Mass of Antimatter

[pSimon]

I came upon a statement yesterday (In the "Science of Superheroes" no less!) that stated that antimatter is acted on by gravity in the same way as normal matter (i.e. the force isn't inverted).

Has this actually been measured, or is it an "assumption" based on theory?

(I'd be surprised if gravitational forces could actually be measured on the tiny quantities of antimatter that we can actually create)

Similarly, I recall (dunno from where), that AM can be considered "temporally inverted" matter - its this the case, or, as I suspect, is it a lot more complicated than that? .... :)

[Preno]

Has this actually been measured, or is it an "assumption" based on theory?Not really (http://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter). But there is no reason to believe that antimatter somehow gravitationally repulses matter, as there really is nothing special about antimatter. It's just particles with the same mass and opposite charge/parity as their counterparts, basically.
Similarly, I recall (dunno from where), that AM can be considered "temporally inverted" matter - its this the case, or, as I suspect, is it a lot more complicated than that?Yes (http://en.wikipedia.org/wiki/CPT_symmetry), basically.

[Ray Moscow]

That's the theory.

I don't know whether it's actually been measured, though. Antimatter in large amounts is hard to come by.

Regarding the relationship between particles and their antiparticles, read about Feynman diagrams (http://en.wikipedia.org/wiki/Feynman_diagram). The bit that came to mind was that a particle becomes its antiparticle if you reverse the direction of time. (easy on paper, but otherwise somewhat tricky)

[Valheru]

The theory for "normal" particles is that they gain the property of mass when they interact with the Higgs field (this, btw, is one of the primary purposes of the LHC - to detect this field that is predicted by the standard model, but hasn't been observed yet).

Does the Higgs field interact with "anti-matter"? If it's merely a question of spin type, then I'd say the answer is yes, but I'm just a layperson. I'm very interested in the responses of others who are more familiar with the subject.

[Preno]

Yes, afaik the Higgs field interacts the same with "matter" and "anti-matter". Anti-matter is not some kind of bizarre, wildly exotic type of matter, it consists of perfectly ordinary particles that behave just like all other particles, so there is no reason why the Higgs boson wouldn't interact with them the same way.

[pSimon]

That's the theory.

I don't know whether it's actually been measured, though. Antimatter in large amounts is hard to come by.

Regarding the relationship between particles and their antiparticles, read about Feynman diagrams (http://en.wikipedia.org/wiki/Feynman_diagram). The bit that came to mind was that a particle becomes its antiparticle if you reverse the direction of time. (easy on paper, but otherwise somewhat tricky)

I think that's where I was getting it from. The old Horizon "The Key to the Universe" programme comes to mind. (dimly)

Interesting the "T" inversion [probably] doesn't extend to gravitation - of course if it does, it would explain where all the antimatter went, without requiring any sort of matter/antimatter asymmetry.

Cool.

[pSimon]

Yes, afaik the Higgs field interacts the same with "matter" and "anti-matter". Anti-matter is not some kind of bizarre, wildly exotic type of matter, it consists of perfectly ordinary particles that behave just like all other particles, so there is no reason why the Higgs boson wouldn't interact with them the same way.

Indeed.

I was just a little skeptical of an unqualified statement made of something that seemed so tricky to actually measure.

As for the Higgs - well we still have to find that too, don't we? ;)

Thanks for the input.

[Loren Pechtel]

Nobody's made enough to weigh, nor are the going to until we have a much better understanding of how to handle it safely. Make a mistake with half a gram and you just repeated Hiroshima.

[lpetrich]

It's VERY hard to make macroscopic-scale quantities of antimatter. As is evident from Einstein's famous formula, it takes enormous quantities of energy to make it. Furthermore, once it is made, there is the serious problem of storing it, because the macroscopic properties of antimatter will be identical to those of corresponding ordinary matter. Same density, same melting and boiling points, same hardness and other such physical properties, same color and other optical properties, same electromagnetic properties, same chemical properties, you name it. Static-electricity charging would be the opposite sign but the same magnitude. Etc.

This is all the result of the electromagnetic and strong interactions being matter-antimatter or charge symmetric. Weak interactions violate that symmetry, but in most cases, that only reverses certain spatial asymmetries and not changes in decay rates. Certain particles have CP-violating, time-asymmetric decays, like kaons and similar ones, but they are very evanescent.

That hypothesis is hard to test, but it's been possible to compare the masses, electric charges, and magnetic moments of various particles and their antiparticles. And within experimental accuracy, they are identical to within appropriate sign changes.


The easiest macroscopic antimatter to make is antihydrogen, but it will have ordinary hydrogen's very low melting and boiling points, so it will have to kept chilled to within a few kelvins of absolute zero. However, it will have ordinary hydrogen's diamagnetism, so it can be held in place with a sufficiently strong magnetic field.

It is possible to make antimatter with higher melting and boiling points, but that requires making the appropriate antinuclei, and that will be as difficult as it is for ordinary-matter nuclei.

[Schneibster]

I came upon a statement yesterday (In the "Science of Superheroes" no less!) that stated that antimatter is acted on by gravity in the same way as normal matter (i.e. the force isn't inverted).

Has this actually been measured, or is it an "assumption" based on theory? It's impossible to measure without antimatter to measure it on.

However, the question might be able to be answered by referencing the nature of the gravity force. This is based upon our understanding of it from general relativity. Its nature is that it represents distortions in spacetime; these distortions cause objects to move toward one another because that is the shape of the inertial path in space.

It is possible to imagine the geometry of space being distorted so that objects instead would move apart; what is not possible, mathematically, is to define this in such a way that an object can do it without that object having negative mass. We have experimented with antimatter, and it does not have negative mass.

How do we know this?

First, particles and antiparticles attract one another, and this attraction is the same strength as the electromagnetic force. Physicists are therefore sure that it is, in fact, the electromagnetic force, and that they are oppositely charged; in addition, the CPT Theorem says that antimatter must be oppositely charged from matter, and that theorem is based on Lorentz invariance, a result of special relativity.

Second, when subjected to a magnetic field, particles and antiparticles spiral in helices of opposite sense. The direction of the helix is dependent upon the electric charge, and its diameter upon the mass and speed of the particle. If antiparticles had negative mass to go along with their opposite electric charge, then the two would cancel and they would spiral in the same direction as the particles do; this is implicit in the Maxwell equations.

So for antimatter to have negative mass, both special relativity and Maxwell's equations, two of the best tested theories in the history of science, would have to be wrong, and let me emphasize it is both not either, and not only that, but badly wrong, and in regimes where they are well tested. And for negative mass not to be required, general relativity, which is if anything better tested than the previous two, would have to be wrong. Either of these is unlikely in the extreme.

(I'd be surprised if gravitational forces could actually be measured on the tiny quantities of antimatter that we can actually create)It's not just that they're tiny quantities, it's that the conditions under which antiparticles are created are extremely high energy, and gravity is very weak. The reason we think it's strong is that it has no antiforce; think of this, the entire mass of the Earth only holds you to the ground with a force of some hundred to two hundred pounds. If gravity were as strong as the electric force you'd be about a micron tall and a hundred feet wide. Gravity builds up, and its effects move at the speed of light. Nothing opposes it, and nothing can shield from it.

Similarly, I recall (dunno from where), that AM can be considered "temporally inverted" matter - its this the case, or, as I suspect, is it a lot more complicated than that? .... :)It's more complicated than that.

There are physicists who believed or believe that this is correct; some of them have died. The first one I'm aware of was Richard Feynman. John Wheeler, a well-known general relativist, also believed this. Today, opinion remains divided on whether this is true, and on exactly what is meant by it. Feynman's views clearly were that a positron was an electron with its time direction reversed, and similarly for the rest of the fundamental particles. As a result of being reversed in time, its charge and parity appear reversed to us. This is a consequence of the CPT Theorem I mentioned above; if one of the three is reversed, then it's equivalent to reversal of the other two. This is completely consistent with the laws of physics, though some physicists ask whether there is any meaning to asserting that a particle has its time reversed.

There is an excellent argument that in fact, there is good and comprehensible meaning to time reversal, but that's for another time.

[BWE]

There is an excellent argument that in fact, there is good and comprehensible meaning to time reversal, but that's for another time.i'd like to hear it. ? Are you just talking about Feynman diagrams?

[BigEvil]

There is an excellent argument that in fact, there is good and comprehensible meaning to time reversal, but that's for another time.

I second the desire to hear it.

[Schneibster]

Two votes aye, none nay, you got it.

It's from relativity.

Short version: relativity says that the shape of space with respect to time is a 3-hyperboloid-of-revolution. A hyperbola has two branches, one with positive curvature, one with negative. The positive curvature side obviously represents forward time; hyperbolic trig gives physical answers for th Lorentz transform with respect to the positive curvature branch and unphysical answers for the negative curvature branch. Imaginary observed mass and such. However, should the direction of the time axis be locally reversed, the negative branch would then give physical answers and the positive branch unphysical ones in the local frame, but the opposite in the global frame. Add in the CPT Theorem and it's clear that a particle with its time axis reversed will be seen by an observer with the time axis normal as antimatter.

[BWE]

This then is only a local phenomenon that falls apart as distance increases?

[lpetrich]

As to antimatter being temporally inverted ordinary matter, that may simply be a quirk in their mathematical description that does not affect their direction of time. So I would not want to read too much into it.

Different ordinary-matter and antimatter masses would violate CPT invariance, which would be really screwy if it happened. Wikipedia has a simple proof of CPT symmetry that relies on some very plausible assumptions.


I've found a Wikipedia article on antihydrogen -- to date, about 100,000 antihydrogen atoms have been made in a lab experiment. This is about 10-19 grams.

I've also found one on the gravitational effects of antimatter -- it brings up the serious question of what happens with particles that are their own antiparticles, like the photon. If matter <-> antimatter interchange reverses the gravitational force, then the electromagnetic field must produce zero gravitational force. By similar arguments, one can show that the strong nuclear interaction has zero gravitational force, and also the gluon field of QCD.

This has the consequence that the binding energies of atoms, nuclei, and hadrons makes zero gravitational force.

It is possible to test that hypothesis with equvalence-principle experiments on chemical elements with different atomic numbers and masses. The article binding energy has a nice graph of nuclear binding energies. They increase to about 8.8 MeV per nucleon for iron and then decline to about 7.5 MeV per nucleon for uranium.

So iron ought to have nearly 1% more gravitational force than hydrogen relative to its inertial mass.


It is more difficult to estimate the binding energies for hadrons, but a very naive bag-model calculation suggests that baryons are 3/4 valence quark and 1/4 sea quark and gluon. The latter has zero gravitational force by this hypothesis. Nucleons have the further complication that the quarks' "hyperfine" spin-spin interaction is very strong. This can be seen by comparing these spin-1/2 particles with the spin-3/2 delta baryons:

Proton: 938.3 MeV
Neutron: 939.6 MeV
Delta Baryon: 1232 MeV

From the quantum mechanics of spins,
Nucleon mass (base mass) - (hyperfine mass)/2
Delta mass = (base mass) + (hyperfine mass)/2

(Base mass) = 1085.5 MeV
(Hyperfine mass) = 293 MeV

So the gravitation-less part of a nucleon would be 13% of its mass -- and would be very close for protons and neutrons. This would mean that electrons would produce 15% more gravitational force per mass than nucleons. But electrons are 0.05% as massive as nucleons, so that effect will be insignificant.

Nucleons also have electromagnetic binding energy, but that's likely to be 1% or less of their masses. Neutrons are more massive than protons because down quarks have greater rest mass than up quarks; electromagnetic effects tilt the balance toward protons. This means that protons will have at least 0.14% more binding energy than neutrons, and likely more.

Electrons' binding energies in atoms is likely to be very insignificant. Treating the inner electrons as orbiting in hydrogenlike fashion, their energy levels become (Rydberg)Z2/n2, where Z is the effective charge that the electron "sees" and n is the principal quantum number. Each shell of electrons contains 2n2 electrons. Doing a a crude shell-model estimate gives an average electron binding energy of about (Rydberg)Z4/3. For uranium, this is about 1% of their rest masses.


Let us see how the numbers work out: In Equivalence principle we find out that Braginsky and Panov did experiments on aluminum and platinum with a difference less than 1 part in a trillion. Before that, Roll, Krotkov and Dicke did an experiment in 1964 on aluminum and gold, finding a a difference less than 1 part per billion.

Platinum has 5 stable isotopes, of which 3 are relatively common, while gold has only one. Also, gold's atomic number is one greater than platinum's. So I will use gold. Aluminum also has only one stable isotope.

The elements compared:
Elem | Z | N | A | Atomic Wt | Binding E frac | Neutron frac
Al | 13 | 14 | 27 | 26.98153863 | 8.87e-3 | 0.52
Au | 79 | 118 | 197 | 196.9665687 | 8.43e-3 | 0.59


Binding-energy fractions: (Al value) - (Au value):
Atomic/nuclear: +4.4e-4
Hadronic: +2e-4 (assuming 0.3% proton-neutron difference)

So one can safely conclude that matter-antimatter gravity differences are less than 1 part per million.

[Schneibster]

This then is only a local phenomenon that falls apart as distance increases?Huh? It's special relativity. What we know how to do right now is make individual particles and single atoms of antimatter. These particles, if Feynman and Wheeler were right, are exactly the same as our particles but reversed in time. As a result, by the CPT theorem, as we see them they also have conjugate charges and parity to normal particles. In the frame in which they are not time reversed, they have normal charge and parity.

However, the only thing we can make that is in that frame is another antiparticle, and we don't know how to take anything and reverse it. If we did, it would be incredibly dangerous- an object the mass of a housefly could create a quarter kiloton explosion if it were to interact with matter. This is sufficient to obliterate an entire city block, there would be a fireball and mushroom cloud.

But according to relativity, there is no way to do this. The rotation of one's time dimension to get to the speed of light is infinity degrees; to reverse in time, one would have to rotate past that. Check out some inverse hyperbolic trig functions on a good calculator sometime. Your calculator better be able to display infinite and imaginary answers or it's just going to give you errors.

[lpetrich]

I'd prefer calling antimatter mirror-imaged in time; its direction of time flow would be the same as for ordinary matter.

By the CPT theorem, this makes it a mirror image in space and in electric charge and other such quantum numbers. More technically, it is in gauge-group multiplets that are conjugate to those of their ordinary-matter counterparts.

[Schneibster]

You can look at it that way. Either way is equally valid. The physical results are the same. Lots of people have trouble with the idea that something can move backward in time. What's really going on of course is that the passage of time (or more properly our movement through time) is an illusion; it's no more real for us to say the future doesn't exist than for someone on a train to think that they're moving along the track and the track in front of them doesn't exist. But because of the 2LOT, we think the future doesn't exist yet. Really the only casualty is the 2LOT, which actually is only valid if the universe starts with low entropy. And even it's not a casualty; you can't send information anywhere, backward OR forward in time, faster than the speed of light, and since we can only make a particle at a time we can't send anything back anyway.

Feynman used to say that you could think of this as if there were actually only one electron in the universe. It's been zipping back and forth creating all the traces we see, first as an electron, then as a positron, and so forth.

[lpetrich]

There's a problem with that analysis that was mentioned in gravitational effects of antimatter: what is the direction of time of particles that are their own antiparticles? Or more generally, that include their antiparticles in their gauge multiplets.

Photons are their own antiparticles. So what is the direction of time for the electromagnetic field?

More generally, in electroweak theory, the are two multiplets of gauge particles, a SU(2) triplet (W+, W0, W-) and a U(1) singlet (B0). THe photon and the Z are mixtures of the two:

(g) = W0 * sin(aW) + B0 * cos(aW)
Z0 = W0 * cos(aW) - B0 * sin(aW)

The mixing angle aW is often called the Weinberg angle, and it is near 29 degrees. The photon and Z are their own antiparticles, while the W+ and W- are antiparticles of each other.

The remaining Standard-Model gauge theory is QCD, with 8 gluons in one multiplet. Each gluon is either its own antiparticle or the antiparticle of some other gluon, depending on how one counts them. The same is true of the W's in unbroken electroweak theory.


Related to this conundrum is what time direction a meson would have, since it is composed of an ordinary quark and an antiquark. More generally, composite systems have the problem that their interaction fields all have ambiguous time directions.


It is hard to make antimatter in bulk so that one can check on whether it follows the second law of thermodynamics, but one can come close with antimatter in accelerators. In particular, Fermilab turns up the heat on electron cooling (http://cerncourier.com/cws/article/cern/28650) describes using electrons to cool antiprotons in Fermilab's Tevatron. And from the looks of it, the Second Law of Thermodynamics has the same time direction for antiprotons as for ordinary protons.

[Schneibster]

There's a problem with that analysis that was mentioned in gravitational effects of antimatter: what is the direction of time of particles that are their own antiparticles? Or more generally, that include their antiparticles in their gauge multiplets.I think this is a mistake in interpretation. You are making the assumption that particles have an intrinsic direction. I don't believe that's the case. With particles that have antiparticles, look this way it's a particle, look that way, it's an antiparticle. With a particle that is it's own antiparticle, it's a particle either way.

To all of us, in other words, they're antiparticles; to a hypothetical antiobserver, they'd be particles and we'd all be antimatter.

I'll remind you that the laws of physics are T-symmetric with a few exceptions.

Photons are their own antiparticles. So what is the direction of time for the electromagnetic field?As with particles and antiparticles, it has no inherent "direction of time." Its laws are T-symmetric. Depends on the frame (gauge? I've thought about that...) of the observer.

More generally, in electroweak theory, the are two multiplets of gauge particles, a SU(2) triplet (W+, W0, W-) and a U(1) singlet (B0). THe photon and the Z are mixtures of the two:

(g) = W0 * sin(aW) + B0 * cos(aW)
Z0 = W0 * cos(aW) - B0 * sin(aW)

The mixing angle aW is often called the Weinberg angle, and it is near 29 degrees. The photon and Z are their own antiparticles, while the W+ and W- are antiparticles of each other.There are problems with the weak field. We already know that it is not CP-symmetric which implies it is not T-symmetric; this is such a strong implication that some authors assert that the neutral kaon asymmetry proves that the weak interaction is T-asymmetric.

My understanding is that the W (both + and -) is involved in the asymmetric interactions. This could be explained by the symmetry breaking that breaks the Higgs and Goldstone into the W, Z, and photon; Z and photon are symmetric, W takes the asymmetry and that's how it manifests. Anyway that's what I thought I heard. You probably know enough to confirm or deny authoritatively.

The remaining Standard-Model gauge theory is QCD, with 8 gluons in one multiplet. Each gluon is either its own antiparticle or the antiparticle of some other gluon, depending on how one counts them. The same is true of the W's in unbroken electroweak theory.I'm not sure I see the problem with the color force.

Related to this conundrum is what time direction a meson would have, since it is composed of an ordinary quark and an antiquark. More generally, composite systems have the problem that their interaction fields all have ambiguous time directions.I'll say again, I don't think there's an inherent "direction in time." There's a direction in which a particle appears to be a particle, and a direction in which it appears to be an antiparticle.

It is hard to make antimatter in bulk so that one can check on whether it follows the second law of thermodynamics, but one can come close with antimatter in accelerators. In particular, Fermilab turns up the heat on electron cooling (http://cerncourier.com/cws/article/cern/28650) describes using electrons to cool antiprotons in Fermilab's Tevatron. And from the looks of it, the Second Law of Thermodynamics has the same time direction for antiprotons as for ordinary protons.I'm not convinced that we would necessarily see 2LOT violations. I think it's more likely that the direction in time to the lowest entropy would determine what we'd see, and that we'd expect antimatter to follow the 2LOT in our universe right along with everything else, in the forward time direction, because of low entropy at the beginning of the universe. Since I saw the FT I don't think the 2LOT is a basic law any more; the FT determines how fluctuations occur and the 2LOT is just a longterm fluctuation.

[Berthold]

...antiobserver...
Nice word with several potential meanings. :D

[lpetrich]

I think this is a mistake in interpretation. You are making the assumption that particles have an intrinsic direction. I don't believe that's the case. With particles that have antiparticles, look this way it's a particle, look that way, it's an antiparticle. With a particle that is it's own antiparticle, it's a particle either way.
That's more like what I'm saying, that's it's mirror-imaging in time rather than reversed time direction.

There are problems with the weak field. We already know that it is not CP-symmetric which implies it is not T-symmetric; this is such a strong implication that some authors assert that the neutral kaon asymmetry proves that the weak interaction is T-asymmetric.
That would be from the CPT theorem, and violations of CPT would be very odd, to say the least.

There are some other places where CP violation could be observed, but it's hard for me to find definite numbers on them.

Neutral mesons with different quark flavors. The neutral kaon is the classic case, but it may be possible to observe similar CP violations in D and B and Bs mesons.

Electric dipole moments of elementary particles, notably the neutron's. The measured upper limit of the neutron electric dipole moment has gradually been decreasing, though it is still well above the Standard Model prediction of it.

My understanding is that the W (both + and -) is involved in the asymmetric interactions. This could be explained by the symmetry breaking that breaks the Higgs and Goldstone into the W, Z, and photon; Z and photon are symmetric, W takes the asymmetry and that's how it manifests. Anyway that's what I thought I heard. You probably know enough to confirm or deny authoritatively.
These effects originate from the quarks' mass matrices not being orthogonal to each other. This non-orthogonality makes a charged weak interaction turn an up-like quark into a mixture of down-like quarks and vice versa.

That is also the case for charged leptons and neutrinos, and that produces neutrino oscillations.

The quark mixing matrix has three CP-preserving parameters and one CP-violating one; there are similar numbers for neutrino oscillations.

The remaining Standard-Model gauge theory is QCD, with 8 gluons in one multiplet. Each gluon is either its own antiparticle or the antiparticle of some other gluon, depending on how one counts them. The same is true of the W's in unbroken electroweak theory.I'm not sure I see the problem with the color force.
I was addressing the question of the direction of time -- if antiparticles are going backwards in the sense of experiencing backwards internal time, then it is difficult to tell which gluons are going forwards and which ones are going backwards.

[Schneibster]

That's more like what I'm saying, that's it's mirror-imaging in time rather than reversed time direction.I think it boils down to the same thing. I'm still thinking about whether a gauge gets fixed by the choice of the direction of time or not. I think it does but I'm not sure what all the consequences are. To answer the question of the OP in these terms, I think that mass is gauge invariant in this context.

That would be from the CPT theorem, and violations of CPT would be very odd, to say the least.But violations of T-symmetry are not.

There are some other places where CP violation could be observed, but it's hard for me to find definite numbers on them.

Neutral mesons with different quark flavors. The neutral kaon is the classic case, but it may be possible to observe similar CP violations in D and B and Bs mesons.According to LBL's decay mode documents linked from Wikipedia's articles on the B and D mesons, the B, B0, and Bs all have CP-violating modes of decay. With the D mesons it is only the D that does, not the D0. The kaon was where it was first discovered.

Electric dipole moments of elementary particles, notably the neutron's. The measured upper limit of the neutron electric dipole moment has gradually been decreasing, though it is still well above the Standard Model prediction of it.Yes, I'd forgotten that. I thought there was a current experiment underway on that that I came across an article on a bit back.

These effects originate from the quarks' mass matrices not being orthogonal to each other. This non-orthogonality makes a charged weak interaction turn an up-like quark into a mixture of down-like quarks and vice versa.That's right, I'd forgotten that part. It's the weak charged currents that make the CKM results weird.

That is also the case for charged leptons and neutrinos, and that produces neutrino oscillations.Now I hadn't heard that before. That's very interesting. Is there a good book out there that has a description of that in it yet?

The quark mixing matrix has three CP-preserving parameters and one CP-violating one; there are similar numbers for neutrino oscillations.Again, I had forgotten but had heard about the quark matrix; I wasn't aware anyone had done anything like it for the leptons. More information urgently desired. :D

I was addressing the question of the direction of time -- if antiparticles are going backwards in the sense of experiencing backwards internal time, then it is difficult to tell which gluons are going forwards and which ones are going backwards.I see, so this is inoperative. It was just from the misunderstanding.

Thanks!

[lpetrich]

Here is a nice reference: neutrino oscillation

For quark mixing, see the Cabibbo–Kobayashi–Maskawa matrix

With the hypothesis that these mixing matrices are "unitary", one can count how many parameters they need.

For n generations, there are (n-1)2 observable parameters, of which n(n-1)/2 are CP-preserving mixing angles and (n-1)(n-2)/2 are CP-violating phase angles.

For one generation, there is, of course, no mixing. For two generations, there is one CP-preserving angle and no CP-violating angles. For three generations, there are 3 CP-preserving angles and 1 CP-violating angle.


According to the Sakharov hypothesis of baryogenesis, CP violation, baryon-number violation, and the Big Bang's time direction can combine to produce our Universe's matter-antimatter asymmetry. It is about 1 part in a billion, but it is enough to make a difference.

So our Universe's having at least three generations of elementary fermions (quarks and leptons) may have been connected with its matter-antimatter asymmetry.

[Schneibster]

And there's the mixing matrix, right in the middle of the article on neutrino oscillation. Thanks, bud. I heard about the oscillations, but I hadn't heard they'd been conceptually connected to the cp-violating angles in the CKM matrix.

The big remaining one is the baryon-number violation.