BLAM

This post is about BLAM - Baryon number, Lepton number, Antimatter and Matter (n.b. the punctuation convention in physics is to omit periods from acronyms, probably because physicists use them so often and it takes longer to type extra characters).

In the Standard Model, baryon number a.k.a. B (the number of quarks minus the number of anti-quarks divided by three) is conserved and lepton number a.k.a. (the number of leptons minus the number of anti-leptons) is separately conserved.

Thus, every interaction that creates a quark must also create an anti-quark, every interaction that destroys a quark must also destroy an anti-quark, every interaction that creates a lepton must create an anti-lepton, and every interaction that destroys a lepton must destroy an anti-lepton.

There is an exception to this rule in the Standard Model, called a sphaleron process, which conserves B-L, but not B and L separately.

A sphaleron (Greek: σφαλερός "slippery") is a static (time-independent) solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton numbers. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative. Geometrically, a sphaleron is simply a saddle point of the electroweak potential energy (in the infinite-dimensional field space), much like the saddle point of the surface z(x,y)=x2−y2 in three-dimensional analytic geometry. 

In the standard model, processes violating baryon number convert three baryons to three antileptons, and related processes. This violates conservation of baryon number and lepton number, but the difference B−L is conserved. In fact, a sphaleron may convert baryons to anti-leptons and anti-baryons to leptons, and hence a quark may be converted to 2 anti-quarks and an anti-lepton, and an anti-quark may be converted to 2 quarks and a lepton. A sphaleron is similar to the midpoint (τ=0) of the instanton, so it is non-perturbative. This means that under normal conditions sphalerons are unobservably rare. However, they would have been more common at the higher temperatures of the early universe.

The Standard Model also conserves electromagnetic charge.

At the scale of the universe, there are strong indications that the global electric charge of the universe is zero.

But, baryon number is not zero or anywhere close. The baryon number of the universe is slightly less than the combined total number of protons and neutrons in the universe, increased slightly by unstable baryons with mean lifetimes of less than a millionth of a second, and decreased slightly by the number of anti-baryons in the universe at any given moment. So, the baryon number of the universe is a bit more than 95% of the total mass of the universe measured in units of GeV/c^2 (often abbreviated to GeV based on the convention that in "natural units" c^2 is one and because physicists are just plain lazy sometimes).

From the perspective of someone trying to trace back the history of the universe to the Big Bang, this is problematic, because if this law of physics holds back to the beginning of the universe, then the net number of baryons at the moment of the Big Bang is the same as it is now. And, if the universe started as "pure energy" (a near universal assumption of cosmologists and theoretical physicists) then we have no know process except the sphaleron to make that transition.

On the other hand, a matter dominated universe is one that makes perfect sense and that we have a process to explain (the same applies to an antimatter dominated universe, but if we lived in an antimatter dominated universe we would call it "matter" and would call matter "antimatter").

* Protons, neutrons, antiprotons and antineutrons are the only remotely stable baryons in the universe (mesons aren't stable either but are irrelevant because they have a baryon number of zero since they have equal numbers of quarks and antiquarks). 

* A proton that encounters an antiproton will annihilate into energy, as will a neutron that encounters an antineutron.

* Therefore, if the net baryon number in the universe is positive, sooner or later, almost every antibaryon in the universe will be annihilated by a baryon, leaving only baryons left over.

The story on the lepton side is a bit more complex. There is only one stable charged lepton, the electron. But, there are three kinds of neutrinos (the electron neutrino, the muon neutrino and the tau neutrino, because somebody ran out of creativity when coming up with names for them), all of which are stable.

If an electron encounters a positron (a.k.a. an anti-electron), they annihilate. So, it makes sense that there are far more electrons in the universe than there are positrons, because they annihilate one to one until only the more numerous kind is left.  The positrons we do observe in the universe are probably overwhelmingly created by recent processes which haven't met their nemesis yet, rather than primordial.

But, the kicker is that it is not true in general that a lepton that encounters an antilepton will annihilate. An electron or positron that encounters a neutrino of any kind, will not annihilate, because that interaction would violate conservation of charge (although an electron and antineutrino could merge to form a W- boson and a positron and an neutrino could merge to form a W+ boson).

Even less widely known is the fact that a neutrino that encounters an antineutrino of the same type will not annihilate into a photon, like charged particles and their antiparticles do, because they don't couple to the electromagnetic force that photons mediate.  Conservation of charge also prevents them from forming W bosons.  And, their lack of QCD color charge means that they can't annihilate to gluons because they can't couple to gluons.

A neutrino and an antineutrino of the same type can couple to form a Z boson, and a Z boson could decay to a particle antiparticle pair of quarks or charged leptons, and these in turn could annihilate.

But, a W boson has a mass of about 80 GeV and a Z boson has a mass of about 90 GeV, while an electron-antineutrino pair have a mass of about 0.00051 GeV and a neutrino-antineutrino pair have a mass on the order of 0.0000001 GeV.  So, these interactions can take place only via quantum tunneling through virtual W or Z bosons (which are highly suppressed in probability by the mass differences unless the particles have relativistic kinetic energies), or they have so much kinetic energy that a real W or Z boson can be produced.

Also, charged lepton-antineutrino merges into W- bosons and the antimatter equivalent, are commonly believed to require that, for example, an electron couple to an electron antineutrino, rather than a muon antineutrino or a tau antineutrino, and likewise a neutrino-antineutrino coupling to form a Z boson is commonly believed to require that, for example, a muon neutrino couple only to an antimuon neutrino.

This isn't totally certain, because the big experimental discovery of the last twenty years or so in neutrino physics has been that neutrinos emphatically do not seem to conserve lepton flavor. A muon neutrino, for example, can, with a well defined probability, oscillate into either an electron neutrino or a tau neutrino, which violates neutrino flavor conservation, but does not violate lepton number conservation.  

(I state this with less than perfect certainty because one of the common way that neutrino oscillation is described is as a blending of weak force neutrino flavor and the three neutrino mass eigenstate. So it may actually be the case that a muon neutrino that starts with neutrino mass eigenstate number two that oscillates to neutrino mass eigenstate one is just a lighter than usual muon neutrino, while a muon neutrino that oscillates to neutrino mass eigenstate two is just a heavier than usual muon neutrino.)

To make a long story short, however, the bottom line is that while there are very efficient processes by which we would expect almost all antiquarks and charged antileptons to be removed from the universe when there are more quarks than antiquarks, and are more charged leptons than charged antileptons, there is not a similarly efficient process by which antineutrinos are removed from the universe.

We also know that the number of neutrinos in the universe (including antineutrinos) profoundly outnumber the baryon number of the universe and the number of charged leptons in the universe (the gross numbers and the numbers net of antibaryons and antileptons are almost the same), combined.

Since virtually all stable positively charged particles in the universe are protons, and virtually all stable negatively charged particles in the universe are electrons, and the net charge of the universe appears to be zero, it follows that the subtotal of the quantity B-L from all particles in the universe other than neutrinos is almost exactly zero, and if the net charge of the universe is zero there is a very good argument that it should be exactly zero.

This implies that if B-L for the universe as a whole is zero, that the number of neutrinos and antineutrinos in the universe must be exactly equal, or very nearly so.

Now, another way to deal with this issue would be for neutrinos to be Majorana particles that are their own antiparticles, and hence, for them to have a net lepton number of zero.  But, this is profoundly problematic because, if that is the case, then the conservation of lepton number principle which was used to predict the existence of neutrinos in the first place wouldn't exist, when there is ample experimental evidence that neutrinos do indeed appears in decays when and only when they are need to maintain the correct lepton number.  This is one of the main reasons that I greatly doubt that proposition that neutrinos have Majorana mass and that they are Majorana particles.  If neutrinos could oscillate into antineutrinos and back with any frequency even if it took immense amounts of energy to do so, lots of lepton number violating processes would be observable experimentally.

What implications does this leave us with?

Either the number of neutrinos and antineutrinos are exactly equal, or the universe does not observe B-L conservation, or the initial value of B-L in the universe is not zero.

Now, nobody has yet measured the ratio of neutrinos to antineutrinos in the universe and getting a representative sample may be difficult. But, the task is simplified by the fact that neither neutrinos nor antineutrinos have meaningful interactions with other kinds of matter, and by the fact that almost all neutrinos observed in nature seem to have relativistic amounts of kinetic energy relative to their rest masses. So, there are not especially strong reasons for the ratio of neutrinos to antineutrinos in the vicinity of the solar system to be much different from other places in the universe.

In particular, if we managed to measure this ratio at some point and, for example, the result was that 66% +/- 6.6% of the neutrino/antineutrinos were antineutrinos, we could say with a high degree of confidence that we do not live in a universe in which the initial value of B-L was zero and the quantity B-L is conserved.

It is hard enough to measure neutrinos at all, and even harder to distinguish experimentally between a neutrino and an antineutrino, but this is not a kind of measurement that is in principle impossible with technology not much more advanced than we already have and resources that the human race collectively can spare for a project like that.  And, smart money is on an excess of antineutrinos over neutrinos.

Now, it is hard enough to come up with an extension of the Standard Model that is consistent with experimental evidence but preserves B-L, but not B and L separately, because the experimental constraints on B and L violations from proton decay experiments, neutrinoless double beta decay experiments, and collider searchers for flavor changing neutral currents, for example, have all placed incredibly severe constraints on B and L violations, and neither the Standard Model, nor almost any common GUT theories, propose violations of separate B or L conservation laws that don't respect B-L conservation.

So, if the percentage of neutrino/antineutrinos in the universe is not statistically consistent with 50% neutrinos, there are basically only three possibilities:

1. The Big Bang had zero B and zero L, but some process in the very early universe not yet conceived violated not just B conservation and not just L conservation, but also B-L conservation.

Coming up with a process that violates B, L, and B-L conservation, but only violates any of them at extremely high Big Bang energies is a real challenge, but perhaps someone is up to it.

2. The Big Bang had non-zero B and/or L.  This is ugly, but is the default answer under the Standard Model.  It is the Standard Model default because the only B-L process in the Standard Model doesn't appear to be capable of creating enough of an imbalance in a small enough amount of time that specifically leads to a large positive baryon number of the universe, to account for what is observed.

3. The universe conserves B-L, and there is a missing pool of leptons or antileptons (as the neutrino ratio indicates) hiding somewhere.

4. The universe conserves B and L, and there is a missing pool of antibaryons and a missing pool of leptons or antileptons (as the neutrino ratio indicates) hiding somewhere.

Where could missing B or L hide in scenarios 3 or 4 above?

* One possibility is that one or more kinds of dark matter have B and/or L numbers, but can't annihilate with SM matter, that balance things out.  

There is estimated to be something on the order of 9 times as much dark matter mass in the universe as there is ordinary matter.  And, a dark sector could easily have enough particles (if they had mass of 100 MeV each or less) to bring the universe's aggregate baryon number to zero.

But, to bring lepton number to zero, dark matter particle with leptons number would have to have very tiny masses, far lighter, for example, than keV scale proposed warm dark matter sterile neutrinos.  And, such tiny masses are inconsistent with thermal relic dark matter.

Within the realm of beyond the Standard Model theories that have any meaningful popularity, scenario 3 with axion dark matter than has lepton number, is probably the only plausible fit to the constraints.

But, there are also good reasons to doubt that non-thermal relic axion dark matter that has lepton number is the solution and you still need a B-L process limited to very high energies that is very efficient to give rise to a positive baryon number for the universe very early one.

* A second possibility is that there are areas of the universe that are predominantly made of antibaryons and the missing leptons or antileptons (at the neutrino ratio indicates). But, this possibility has been examined rather carefully by physicists and had been pretty much ruled out, essentially, because there is no mechanism to segregate the two parts of the universe and because the boundary area would be obvious as matter-antimatter annihilations flared constantly.

* Another possibility is that missing antibaryons and missing leptons or antileptons (as the neutrino ratio indicates) are hiding outside the observable universe while still being within the light cone of the Big Bang.  This leaves essentially two possibilities (which are not mutually exclusive).  

One is that the missing particles have been preferentially gobbled up by black holes which are not observationally accessible because they are separated from the rest of the universe by an event horizon. But, there is no obvious reason that antibaryons and the wrong kind of lepton should be preferentially absorbed by black holes when the attraction is seemingly all gravitational.

The other is that the missing particles are out there but are hiding earlier in time than the Big Bang. The are some heuristic motivations to think that this could lead to segregation because antimatter involves a flip of CPT from normal matter and one of the way that can happen is time, but it is still a bit of a sketchy concept that basically requires the second law of thermodynamics which is one of the main arrows of time to work in the opposite direction before the Big Bang.

For now, we won't get many hints until we can measure the universe's neutrino-antineutrino ratio, so we'll have to just ponder and guess.