Standard Model Neutrinos Considered

Background: Standard Model Dirac Neutrinos

In the Standard Model there is one neutrino for each of the three charged leptons called, not particularly creatively, the electron neutrino, the muon neutrino and the tau neutrino. All three neutrinos have a zero electromagnetic charge and an intrinsic spin of 1/2 which means that it is a fermion rather than a boson. Neutrinos an extremely low mass, perhaps a a billion times lighter than an electron - the exact number isn't known. The electron neutrino and muon neutrino quite close in mass and the tau neutrino is a couple of orders of magnitude heavier.

They do interact via the weak force of the Standard Model, however. All of the other fermions of the Standard Model come in four varieties, left and right handed versions of the particle itself, and left and right handed version of its opposite charge, identical mass antiparticle, of which only the left handed versions interact with the weak force. Standard Model neutrinos come in only two varieties: left handed particles and right handed antiparticles, both of which interact with the weak force.

Some people hypothesize that neutrinos get their mass in a manner different from other Standard Model fermions, a Majorana mass, but I'm going to assume that they get their mass the same way that all other fundamental Standard Model particles do, a kind of mass that is called a Dirac mass.

I make that assumption because Majorana neutrinos are neutrinos in which the particle is identical to its antiparticle, yet the very reason that neutrinos were predicted at all (well, one of the reasons anyway) is that the distinction between neutrinos and antineutrinos is necessary to conserve what is known as "lepton number" in weak force interactions like beta decay. Ordinary leptons like electrons and electron neutrinos have a lepton number of 1. Antiparticles of leptons like anti-electrons (aka positrons) and electron antineutrinos have a lepton number of -1. All other particles have a lepton number of zero.

In the Standard Model, if a W- boson, which has a lepton number of zero decays by its most common route (seen in beta decay), it produces an electron and an electron antineutrino, never an electron and an ordinary electron neutrino. The W- boson has a lepton number of zero, and so do the sum of the lepton numbers of its decay products, the electron (+1) and the electron antineutrino (-1). The weak force does not treat the neutrino and antineutrino as identical, even though electromagnetism, the strong force and gravity do treat them as identical. Instead, the weak force treats neutrinos and antineutrinos as opposites for purposes of lepton number conservation, which is a perfectly observed symmetry in the Standard Model and has never been observed to be violated in any experiment ever.

Another rule of the Standard Model is that when a fermion and its antifermion run into each other that they annihilate into pure energy having exactly the same mass-energy (pursuant to E=mc^2) as the inputs. It isn't obvious that this rule makes sense in the case of Majorana neutrinos. (When the W+ boson and the W- boson which we think of as antiparticles of each other run into each other they can produce a Z boson instead of a photon, so the rule doesn't apply quite the same way for bosons of instrinsic spin 1 as it does for fermions of intrinsic spin 1/2.)

Thus, when an electron neutrino collides with an electron antineutrino, the result will typically be a photon with energy equal to the combined mass-energy of the colliding neutrino and antineutrino. Conversely, any photon with enough energy to provide rest mass for an electron neutrino and an electron antineutrino pair can spontaneously turn into such a pair (if I understand the theory correctly).

Neutrinos oscillate from one flavor (electron, muon or tau) to the another, via W boson interactions, with probabilities that are still being empirically determined. But, electron and muon neutrinos which are closer to each other in mass, oscillate into each other much more readily than either of them do with tau neutrinos.

Neutrinos also interact with Z bosons, the so called neutral currents, which I discuss further below.

Meet Z bosons

So far we have been "on the reservation" reviewing settled Standard Model physics. This section is a bit more speculative. While I don't propose new particles or dimensions or forces or coupling constants, I do make a supposition about the sign of the weak force created between neutrinos and/or antineutrinos exchanging Z bosons which is neither definitively established, nor definitively ruled out by experiment. This is where a little bit of conjecture steps in.

Generally speaking, in many ways, Z bosons behave more like heavy photons than they do like W bosons. A fermion can emit a Z boson without changing the type of particle that it is, and can also absorb a Z boson - events that happen with equal probabilities. Z bosons can decay to any set of energetically permitted particles that are electromagnetic charge neutral like the Z boson, have a net zero lepton number and a net zero B number (equal to the number of quarks minus the number of antiquarks) and the relative probabilities of each energeticallly permitted outcome are fixed.

In the case of charged fermions, when a Z boson is exchanged between two fermions of like charge it gives rise to a repulsive force, just like electromagnetism, while an exchange of Z bosons between oppositely charged fermions attracts.

Z bosons interact with neutrinos too, but Z bosons operate at such short ranges for such short time spans, and neutrinos and antineutrinos are so hard to detect (usually they are inferred from missing energy in a particle accelerator), that the repulsive or attractive nature of the force created when neutrinos exchange Z bosons hasn't been experimentally measured and depends to some extent on whether neutrinos are Majorana or Dirac fermions.

If neutrinos are Majorana fermions, then neutrinos and antineutrinos are identical and thus presumably have like charge and are repulsed from each other by Z boson exchange. But, if neutrinos are Dirac fermions, like all other Standard Model particles are, then it isn't unreasonable to expect that exchanges of Z bosons between two ordinary neutrinos, or between two antineutrinos are repulsive, while exchanges of Z bosons between an ordinary neutrino and an antineutrino are attractive.

Now, as I mentioned before, if our neutrino and antineutrino brought together by Z boson exchange are of the same type (e.g. an electron neutrino and an electron antineutrino), then we know how this is going to end. The neutrino and antineutrino annihilate and we get a photon which just coincidentally happens to have something very close to the same wavelength as the observed cosmic background radiation.

Composite Two Neutrino Pairs Linked By Z Bosons?

But, since neutrinos oscillate, unlike other kinds of fermions, where the "first generation" version is the only stable variety and second or third generation versions decay to lighter fermions in a matter of fractions of a second by emitting W bosons (they can go the other way, but it takes an injection of energy to make it happen), neutrinos of the first and second kind routinely oscillate back and forth between each other with a fairly high probability (this is called bimaximal mixing), and every now and then one will flip all the way up from a first or second generation version to a third generation version before oscillating back again (with this variation we have tribimaximal mixing).

So, there is a pretty good chance that an attracted neutrino and antineutrino could be an electron neutrino and a muon antineutrino, or a muon neutrino and an electron antineutrino, and there is a non-negligable chance that they could be an electron neutrino and tau antineutrino, a tau neutrino and an electron antineutrino, a muon neutrino and a tau antineutrino, or a muon antineutrino and a tau neutrino.

Like all neutral particles, these neutrino and antineutrino pairs will oscillate. But, there is a good chance that most of the oscillations will happen on one hand between pairs with an electron neutrino and a muon antineutrino and pairs with a muon neutrino and an electron antineutrino, which will have the same mass and be almost indistinguishable from each other to an observer, or on the other hand, one of the kinds of pairs with a tau neutrino or antitau neutrino and another kind of counterpart. The tau types will also oscillate back and forth, mostly between different tau types, but the tau-electron pairs and tau-muon pairs won't be identical in mass, although they will be so similar it will be very hard to distinguish them.

In this scenario, the two neutrino pairs, like the constituents of the composite particle will have no electromagnetic charge and no strong force color charge. They should have a cross-section of interation on the same order of magnitude, or within one order of magnitude or so (given the effective range of the weak force which is ca. 10^-24 cm, plus the cross section of each component neutrino), as a neutrino. They should still interact with the weak force. Thus, these neutrino pairs would be very difficult to distinguish from neutrinos, except on the basis of their mass, and the pairs that include tau neutrinos would be even harder to distinguish from each other.

Are Neutrino Pairs Rather Than Sterile Neutrinos What Cause Neutrino Detection Experiments To See More Than Three Generations Of Neutrinos?

This could explain the neutrino physics results that have seen four or five generations of neutrinos, a result attributed by most physics observers not simply chalking the result up to experimental error, to a new class of right handed sterile neutrinos. But, if there are three composite neutrino pair mass eigenstates (since anti-particle equivalents have the same mass) and one of the mass eigenstates (no tau neutrino pairs) is much more common and lighter, while the other two of the mass eigenstates (tau neutrino pairs) are much less common and almost indistinguishable on the basis of mass, one could expect some results to see four mass eigenstates of neutrinos, some results to also see a rarer fifth mass eigenstate, and none to see the true six mass eigenstates, even though there actually are six, because their experimental equipment isn't sufficiently precise to distinguish two of them.

Indeed, it is hard to come up with any other model that doesn't require a new fundamental particle and it otherwise consistent with the Standard Model (given only some assumptions that have not been experimentally tested one way or the other about how the sign assumptions that apply when neutrinos and antineutrinos that exchange Z bosons).

Also, another virtue of a situation when what appear to be more than the three expected neutrino mass eigenstates are composite, is that it explains why precision electroweak measurements strongly predict extactly three neutrinos will masses of under 45 GeV (half the Z boson mass). A core element in W and Z boson decay (and perhaps creation of matter-antimatter pairs from high energy photons that turn into matter- I'm less clear on that point) is that they are democratic (the idea is also called "universality"): each energetically permitted decay option has exactly the same basic probability (with quarks counting three times as much as leptons since they come in three varieties). More fundamental neutrinos would open up more options unless they were "sterile" (i.e. not weak force interacting).

Could Neutrino Pairs Bound By Z Bosons Be Dark Matter?

How heavy will these pairs be? Probably quite a bit heavier. When quarks are bound by gluons, the gluon exchange adds almost all of the mass to protons and neutrons (and other hadrons). It isn't unreasonable to think that Z boson exchange between paired neutrinos might also add a great deal of mass arising from binding force energy to the pair as well.

If that mass is in the keV range for the pair, which a similar but more exotic proposal in the physics literature suggests is about right for composite neutrino particles interacting with a force of the electroweak scale, then these paired neutrinos have just the right mass to give rise to warm dark matter, the dark matter proposal that is the best fit to current empirical data from astronomy.

Also, since the keV mass range proposed for warm dark matter is really a proxy for an expected dark matter particle speed relative to the speed of light, another mechanisms that could influence particle speed (like kinetic energy dumps due to Z boson emissions) might provide a correct fit for warm dark matter models even if the mass is not quite right.

Now, of course, even if composite neutrino pairs don't account for most of dark matter, they could still account for the apparent extra neutrino types observed in neutrino detection experiments, or for part of the dark matter balance in the universe.

I did consider the possibility of larger composite groupings of neutrinos, and an atomic nucleus-like arrangement seems impossible, since anti-matter anihilation crops up swiftly in more complex combinations. But, the possibility of longer filament-like arangements of alternating neutrinos and anti-neutrinos bound by Z boson interactions was not obviously ruled out.

Neutrino Condensates As A Contributor To Dark Energy?

Now, because of CP violations in the universe, the amount of matter and antimatter isn't the same. Mostly, the universe is matter dominated.

As a result, There are far more natural processes that produce antineutrinos than ordinary neutrinos and if annihilation and dark matter Z boson mediated composites pair off all the matter with the antimatter in the neutrino sector, we will be left with an excess of antineutrinos that repel each other when they interact via Z bosons.

What does that give rise to? Some physics papers suggest that a sea of like charge neutrinos mediated by the repulsive force of Z bosons will give you a universe-wide, more or less evenly spaced neutrino condensate that replicates the observed properties of dark energy, right down to its otherwise mysteriously small magnitude.

So, could most of the matter and energy in the universe really be made out of neutrinos? Maybe so. While decay process that give rise to new particles (baryonesis and leptogenesis) are democratic to the extent that they are energetically permitted, it takes a lot less energy to produce neutrinos from decay, than it does to produce heavier fermions. So, it stands to reason that there will be more times when neutrinos and antineutrinos can be produced than heavier fermions and that their absolute numbers will be greater and there isn't any particularly strong theoretical bound on the number of excess neutrinos created (global charge neutrality greatly limits the overall number of charged leptons relative to quarks).

This analysis also has some interesting things to say about hidden decay channels in decays involving neutrino products, but that will have to wait for another post. In a nutshell, it is much harder to see extra neutrinos in reactions that give rise to dark matter than it is to see predictions of non-standard model non-lepton number conserving theories that predict things like the double neutrinoless beta decay (never observed) that Majorana neutrinos would imply.

Composite Two Neutrino Pairs As An Explanation For Lepton Generation Number Violations?

Usually, but not always, weak force decays preserve not just lepton number, but lepton generation number.

In other words, for every ordinary electron generation lepton created, an electron generation anti-lepton is created. Similarly, if a muon generation lepton is created, a muon anti-lepton is created. And, if a tau generation lepton is craeted, a tau anti-lepton is created.

Thus, in beta decay, one typically sees an electron and an electron-anti-neutrino created.

But, sometimes, lepton generation number conservation doesn't seem to be observed (although charge is always still conserved and lepton number is always still conserved).

This could simply be because sometimes a W will decay into a muon and an electron-anti-neutrino, for example. But, it could also be caused another way.

Sometimes W decay produces more than two leptons. For example, instead of on electron and on electron-anti-neutrino, you might see an electron, an ordinary electron neutrino and two electron-anti-neutrinos.

Imagine that instead of that, a W- boson decay produces an electron, an electron-anti-neutrino, a muon-neutrino and a muon anti-neutrino. Fine. It conserves lepton number, lepton generation number, and charge. But, suppose that the electron-anti-neutrino and the muon neutrino bond via Z bosons to form a composite two neutrino particle, and that the composite two neutrino particle is not detected.

Then, it would look as it the W- boson decay produced an electron and a muon anti-neutrino and the linear momentum of the departing muon anti-neutrino would be overestimated. This would seem to violate lepton generation conservation even though it actually didn't.

The fact that there is a path that looks like lepton generation number violation that isn't actually lepton generation number violation, doesn't imply that observations of lepton generation number violation are actually wrong. But, it does suggest that the experimental findings in support of lepton generation number violation should be reviewed to see if that could be the cause of the observations.

Conclusion

I'm a lawyer who studied physics and the math that you need to do physics a couple of decades ago. And, I'm doing this in my spare time without colleagues to bounce ideas off. The conjectures in this post aren't peeer reviewed science, and might not be correct in some or all respects. For the most part, I have also made this arguments at a very general level, whichout actually invoking the relevant equations that make the points argued true. Most importantly, I haven't even done a good back of napkin estimate of my own of the potential binding energy contribution to the mass of a neutrino-antineutrino pair bound by attractive Z boson mediated weak forces, or done any sort of statistical mechanics style simulation to see what these interactions would look like on a larger scale with realistic parameters.

But, given the extraordinary and frankly unexepcted by most physicist confirmations of the Standard Model and strict exclusions of non-Standard Model physics that we have seen at LHC and elsewhere in the last few years, it seems imperative to look for solutions to the outstanding open questions of physics within the Standard Model rather than in extensions of it.

Composite neutrino pairs, and more generally, Z boson interactions between neutrinos, seems like a natural place to look for "new physics" that isn't actually new, just unfamiliar. A this first exploratory peep at what can be achieved to deal with unsolved questions of physics using these kinds of interactions, even if only some of the hypotheses above are correct, rather than all of them, seems fruitful and worthy of further investigation.

POST UPDATED October 17, 2011.