sábado, 26 de novembro de 2011

13. WIMPs and Supersymmetry - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture ties right in with my previous review on stepping back to see the larger picture in the process of science. How scientists propose unique and testable theories when faced with great unknowns. Sean admits this lecture is all conjectural in the effort to characterize the particles of dark matter. So we should be prepared to get out of this presentation a good exposure to this big picture, not necessarily to understand how the hypothetical theories actually work. This lecture should motivate you to do that with other, more appropriate sources. Otherwise it could make for a frustrating experience!

Scientists would like to use existing particle physics theories to characterize dark matter instead of making up a new one just for dark matter. Supersymmetry is one such theory that naturally predicts fermion WIMPs, a leading dark matter candidate. These are the fermionic superpartners of bosonic particles, with names such as the zino, higgsino, photino, or neutralino. Their stability may be due to conservation of some new quantity, they are heavy to the effect of 1000x the proton mass, and they are weakly interacting. Direct detection is promising, but depends on the various models. Indirect detection could occur when particle anti-particle annihilation produces gamma rays, which the GLAST satellite could observe. Making our own fermion WIMPs is possible with Fermilab but should be even more possible at CERN with the LHC.

Other dark matter particle candidates, apart from supersymmetry, are:

A Kaluza-Klein particle that arises from the idea of an infinite number of partners resulting from curled up spacial dimensions like we'll see later in string theory.

Sterile neutrinos don't feel weak interactions, just gravity. But this theory does not get anything extra out of it, as the many spinoffs of supersymmetry would.

A bosonic dark matter particle is known as an axion. They have a very small mass, but a large density that agrees well with other theories discussed in later lectures.

This ends the speculation phase of the second larger cycle in the course. We start anew next time with dark energy.

By now, we've squelched any remaining suspicion we might have in our minds that the dark matter, found from evidence in the dynamics and motions of galaxies and clusters, could possibly somehow be ordinary matter that was somehow hidden. It can't be gas or dust, since that would fall into clusters of galaxies, heat up, and we'd be able to see it in x-rays. It also very probably cannot be ordinary stars, brown dwarfs, white dwarfs, neutron stars, or black holes, since all of them lead to microlensing events, for which we've searched for and can't find enough.

Finally, the real reason we know that ordinary matter in some hidden form, can't be the dark matter that we have evidence for, is both Big Bang nucleosynthesis and the CMB, both put a very tight constraint on how much ordinary matter there is in the universe. It's only 5% of the critical density, while the dark matter is something more like 30%. In other words, we have to turn to some unordinary kind of matter, some new kind of particle.

So in this lecture, we're going to start getting serious and start asking what kind of particle the dark matter could be? We have to go beyond the particles we've already established to exist in the standard model of particle physics. So what are the requirements for a new dark matter particle? Most obviously it must be dark, yet the other important requirement is that it must be cold.

So "dark" means not only is it hard to see, but that it doesn't interact very much. When you look at a galaxy, the shiny part of it that's easily visible from stars, all comes from the ordinary matter of course. The reason why the galaxy is able to contract, is because ordinary matter interacts. Ordinary matter, in the process of collapsing under its own gravitational field, will get stuck when one little bit of ordinary matter comes into contact with another one, so it can cool off and settle down into the bottom.

Dark matter seems to be distributed in a big, puffy halo, around the galaxy. It's not condensed right in the middle, like visible matter is. The explanation for this, is very easy to come up with. The dark matter particles just pass through each other and go right out. So dark matter needs not only to be dark, but also to be not interacting with itself in any obvious way.

The other requirement for the dark matter particle is that it should be cold. In other words, even if the dark matter existed and had a small mass, yet was moving at a high velocity, and close to the speed of light in the early universe, then when it tried to collapse it would go right outside and just keep going, not oscillating back and forth like a real good dark matter particle would do.

So we're trying to invent a new kind of particle that is dark and cold. Let's just check that there's no such particle lying around in the standard model already. Well, which particles in the standard model are dark? Of course we don't want the ones that decay, so neutrons would not be good examples of dark matter particles since they decay away and we need something that will stick around. The only neutral particle in the standard model that is stable, is the neutrino.

Neutrinos are very obvious dark matter candidates. However as it turns out, when you go through the details, because neutrinos are so light, they are not cold. When they decouple or freeze out from the primordial plasma at very early times, they're moving very fast. They qualify as hot dark matter.

If the dark matter we observe is hot, then structure on small scales in the universe doesn't form. You don't make galaxies in the universe, which is mostly hot dark matter. Whereas the stuff would want to collapse, the neutrinos are moving out very quickly and tend to smooth everything out. Hot dark matter is actually quite strongly ruled out as a possible way for the dark matter to behave, so much so that these days we turn it around. We use cosmology to place a constraint in the mass of the neutrino. If it's too big, is would be the dark matter. Yet we know it can't be the dark matter because we know the dark matter is not hot. So that's a good way to get an upper limit on how big the neutrino mass could be.

So that's the only possibility in the standard model of particle physics, and we need to turn to particles beyond the standard model. So lets think of what the requirements are on those particles. Of course they must be dark and cold, yet in lecture 9 we gave an explanation for how to calculate the relic abundances of particles left over from the early universe. If a particle interacts strongly in the early universe, then that particle and its anti-particle will all annihilate away. By the end of the universe's history, by today, we won't have anything left over. So what you need for a particle to be left over in sufficient amounts to be the dark matter, is a particle that does not annihilate very strongly, one that is weakly interacting.

Now when we say "weakly interacting" you might reasonably think it means not interacting very much, or not interacting very often when coming together with another particle. That's true, but now lets actually plug in the numbers. Let's do our calculation of what kind of particles give rise to the right kind of abundance of a particle today to be the dark matter, and ask how often should particles annihilate in order for them to be good dark matter candidates?

The answer is that the right rate of interaction for a new particle to be the dark matter candidate, is exactly that which it would have, if it interacted through the weak nuclear force. So when we say weakly interacting particles are good dark matter candidates, we don't simply mean particles that don't interact very much, but those that interact via a W and Z boson, via the weak interactions of the standard model.

It's not the only possible way to get dark matter, but it's suggestive. It's telling us that if we invent a new particle that is stable, that is not interacting through electromagnetism or the strong interactions, but does interact through the weak interactions, it is a natural dark matter candidate. So the name attached to such a candidate is a WIMP (Weakly Interacting Massive Particle), as opposed to the MACHOs which are the compact collections of ordinary matter.

So we want to make WIMP candidates, new examples of particle physics that give us WIMPs that are stable and could be the dark matter. For most of this lecture, we'll talk about one specific example of a particle physics model that naturally leads to a candidate WIMP dark matter particle. This specific example is called supersymmetry. Yet really what we should be getting out of this lecture, is not the details of supersymmetry as a candidate way to get dark matter, but just an example of the kinds of thought processes that physicists go through when trying to invent new particles. The point is you don't want to just say, "Oh yes, there must be some new particle, and that's the dark matter."

Particles have interactions and come with different properties. We know a lot already about the particle physics of the standard model. So when you're inventing a new particle, that has to fit in somehow. The best dark matter candidates will be those that have some natural interpretations in terms of the particle physics all by themselves, even if we didn't know there was such a thing as dark matter. Supersymmetry is an excellent example of that, which is why it's worth going into in some detail.

So supersymmetry is a hypothetical idea which invents a new symmetry onto those we already know about in the standard model. We already mentioned that the standard model of particle physics is characterized by a great amount of supersymmetry. For example, the most obvious thing that you see in the standard model, is that when you look at the fermions, they come in three generations. You have the up and down quark in a doublet, the electron and its neutrino in a doublet, and all by themselves those four particles form a self-contained set.

Then you have another four particles that repeat that pattern. Two quarks and two leptons, the charmed and strange quark, and the muon and muon neutrino. Then it happens yet again with the bottom quark and top quark, and the tau and tau neutrino. So the fact that you have a similar structure repeating itself over again, is an example of a symmetry. At a deeper level, symmetries are responsible for the forces between particles, the strong nuclear force, the weak nuclear force, and the electromagnetic force.

So supersymmetry is a very specific kind of symmetry, something different than we've ever seen in the standard model. It's a symmetry that relates bosons to fermions. Bosons are the force particles that can pile on top of each other to give rise to electromagnetic fields, gravitational fields, and so forth. Fermions are the matter particles that take up space. These two seem very different from each other. Remember that there's a thing called spin, and bosons always have an amount of it that is integer. Yet fermions always have a spin that is fractional. So supersymmetry is a speculative idea, saying somehow there could be a symmetry relating particles with different amounts of spin.

If that is true, the nice thing is that you can have a lightest supersymmetric particle, which is a perfect dark matter candidate. Such a particle is sometimes called the neutralino, and that's what we'll explore now. So if supersymmetry existed, for every kind of fermion particle, there would be a boson particle, with the same kinds of charges and the same mass. Vice versa for every boson and a corresponding fermion.

So for example, you have a bosonic particle with a certain mass, electric charge, and interaction with the weak and strong nuclear forces. If supersymmetry existed, there would be a fermion with the same mass, the same electric charge, the same weak and strong nuclear force interactions, yet at different spin. Now you can look in the standard model. There are certainly particles of both kinds of spin in the standard model, bosons and fermions. Yet they certainly don't match up. You can't take the bosons of the standard model and say any certain fermion is its superpartner. It doesn't quite go like that.

You could also imagine that there are new particles, which we don't see in the standard model yet, but that could be the superpartners of the particles we know and love. For example, the electron would have a partner that was a boson, and would be called the selectron. It would have a charge of -1, just like the electron does, a lepton number of +1, and a quark number of 0. It would not interact with strong interactions, but would interact with weak interactions.

Yet if supersymmetry were exactly right, that selectron would have exactly the same mass as the electron, which is clearly not true. If there were a bosonic particle with the electric charge of the electron and the same mass as the electron, we would have noticed it long ago! So somehow we have to invent an entire new set of particles we have never yet seen. What we have done is given them names. That's a good first start if we haven't actually found them yet. At least we can come up with their names.

The new particles we need to imagine, if we're going to believe that supersymmetry is right, are the fermionic partners of the existing bosons, and the bosonic partners of the existing fermions. The bosons that are the partners of the existing fermions are given names that are derived by tacking an "s" onto the beginning of the name of the fermion. So we have different kinds of quarks for example, whose bosonic superpartners are called squarks. We have different kinds of leptons whose bosonic superpartners are called sleptons. So you have the electron and its partner the selectron, the neutrino and its partner the sneutrino, etc. You can have great fun with this if you go very far!

For the existing bosons, they have fermionic partners that are given names by tacking the suffix "-ino" at the end of the particle name. So you have for example he photon, which is a boson, and its fermionic superpartner is the photino. The graviton is a boson, so there's the gravitino fermion. The Higgs boson we think exists, has a partner called the Higgsino, and so forth. So you get all sorts of particles.

If supersymmetry is right, given the fact that there is no way to match up particles we already observe, supersymmetry is hypothesizing that we have doubled the number of particles in the real world that we have actually observed in the standard model of particle physics. So it's a very economical idea in the sense that it's just one little idea to say there's a symmetry between bosons and fermions. It's easy to say, yet it becomes quite prolific in terms of what kinds of particles it predicts. It's not just one more particle tacked onto the standard model, but it's doubling the number.

Now you might ask if it's worth doing that? Why are we contemplating doubling the number of particles that we have in nature? Well dark matter is a nice benefit from inventing supersymmetry, yet it's not the primary motivation. In fact the very first reason why supersymmetry was invented, was because it is a prediction of string theory. We'll discuss this later in the course, which is a hypothetical way of gravity, and turns out to only work if you have supersymmetry.

Yet then it was recognized that even if string theory isn't right, supersymmetry by itself is not only aesthetically pleasing, not only is it a very nice and elegant theory of nature, but it also solves some naturalness problems that exist in the standard model. The foremost one is called the hierarchy problem. We won't go into great detail about this, but it's basically the fact that the different mass scales of particle physics are very different from each other. That is the kind of thing that particle physicists don't like, for things to be very different from each other without some good reason.

So the mass of the Higgs boson in the standard model is actually what sets the scale for all the massive particles in the model. Yet it's is somehow very different than the high-energy mass scales we're familiar with from gravity, from the Planck scale, or from GUT (Grand unification Theory). So why is the Higgs boson so much lighter than the particles we would expect to exist at the very high energies? That's called the hierarchy problem.

It turns out that in supersymmetry, there's a natural explanation for the hierarchy problem. That's why most particle physicists like supersymmetry as a candidate for physics beyond the standard model. The problem of course is that we don't see selectrons, squarks, etc. Somehow they must be hidden from us. In particular, they must weigh a lot more, they must have a much larger mass than we would naturally expect.

How do you do that? The answer is that this symmetry we're inventing, supersymmetry, must somehow be hidden from our immediate view. The idea that symmetries are hidden, is a very familiar one in particle physics. In fact, it's the correct way to think about the weak interactions. We mentioned that the W and Z bosons that carry the weak interactions, are very heavy particles, unlike photons, gluons, and the graviton, which are very light particles.

Why is that? In their natural state, the W and Z bosons that carry the weak interactions, would be massless. Yet it turns out that the symmetry associated with those particles is broken by empty space. In fact, it's broken by the Higgs field, which is why it must exist. The role of the Higgs field is to break the symmetry of the weak interactions and give mass to the W and Z particles.

This maybe sounds like cheating, by trying to sort of hide something in a broken symmetry, to explain things you don't otherwise understand. Yet the idea of properties of particles changing that depends on where they are in the medium through which they move, is very natural. For example, light does not always travel at the speed of light. The speed of actual light rays is different in air, water, or glass, than it would be in empty space. That's because the medium through which the light is traveling, has properties all by itself. So when we speak of the speed of light, we really mean the speed of light in a vacuum. Yet in stuff, the speed of light can be very different.

Similarly, the idea of a broken symmetry is that some field pervades empty space. Modern particle physics says that even in empty space, there is a Higgs field, something that has a non-zero value. The reason why W and Z bosons have mass, is that they're traveling through this Higgs field. That's a very successful idea, and the particles predicted by this idea, have largely been discovered and Nobel Prizes have been given out.

So we just want to do this same kind of thing, but now with supersymmetry. We want to break supersymmetry, and there must be some mechanism that does this at a deep level. If that happens, then all of the superpartners of the particles in the standard model, become heavy. So basically you take a whole bunch of particles in the standard model that had the same masses as those we observe. Yet you lift their masses by a large amount, you raise them by breaking the symmetry, and end up with a whole bunch of particles, all of which are very heavy, at least 1000 times the mass of the proton. So the reason why we haven't discovered supersymmetric particles yet, in this scenario, is that it's just too hard to get there. It's just out of our reach, although we're trying to do it right now.

So an interesting wrinkle of this possibility, is that there could be a new conserved quantity associated with supersymmetry. Remember that there are things called quark number, lepton number, electric charge, all which have quantities that can neither be created nor destroyed. An electrically charged particle cannot decay into a neutral particle.

Well what if "superness" is also a conserved quantity? What if whether or not you are in the standard model, or superpartner of the standard model, is a conserved quantity? Then the superpartners of the standard model, would not be able to decay into the partners we see, the actual particles we know to exist in the standard model. So therefor, the lightest, supersymmetric particle would have to be stable. There would be nothing for it to decay into.

So we're saying that there would be a kind of particle that would be stable because it carries some conserved quantity. It's heavy, some 1000 times greater mass than the proton, so we haven't seen it yet, and it can very plausibly be weakly interacting. These are particles that are part of the supersymmetric standard model, they're not completely separate. So you could have particles like the partner of the Higgs boson, the Higgsino. That would be an electrically neutral particle that would feel the weak interactions.

Likewise the Zino, the partner of the Z boson, or even the photino, the partner of the photon, these would all be massive, possibly stable particles, any one of which is a candidate for the lightest supersymmetric particle, and any one of them would make an excellent WIMP. They are all weakly interacting, massive particles, yet we don't know which one is the right one, since we don't know which one is lightest. Under different scenarios of supersymmetry, different particles are going to get different masses, but that's one of the things we need to figure out by taking data. We're not going to know until we do experiments and find the superpartners, which one of them is actually the lightest, the LSP (Lightest Supersymmetric Particle), or the neutralino.

So the reason why we like this theory is because supersymmetry was not invented to give us a dark matter candidate. It was invented for other reasons, but lo and behold, a perfect dark matter candidate pops out! It's easy in supersymmetry to get particles that are stable, weakly interacting, and massive. So what you want to go do, is test this idea, to go look for these particles. There are various ways to do this.

The most promising method over the next few years is called direct detection, which means building an experiment which will actually find a dark matter particle directly. The problem is dark matter particles by construction are weakly interacting, they don't interact very much. So what we have to do is very similar to what has already successfully been done with neutrinos. We need to build a detector that is deep underground, shielded from the noise we're subjected to on the surface of the earth, and is very sensitive to particles coming in and lightly glancing off an atomic nucleus in the detector.

We've already done this for neutrinos, yet neutrinos are, firstly, at a very different energy scale than the dark matter particles are, and secondly, there's a shining beacon in the sky that emits neutrinos, namely the sun. For dark matter particles, we're looking for a background of them, since we don't have a shining source to look at. This makes it more difficult, yet there's a number of experiments going on right now that are actively trying to do exactly this experiment. It's very plausible that over the next few years, there will be a headline in the papers saying that scientists have directly detected the dark matter of the universe.

Yet maybe they won't, we don't know. That would be a hard thing to do, and in different models it becomes very easy or very difficult, so we're trying other ways. One other way is a very clever idea, taking advantage of the fact that not only do you have dark matter particles, but you have dark matter anti-particles! The reason why the dark matter particles have a certain density, is because they have stopped annihilating because the universe has expanded. You have both the particles and their anti-particles in the dark matter, yet they just don't annihilate since they don't interact with each other because there aren't that many of them around, per cubic cm. Much like neutrinos, they can pass right through each other very easily. You'd need a very high density of dark matter particles before you begin to see them annihilate.

Yet there are places in the universe where the density of dark matter particles might be very high. The center of galaxies or of clusters of galaxies, where dark matter particles were very spread out, will collapse, contract, and gather in the same place. There you will begin to see dark matter particles annihilating with dark matter anti-particles. When that happens they're going to give off radiation, high-energy photons. In most models they will give off gamma rays, which are hard for us to observe here on earth. If one comes to us here at the surface, it will be absorbed by the atmosphere.

So NASA and the DOE are building a new satellite called GLAST that will be launched in 2007, to look at gamma rays in the centers of galaxies and clusters of galaxies. That means we'll be indirectly detecting dark matter. If we see a signal of gamma rays at a very specific source, at a very specific energy, that is exactly what you'd expect if a particle and its anti-particle were annihilated. Again, this may or may not happen in different models. We have to go out there and do the experiments to see if nature is being nice to us in this way.

Finally we have perhaps the most direct method of all, which is forgetting about the dark matter that surrounds us. Lets just go and make our own dark matter. This is what particle physicists are paid to do! They collide energetic particles together and make new ones. This is what we're trying to do right at this moment, building better particle accelerators to do even better. The reason why it's not a surprise that we haven't yet made dark matter particles, is because it's hard to notice, even if we do! Dark matter particles are weakly interacting, so they're very hard to make, and are neutral, so they're very hard to detect once you've made them.

In other words, we might be making dark matter particles all the time in current particle accelerators, yet we just don't have enough data to be sure that this is what's going on. As of 2007, the most high energy collisions we can produce here on earth, come from the Fermi National Accelerator Lab (Fermilab) outside Chicago. They make high energy collisions at about 1000 times the mass of a proton, at about the place you'd just expect to see these superpartners being created. The problem is that since it's just at the edge, you might make one or two and yet never know. So we're crossing our fingers and it's certainly possible that the Tevatron accelerator at Fermilab, could make supersymmetric particles, yet we can't guarantee it.

Therefor we're trying to build even better accelerators. The LHC (Large hadron Collider) is being built right now at CERN, a European particle accelerator outside Geneva. It's scheduled to turn on by late 2007, yet will take at least a year for energies to ramp up. Once they do, they should be 10 times more than the energies at Fermilab. We'll be able to create vastly new numbers of particles at the LHC that we could only barely hint at, with the Tevatron. So again, it's very plausible that just a couple of years after the accelerator turns on, we'll be awash in supersymmetric particles.

The problem there will be too many new particles, and we'll have to figure out what is going on. It's not going to be an overnight project, yet there will be a lot of excitement involved when we discover new particles at the LHC, and try to make sense of them, to figure out how they fit into particle physics, and whether or not one of them could be the dark matter.

It's also possible of course that there is dark matter, and it's some neutral particle that does not interact very strongly, yet does not come from supersymmetry. So there are candidate particles from dark matter, both that qualify as WIMPs and other kinds of dark matter particles. So we'll get one example of a particle that is a different way to get a WIMP. One that is neutral, stable, and feels the weak interactions.

That's something called the lightest Kaluza-Klein particle. This is an idea that has nothing to do with supersymmetry, but says that there are extra dimensions of space. There are tiny directions you can go in space that are curled up into little balls so you can't see them. We'll talk about this in detail when we get to string theory in the last few lectures. Yet the point is that if you have these tiny curled up dimensions, then every particle we already know and love, electrons, photons, and what have you, have an infinite number of partner particles that correspond to particles moving in these extra dimensions, with different amounts of momentum.

Due to quantum mechanics, these different amounts of momentum are not arbitrary, but are quantized. So there is a minimum amount of extra energy that a particle can have, from spinning around in the extra dimensions. This would show up to us as something called the lightest Kaluza-Klein particle, and could very easily be weakly interacting and massive. it's another very promising candidate for a WIMP, and therefor for the dark matter.

Then there are also particles that are not weakly interacting at all. In other words, they're the dark matter, yet don't feel the W and Z bosons. One example are neutrinos, but sterile neutrinos. This is exactly a neutrino that doesn't feel the weak interactions, which is what the word sterile means in this particular context. So you can invent new kinds of neutrinos, which already don't feel the electric force or strong nuclear force, but also don't feel the weak force. These are the kinds of neutrinos that don't feel electromagnetism, the strong force, or the weak force. All they feel is gravity, and they can occasionally interact with other kinds of neutrinos. So people are making models of massive sterile neutrinos, calculating how many you can make in the early universe, and it turns out to be easy to get the right abundance to be the dark matter.

The only reason this model is not as popular as supersymmetry, is that you don't get a lot extra out of it. The bonuses you get from supersymmetry are quite considerable, just from the particle physics perspective. Sterile neutrinos help you a little bit, but we don't know if they're part of some larger picture as of yet.

Finally we'll mention axions. They are perhaps the second leading candidate for dark matter particles, after supersymmetric particles. Yet axions are really completely different in conception than the supersymmetry, LSP, or neutralino would be. Axions are bosons, whereas the supersymmetric particles that would be the dark matter, are fermions. The supersymmetric particles are very heavy, some 1000 times the mass of the proton, while axions are very light, with the same sort of mass like the neutrino. They are very low-mass particles, which ordinarily we'd expect to be fast moving.

Neutrinos can't be the dark matter, because they're so light, they're moving very fast, and they do not make good dark matter candidates. Why is it that axions, which are very light, can nevertheless be cold dark matter? The answer is the axion is created by a very different mechanism than neutrinos or WIMPs are. The axions in the models that people write down, were never interacting with the rest of the particles in the plasma of the very early universe. They were never heated up by interacting with the rest of the stuff in the primordial soup.

Instead, there was a kind of field, an axion field that didn't change. It was just stuck there, and it contained energy. This energy was just constant, not going away until a phase transition happened and this field melted. When that happened, it went from being a constant amount of energy per cubic centimeter, to a bunch of axions with zero velocity. So this is a completely different mechanism than the one you get by creating WIMPs or neutrinos.

It turns out that there are enough free parameters in the model, to make this kind of axion from a melting field, with exactly the right kind of densities to be dark matter. So this is good news and bad news. It's good since it's a completely different way to get dark matter particles, yet bad because therefor the ways to go look for axions are completely different also! The kinds of experiments we are doing to try to find WIMPs in underground detectors, in the sky, in the lab, have a set of corresponding experiments we'd like to do for axions, but they're different experiments.

So people are still doing those experiments, and we're very hopeful we'll find either WIMPs or axions, and might even get especially lucky. The best universe, if you're a theoretical physicist, would be one in which half the dark matter is supersymmetric particles, and half is axions! We'll actually have to do the experiments to see whether nature is so kind to us as that.

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