I Neutrino Mass, Baryogenesis, Dark Matter (Beyond the SM)

1. Mar 22, 2017

### Trixie Mattel

Hello,

So I am aware that neutrino masses, Baryogengesis/Baryon Asymmetry, and Dark matter cannot be explained by the standard model.

However each can be explained by right handed neutrinos.

I know that right handed neutrinos show up in many extensions to the standard model, e.g. vMSM (where the RH neutrinos are singlets) and Left-Right Extensions of the standard model (where the RH neutrinos form doublets).

I was wondering if the right handed neutrinos in both of those models explain the three problems listed above in the same way?

Thank you

2. Mar 28, 2017

### ohwilleke

Right handed neutrinos don't necessarily explain neutrino masses. And, the Standard Model still has no explanation for why the Higgs boson Yukawas are what they are, so particle masses in the Standard Model remain an issue even if one has a partial answer. In particular, I am highly skeptical of the ever popular see-saw models to explain neutrino masses which seem baroque and ill motivated.

Right handed neutrinos are not a particularly attractive solution to Baryogenesis or Baryon Asymmetry either. Even if neutrinos are Majorana in nature, neutrinoless double beta decay is far too rare to explain lepton asymmetry (which may or may not exist), let alone the matter-antimatter imbalance of baryons and charged leptons.

A sterile "neutrino" does remain an attractive warm dark matter candidate if it is the right mass (ca. 2-8 keV). But, there is no reason that a dark matter particle with sterile neutrino properties would actually have to be a right handed neutrino.

Honestly, I don't think that any these problems have really satisfactory answers.

3. Mar 29, 2017

### Orodruin

Staff Emeritus
I used to think like this, then I studied neutrino physics and QFT. You need to understand why the seesaw models are popular. You might say that you are fine with neutrinos getting masses in the same way as quarks. To do that you need right-handed neutrinos. As soon as you include those in your theory, your lagrangian allows the inclusion of a Majorana mass term for them. Mixing with left-handed neutrinos after EW symmetry breaking leads directly to left-handed neutrinos being Majorana particles.

I think you have a serious misconception here. Leptogenesis does not happen via neutrinoless double beta decay. A priori, it is not even related to the same CP-violating parameters.

Uhmmm, there is no practical difference between a right-handed neutrino and a sterile neutrino. It is just a matter of what you choose to call it.

4. Apr 3, 2017

### ohwilleke

I'm honestly pretty skeptical about right handed neutrinos as well, and I'm even more skeptical of right handed neutrinos with masses different than left handed neutrinos. I don't claim to have the solution to neutrino mass, although weak force self-energy seems like a pretty plausible source of the mass of the lightest neutrino mass eigenstate as it would have the right order of magnitude relative to the electron. I also wouldn't be surprised if neutrino oscillation and the associated PMNS matrix was discovered to have a mechanism involving a carrier boson of some sort (perhaps a massless neutral scalar boson) that mediated its interactions in a manner analogous to the way that the W boson mediates the flavor changing transitions of quarks via the CKM matrix, and if that interaction played a part in the mass generation mechanism for neutrinos, perhaps smearing the total mass of the neutrino sector between the three mass eigenstates. Or maybe mass smears off from the charged leptons to the neutrinos of the same generation in a manner that is highly suppressed in a non-linear way. The good news is that we are getting much closer to filling in the last Standard Model constants related to neutrinos which should help solve the puzzle.

The connection between neutrinoless double beta decay and baryongenesis or baryon asymmetry is that both require non-conversation of baryon number and lepton number. No phenomena of any kind that do that have been observed for example in neutrinoless double beta decay, proton decay, flavor changing neutral currents, all up to intense exclusions. If you want to come up with a phenomena that can explain massive amounts of baryon number non-conservation and lepton number non-conservation in the universe it would help to have some kind of observable process that does that, and there isn't one.

The difference between a dark matter particle with sterile neutrino properties and a true right handed neutrino is that the right handed neutrino would oscillate with other neutrinos and come in three generations, while a dark matter particle with sterile neutrino properties could be a singlet that does not oscillate with or otherwise interact with other neutrinos.

[Post edited by moderator]

Last edited by a moderator: Apr 4, 2017
5. Apr 4, 2017

### Orodruin

Staff Emeritus
You do realise that this leaves you only with the possibility of having Majorana masses and that essentially means lepton number violation. Weak interactions do not violate lepton number (at the perturbative level).

Including right-handed neutrinos into your model there is nothing preventing them from having a Majorana mass term and that automatically means different masses. However, the L and R would not be the mass eigenstates - it is just that the heavy eigenstates would be mostly R in the usual seesaw.

First of all, the Standard Model already has B+L violation built in through perturbative effects. Second, the vanilla leptogenesis models do not depend on the same CP-violating parameters as neutrinoless double beta decay.

Also, the PMNS is the exact lepton analogue of the CKM. It tells you the mismatch of the mass and interaction eigenstates of the W.

6. Apr 4, 2017

### ohwilleke

I don't agree. I agree that this leaves you with mass that can't arise from interaction with a Higgs field like the other Dirac fermions do. But, I don't agree that Dirac mass arising from a Higgs field interaction and Majorana masses are the only theoretically imaginable means by which mass can arise, even though it is often posed as an either/or possibility. There are more than a dozen well developed theoretically possible mass generation mechanisms. The SM Higgs mechanism is the one that works for all of the fundamental particles in the Standard Model but the neutrinos. But, there is more than one possible alternatives to it that could be applied to the neutrino case.

Mass could also arise by some other unspecified mechanism. This is the kind of thing that theoretical physicists get paid the big bucks to come up with. Until Higgs and company came along, nobody had imagined that fundamental particles were fundamentally massless and acquired rest mass only through interactions with a scalar field. I'm sure that someone could come up with another alternative, although I don't intend the examples that I myself have given to be anything more than place fillers for "some" unspecified alternative. Honestly, there are lots of mysteries in physics surrounding mass in general and neutrino mass in particular. I am skeptical of the proposition that we have considered every possible solution to the problem even though the question is often presented that way.

In any model in which neutrinos do not acquire mass via a Higgs field Yukawa, you have to do something different than the other fundamental Standard Model particles in any case. It is not as if you would lose theoretical consistency in the process.

There is no other instance in the Standard Model when particles that differ in no respect other than parity have different masses. Indeed, I can't even think of any composite particle for which this is the case. And, there is no terribly compelling reason that neutrinos should be different in this respect.

B and L Violation Are Theoretically Possible In The SM, But Doesn't Necessarily Actually Happen

The SM has the sphaleron a theoretically possible process that violates B and L number individually (while preserving B-L). But, this phenomena has never been observed even though it is theoretically possible. And, even if it does exist it doesn't generate enough B and L violation to lead to observed matter-antimatter asymmetry from a starting point of B=0 and L=0 at the Big Bang. And, I would not be at all surprised if it was discovered that there was some accidental symmetry or subtle relationship not yet recognized that actually makes this phenomena impossible.

By analogy, General Relativity recognizes the theoretical possibility that a black hole could have a mass of less than three times the mass of the Sun (these are sometimes called "primordial black holes"). But, no one has ever observed such a black hole, and no one has identified any process after the Big Bang era in which one could form. Even hypothetical processes that could generate primordial black holes in the Big Bang era are very sketchy and have not been worked out in convincing detail (which would require renormalizing all of the laws of physics to extremely high energies beyond the ordinary domain of applicability of these physical laws in the UV direction that has been well confirmed by experiment).

It is entirely possible that no such process ever existed in the Big Bang era either and that black holes with a mass of less than three times the mass of the Sun do not exist now, never have existed, and can't exist at any point in the future, even though they would not violate any of the laws of physics if they did exist. The same thing might be true of sphalerons.

B and L Violation Aren't Theoretically Necessary Or Compelled By Empirical Evidence

Also, there is no a priori reason that aggregate baryon number or aggregate lepton number needs to be zero immediately following the Big Bang. This would be neat and beautiful if it was the case, but ultimately, one can have a perfectly consistent set of laws of fundamental physics in which these numbers at t=0 are not equal to zero, in much the same way that the other fundamental constants of the Standard Model are non-zero at that point. Nobody insists that the fine coupling constant be zero at t=0.

This assumption is not a provable law of Nature and Nature is not obligated to tell us "why" it chose to set the laws of physics and physical constants of Nature at the value that it did.

If theoretical physics has had once vice over the last thirty years, it has been its insistence that "naturalness" is a worthwhile principle from which to generate hypotheses about the laws of Nature, a conceit that has wasted an immense amount of time and resources from very smart people who should know better.

I'm not saying that theories that could get you to aggregate B=0, L=0 for the universe at t=0 aren't well motivated theoretically, if by beauty if nothing else. I'd love to see someone come up with a scientifically demonstrable and provable process by which this could happen.

But, if you don't have to make an assumption to be theoretically consistent, and you also don't have to make that assumption to be consistent with the experimental and observational evidence, you shouldn't insist that only theories that include that assumption are considered. Many of the big breakthrough of modern physics have involved abandoning assumptions that seem obvious or beautiful or natural, but aren't necessary to be theoretically consistent and aren't necessary to be consistent with empirical evidence.

Nothing fundamental in physics breaks down if we abandon the assumption that aggregate B=0, L=0 for the universe at t=0, so it is not absolutely necessary to have either B number violation or L number violation in a fundamental theory of everything (TOE) or a grand unified theory (GUT).

No it isn't.

In the CKM matrix you are looking at transitions from a set containing three fermions via the W+ boson to a disjoint set containing three different fermions, and from the second set via the W- boson to the first set. In short, it involves the interactions of seven particles (eight if W+ and W- count as different particles) in a particular way.

In the PMNS matrix you are looking at transitions from a set containing three fermions without an intermediary to a disjoint set of three masses. In short it involve the interaction of three different particles that can each be in one of three different states. I have not seen any description of the PMNS matrix that suggests that neutrino oscillation is mediated by a boson of any kind (e.g. the W boson). And, unlike the CKM matrix which governs flavor transition of all six quarks, the PMNS matrix only applies to three of the six leptons.

And, of course, if the PMNS matrix were coding a W boson mediated transition, it would require pairs of W boson interactions, because neutrino interactions are charge neutral, but W boson interactions change charge.

They are similar, and they are analogous, but they aren't exactly analogous.

You can have W boson interactions causing, for example, a tau to decay to a tau neutrino and a W- boson which in turn decays to a muon and a muon anti-neutrino, but those interactions are not included in the PMNS matrix which applies only to the neutrino sector. You don't need the equivalent of the CKM matrix or PMNS matrix for charged lepton flavor changes via the W boson because the charged leptons are democratic.

Similarly, you can have in the Standard Model, a regular neutrino that emits a W+ boson giving rise to a charged lepton of the same type, a charged anti-lepton of the same or another type, and a neutrino of the same type as the charged anti-lepton.

An exactly analog to the CKM matrix would be a matrix demonstrating the probability of W boson transitions from charged leptons of a particular type to charged leptons of another type together with a neutrino and visa versa. And, indeed, you can create a matrix that carries out this exact analogy. But, every entry in the matrix would be exactly the positive square root of 1/3 (i.e. 0.5773502 . . .), which would be trivial. Who knows? If the hints of charged lepton non-universality in a few outlier LHC results that have been observed lately turn out to be true, it may be necessary to develop a non-trivial exact analog to the CKM matrix.

But, I have seen nothing in the literature to indicate that the PMNS matrix is coding virtual pairs of these W boson interactions. Neutrino oscillation is not mediated by W bosons or in the Standard Model by any kind of particle.

Last edited: Apr 4, 2017
7. Apr 5, 2017

### Orodruin

Staff Emeritus
Well that makes you wrong, I am sorry.

First of all, you have been here long enough to know that Wikipedia is not an acceptable reference here. Second, you are equating Dirac mass to "mass generated by the Higgs mechanism". This is just wrong.

There is no other instance of a SM singlet in the SM, the right-handed neutrino would be unique in that respect. In the same way, since you do not like right-handed neutrinos, I can argue that there are no other cases in the SM where there is no right-handed fermion corresponding to a left-handed fermion field. This is a non-argument.

Yes there is. Right-handed neutrinos are different. See above. If you understood QFT you would understand why people put in all of the terms allowed by symmetry in their Lagrangians, the right-handed Majorana mass is such a term.

The sphalerons are a prediction of the SM, you cannot get rid of them and still call it the SM. Yes, you need an additional mechanism to generate B-L, but your statement was that you needed a mechanism to generate B and L. You are moving the goal posts.
Bad analogy. GR allows those black holes to exist, the SM predicts that sphalerons to occur at high enough temperatures.

You are seriously equating the fine coupling constant with a quantum number such as B or L? Is it possible to start out with non-zero B and L, certainly. However, if you believe in inflationary models this would have to come from the reheating process and thus you could just as well ask the question why the reheating process generates a B or L.

Yes it is and it should worry you if you think otherwise because it means you have serious flaws in your understanding of the Standard Model. The PMNS is the exact analogue of the CKM in the lepton sector.

This is just wrong. The PMNS matrix governs the charged current interactions (i.e., it gives the coupling constants for the different W vertices) between the charged leptons with definite masses and the neutral leptons (neutrinos) with definite masses. Just like the CKM governs the charged current interactions between up-type quarks of definite masses with down-type quarks of definite masses. You need to review your knowledge on the PMNS matrix.

You write "of course" but again display the same misunderstanding. The single W interactions between the charged leptons and the neutrinos is what the PMNS matrix describes. Neutrino neutral current interactions (via the Z) are flavour diagonal in the SM and have nothing to do with oscillations.

Again wrong and I find it hilarious that you are trying to explain the PMNS matrix to me. You are aware that I do neutrino oscillation physics for a living, yes? Even if you would not take me seriously on any other point, you should take me seriously on this one.

This is because if you are looking at the flavour states you are doing it wrong. The flavour states are not the neutrino mass eigenstates which is what would correspond to how we look at W interactions in the quark sector. The difference between the quark and lepton sectors is that the neutrino mass eigenstates have very similar masses and this allows them to stay coherent for much longer and display an interference pattern. This is what makes tau decays produce tau neutrinos and not three different types of decay (i.e., decays to the different mass eigenstates) and also what leads to neutrino oscillations.

Again, this is not the lepton sector analogue of the quark interactions with the CKM. The flavour neutrino states are not the physical states, the mass eigenstates are.

Which is exactly what the PMNS is. The PMNS describes the probability of a charged lepton transitioning by way of a W to the different neutrino mass eigenstates. Just like the CKM describes the probability of an up-type quark transitioning by way of a W to the different down-type mass eigenstates.

Neutrino oscillations are not mediated. They are an interference phenomenon caused by the neutrino mass eigenstates created in lepton charged current interactions acquiring different phases due to their different masses. The observation of neutrino oscillations need the charged current interactions with the W exchange creating a charged lepton. This is where the PMNS comes in.

I suggest that you read Evgeny Akhmedov's lecture notes on neutrino physics https://arxiv.org/pdf/hep-ph/0001264.pdf - section 7 describes exactly where the PMNS matrix arises and you should see that it is exactly equivalent to how the CKM arises in the quark sector.

8. Apr 5, 2017

### nikkkom

Orodruin, please help me here: is it correct to say that by a historical accident, in particle physics *mass eigenstates* of quarks are called "u,c,t,d,s,b quark", and "e,mu,tau lepton" are *mass eigenstates* too, but what we call "v(e),v(mu),v(tau) neutrino" _are not_ mass eigenstates: what we call "electron neutrino" is exactly the mix of *mass eigenstates* of neutrinos which results from electron emitting a W-?

If we would want to use the same system for quarks, then d,s,b quarks would stay the same, but up-type quarks would need to be relabeled: for example, the "new u quark" would be the mix of mass eigenstates of up-quarks which results from d-quark emitting a W-. (and thus, the "new u quark" would not have a definite mass).

Do I get it right?

9. Apr 5, 2017

### Orodruin

Staff Emeritus
Yes, this is correct. We define the charged leptons $e,\mu,\tau$ as the charged lepton mass eigenstates (ordered from lowest to highest mass) and we define the neutrino flavour fields as the fields that couple to those charged leptons under W-exchange. These flavour states are indeed not the mass eigenstates, those we call $\nu_1, \nu_2, \nu_3$.

In essence yes, but it is usually introduced the other way around, i.e., defining the up-type quarks u, c, t as the mass eigenstates. The down-type quarks interacting with those up-type mass eigenstates are sometimes labelled d', s', b' and are just approximately equal to d, s, b with the CKM matrix parametrising how "off" they are. In the lepton sector, the mixing angles are large and it does not even make sense to say that the flavour states are approximately the mass eigenstates.

Note that if you did this for the quarks, your mass eigenstates would quickly decohere due to the large mass splittings. This is the reason to use the mass eigenstates in the quark sector. In the lepton sector on the other hand, the neutrino mass eigenstates stay coherent for much longer, giving rise to neutrino oscillations. I am not sure I would call it "historical accident" as much as what is pragmatic in either case. The historical part would be that before neutrinos were known to be massive, you could just pick any basis in neutrino flavour space - it would not matter and the one basis that would be singled out by any physics would be the flavour basis.

In essence, yes.

10. May 30, 2017