sábado, 26 de novembro de 2011

8. The Standard Model of Particle Physics - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe



As promised we now get more systematic as we step through the Standard Model of particle physics. This effort to characterize dark matter and dark energy seems to have started a new and large cycle on the atomic scale, eventually to return to the cosmological. The observations of last lecture now cycle back to the theory of this one.

Only three fermions and two bosons make up the grand total of visible matter, yet this is only 5% of the universe. Might the 95% be made of something from our Standard Model?

Lets face it, there are an overwhelming number of particles and forces with enough combinations of properties and symmetries to require categories of doublets, octets, groups, families, and generations. So I will only include highlights and conclusions.

The lecture and course guide presents the Standard Model well enough, and the appendix is also helpful so I won't duplicate that. But from early on and throughout, it hints that dark matter is not composed of any particle we are yet aware of. We are looking for a stable, electrically neutral, weakly interacting, massive particle not affected by the strong or weak forces. Dark energy is even from an entirely different model. So it seems this lecture and the last are just as much to prepare for the rest of the course on the big bang, as to tell us what dark matter/dark energy are not made of.

The important lecture material not in the guidebook is that of symmetry. The two doublets of the first fermion family pairs the up and down quark and the electron with its neutrino. Each pair turns out to be the same particle with a difference in charge. The up quark's charge of +2/3 is one off from the down quark's charge of -1/3. Similarly the electron's charge of -1 is one off from the electron neutrino's charge of 0. This hidden or broken symmetry is the reason for the Higgs field. Only at high energy, or high IQ, can we see it! This concept will be important later on when inflation is discussed.

The color of quarks has an interesting symmetry not documented in the course guide. As the electron's electric charge is the source of the interactions with photons, the quark's color is the source of the interactions with gluons. The quark color explains the combination of three different colors that make baryons, and the two same colors that make mesons. They all add up to no color, since the red, green, and blue make white. Also since any color plus its color from an anti-particle, also cancel each other.

The gluon is also made of color/anti-color pairs, but not necessarily of the same color. Red can pair with anti-red, anti-green, and anti-blue for a total of 9 possible pairs. Yet one pair doesn't seem to exist, so it makes 8 gluons in total.

More on conservation and symmetry in the next lecture.

In the last lecture we talked about atoms. There's a lot of different kinds of atoms that we know about. They make up all of chemistry and they string together to make up all of biology. We have a periodic table of the elements to explain how the different atoms fit together to make atoms. The remarkable fact is that an atom is just a different rearrangement of three different elementary particles, the electron, proton, and neutron, with the electron spinning around the proton and neutron in the nucleus.

Then we know that the proton and neutron are both made of smaller particles called quarks. You only need two kinds of quarks to make protons and neutrons, the up quark and the down quark. So you have three fermions that make up everything you've ever seen in the universe, the up quark, the down quark, and the electron. They're held together by two different kinds of bosons, the photon that carries the electromagnetic force, holding the electron to the atomic nucleus, and the gluon that keep the quarks together, inside the proton and neutron. So that's five kinds of particle that describe everything we've ever seen in the universe.

However, the theme of our lectures is that all that stuff, all that ordinary matter is only 5% of the universe. Who really cares about the 5% of ordinary matter? We're interested in the 95% that is the dark matter and dark energy, which we'll say later are not made of electrons, protons, and neutrons, not any arrangement of up or down quarks, or electrons for that matter. We need to find some new particle to make up the dark matter.

So in this lecture, we'll go through all the known kinds of particles. It turns out that there are more particles that exist, that we know about in nature, that we've discovered through doing experiments, than just the two quarks and the one electron. They fit together in nice patterns, and together all these particles and their patterns are called the standard model of particle physics.

So in this lecture, we'll go through all the particles of the standard model, a total of 12 different kinds of fermions, and 5 different kinds of bosons. We'll systematically point out why they can't be the dark matter, and no particle of course can be the dark energy, so we're stuck with that as a mystery as well.

When we're thinking about what could be the dark matter, it's something that is massive. It's heavy enough to be slowly moving. It's weakly interacting, which means it does not feel the strong force or the electromagnetic force, and it's electromagnetically neutral.

Of all the particles in the standard model, there are some particles characterized by those properties, namely what we call neutrinos. So we'll explain why in some detail, neutrinos are almost good enough to be dark matter particles, yet not quite. So lets get along because the standard model is so complicated, we'll start by giving away the punchline, telling us all the particles, then we'll back up and be a little bit more systematic, saying why we believe all those different particles are there.

We see a picture of all the different fermions in the standard model of particle physics. All the 12 different kinds of matter particles that make up what we find in particle experiments done all over the place. So we see that they come in patterns, with a set of three families, with four different fermions each. We see a pattern of four fermions, which is repeated two more times.

The lightest family contains all those three particles we've already talked about, the up and down quarks, and also the electrons. Yet there's a fourth particle there, which will be called the neutrino. The neutrino and electron together, make up a doublet (a pair) of fermions that are not quarks. We mean that these are fermions which do not feel the strong nuclear force.

So you have a nice kind of pattern in which there are four particles, where two of them form a pair that do indeed feel the strong nuclear force, and we call those quarks. Yet the other two form a pair that don't feel the strong nuclear force, the electron and neutrino, which we call leptons. That kind of makes sense, and then it's repeated again and again, which actually doesn't make sense! At this point in our knowledge of the universe, it's a complete mystery to us, why there are three families, or sometimes called generations, of elementary fermions.

Then you have the bosons, in the standard model of particle physics, which have five different types. We've seen two already, first the photon which is the most obvious particle in the world. It carries the electromagnetic force, and is responsible for all of chemistry through the exchange of these photons between different kinds of atoms. Then you have the gluons that will turn out to be eight different types, all carrying the strong nuclear force.

By the fact that there is something called the strong nuclear force, we'll probably have guessed that there is something called the weak nuclear force. This is carried by three different bosons, the W that comes in a positively charged type and a negatively charged type, and the Z boson that is neutral. So the W+, W-, and Z, are the three bosons that make up the weak nuclear force.

Then of course you have the graviton, the particle that carries gravity, which is the most obvious force there is. Yet the graviton is hard to find, since gravity is so weak and we have a difficult time decomposing the gravitational field into its individual particles. Yet the basic tenants of quantum mechanics say that it should be there, so most of us believe there is something called the graviton.

You may have heard that there are four forces of nature, which are the ones just described. The electromagnetic force with the photon, the strong nuclear force with the gluons, the weak nuclear force with the W and Z bosons, and the gravitational force with the graviton.

The fifth kind of boson in the chart, is called the Higgs boson, which does give rise to a force, just like the other ones do. Yet it's a little bit different since it has no spin, like the other particles, and most importantly it has not yet been discovered. So we think that there are five forces of nature in the standard model of particle physics, yet we've only found four of them yet.

So that's the general picture, so let's back up a bit and ask how we know, how do we get to the point that we believe in all these different kinds of particles? The neutrino in particular, doesn't feel the electromagnetic force or the strong nuclear force. When we say that a particle doesn't feel the electromagnetic force, we're saying that it's electromagnetically neutral, so it has no charge. The electron has charge -1, the up quark is +2/3, the down quark is -1/3, the neutrino is 0. So if the neutrino doesn't feel either the electromagnetic force, or the strong nuclear force, the question is how do you find it? Of course that's exactly the reason why it was the last of these four fermions to be discovered, since it's so hard to find.

It does however, feel the weak nuclear force. It turns out that every fermion in the standard model, feels the weak nuclear force, so that's how you find it. As a matter of experimental history, the way in which neutrinos were figured out, was through the decay of the neutron. It's a heavy particle, made of two down quarks and one up quark, yet is unstable. Left by itself, it will decay with a lifetime of about 10 minutes.

The reason why neutrons exist in nature in such abundance is that when you stick them together with protons, into an atomic nucleus, they can become stable. That's why some nuclei are stable and some are not, since you have to stick them together in exactly the right combination. Yet all by itself, the neutron sitting there will decay in a lifetime of about 10 minutes.

When people first observed these decays, they saw a proton coming out, and an electron coming out. That kind of made sense, since the neutron is a little bit heavier than the electron plus the proton together. The neutron is electrically neutral, and the proton has a positive charge which exactly cancels the electron. So it makes sense that the neutron would decay into a combination of a proton and an electron.

Yet when careful experiments were done, people measured the energy of the neutron ahead of time, and then the energy of the proton and electron that came out, and they didn't match. So when we talk about the energy, we're of course including the mass of the particle. We have a neutron at rest with an energy from E=mc², and then we add up the rest energy and kinetic energy of the outgoing proton and electron, and you get a number that is slightly less than the energy of the neutron that you started with.

So we're talking about early times, in the 1920s and 30s, when people were reinventing the laws of physics. Quantum mechanics had just burst on the scene, and we were in the midst of a revolution that was getting rid of most of Newtonian mechanics, on the basis of which we've understood all of physics for the last several hundred years. So people were willing to believe that cherished notions were ready to be violated.

So the first thing they did when they realized the neutron was decaying into a proton and electron, with less energy overall, was they said, "Well maybe energy is just not conserved?" Conservation of energy was something they were willing to do away with, to explain the decay of the neutron. Yet Wolfgang Pauli had a different idea, and asked what if energy is conserved, so that the other amount of energy we seem to be missing in this decay is coming out in an invisible particle? He invented such a particle which then Enrico Fermi called the neutrino. This was Italian for "little neutral one." The neutrino is sort of like the neutron, but much lighter, and still doesn't feel the electromagnetic force.

Now in this day and age, we've got a much more complicated theory of neutrinos, so Sean will just tell us ahead of time that the correct description of the decay of the neutron, is a proton, an electron, and what we call an electron anti-neutrino. The reason for the latter name will become clear over the next lecture or two, but it's a neutrino-like particle.

It turns out that Wolfgang Pauli was mad at himself for proposing the idea of the neutrino. He was actually kind of embarrassed because Pauli was an irascible, old physicist, who was famous for making fun of other physicist's bad ideas. Then he came along and suggested a particle that, as far as he knew, could never be detected. He thought of it as a kludge or mistake that tried to cover up something we didn't understand.

Yet these days, we do know better! We know there's an interaction that gives rise to the decay of the neutron into the proton, electron, and electron antineutrino. Therefor, since there is an interaction which produces the neutrino, it must interact. We're just much better now, at building detectors that are able to find very faintly interacting particles. So we have detectors that are able to discover neutrinos in large amounts. In fact we're able to measure their properties.

There's something called the Sudbury Neutrino Observatory in Canada, that actually looks at neutrinos produced by the sun, and looks at different types of neutrinos changing into each other. On the basis of this kind of experiment, we're able to measure that neutrinos have a small non-zero mass. When Pauli first suggested the neutrino, and Fermi developed the theory of it, they set the mass equal to zero, thus taking away its kinetic energy. Yet it turns out that today we know there's a tiny bit of mass in the neutrino.

We're still allowed to ask though, why neutrinos really exist? On one hand we can say that it hardly seems fair for there to be two quarks, the up and down, and only one lepton, the electron. Yet the neutrino completes a pattern. The up and down quarks belong together as strongly interacting particles that differ in electric charge by one. The up quark is +2/3, while the down is -1/3.

Now along with the neutrino, the electron is now a lepton that has a pair, so its other particle differs from the electron by one unit of charge. The electron has charge -1, and the neutrino has charge 0. So there's a pattern where you have two pairs of particles. It turns out that this structure is actually reminiscent, a remnant of an underlying symmetry that we don't see. In the deep down laws of physics, the electron and the neutrino are absolutely identical particles. The up quark and down quark, are also absolutely identical particles.

It turns out that the symmetry relating these particles is actually broken. It's hidden from us, so is a secret symmetry that is not obvious to us. You have to go either to very high energy, or very high IQ points, to figure out that there's some symmetry underlying this. That's the reason we know that either the Higgs boson or something like it exists, because the roll of the Higgs boson is to break that symmetry. We'll talk about that a little bit more later.

Still, even though the neutrino serves a purpose, the other fermions of the standard model, as far as we know, have no explanation. We have this nice structure where there are two quarks and two leptons, which fit together in a family. Yet then in studies of cosmic rays coming from the sky, Carl Anderson discovered another particle called the muon. It looked exactly like the electron, the same kind of interactions, the same charge of -1, and so forth. Yet it was heavier. No one knew how to fit it into the structure of the particles they already knew. It didn't fit into this nice pattern of two quarks and two leptons.

At the time we didn't know about the quarks, but we had the proton and neutron, and they formed a nice pair. Then people just kept finding new particles, so they filled in an entire new family. Along with the up and down quarks, we now get the charmed quark and strange quark. They are another pair of particles which form a doublet. Along with the muon, there is another kind of neutrino. So the old neutrino was rechristened the electron neutrino, while the new neutrino was called the muon neutrino.

Then it all happened again! Another pair of quarks, the top and bottom, and another pair of leptons, something called the tau and the tau neutrino. So there are these three families in the standard model of particle physics. We can see some kind of pattern there, and sounds like some sort of symmetry going on, yet nobody knows precisely what it is. The reason why there are three families of fermions in the standard model, is still a complete mystery.

Then of course we have the bosons of the standard model, the force carrying particles that can pile on top of each other, while fermions take up space so you can't squeeze them too close together. Bosons can pile on top to make a big, noticeable, classical field. So the electric or magnetic field are manifestations of many different photons piled on top of each other, and likewise the gravitational field is a manifestation of many different gravitons piled on top of each other.

So lets go through all the bosons in the standard model, and learn what we need to understand about the forces that hold the particles together that we see. So there is the photon of course, which carries the electromagnetic charge, yet is not itself charged. In other words the electric charge of the photon is zero, so it doesn't feel the electromagnetic force itself. It carries the electromagnetic force between other charged particles. So the electron and other charged particles exchange photons in an electromagnetic interaction, yet the photon itself does not interact with other photons. That's just a true fact about photons, not a fundamental fact of nature. Other bosons do interact with themselves.

For example, we have the gluons that carry the strong nuclear force. They are self-interacting, so they can bump together and interact with themselves. Yet they're much more complicated in their interactions than photons can ever hope to be, which is a little bit less natural and intuitive to us. So it's worth delving into the world of gluons to take a slightly closer look.

The important fact about gluons and quarks, the particles that feel the strong nuclear force, is that they are confined. The strong nuclear force is so strong that we are not able to separate any two particles that feel the strong nuclear force. This is not just because we don't have access to quite enough energy to pull these particles apart, but it's a matter of principle! You cannot pull apart to quarks, far away enough to they look like elementary particles all by themselves. Quarks will always be bound together inside bigger particles which we call hadrons, which are collections of particles that feel the strong nuclear force.

So why is it that quarks are bound together inside strongly interacting particles? The reason is that unlike the electric or gravitational forces that grow weaker with distance, the strong nuclear force grow stronger as you pull things apart. When close together they don't feel that much force, and they just zoom around. Yet if they try to separate, the force becomes stronger and pulls them back together.

So pulling apart two strongly interacting particles like quarks is like stretching a rubber band, and trying to get a rubber band with two ends to break, where you only have one end over here and another end over there. You cannot break a rubber band with two ends to make two separate ends that aren't connected to each other, because it snaps and you just get two more ends! Every time you have a piece of rubber band, there are always going to be two ends, so that you won't find one with just one end on it.

That's how the strong interactions work. If you pull apart two quarks, you will make a new "quark, anti-quark" pair in between, and they will snap off to make two more bound systems of quarks. You will never see a free quark or a gluon all by itself, because they are so strongly interacting. In fact, as a little preview, this idea that when you pull things apart and they snap like rubber bands, is the origin of the idea that instead of little particles, we're dealing with little loops of string. So if you chase that concept to its logical consequences, you end up with something called string theory. Yet this turns out not to be such a good theory of strong interactions, but is a good theory of gravity, as we'll talk about later.

So that's the important feature of quarks and gluons, their being confined. Lets think about into what kinds of particles they become confined. When people looked at all the different strongly interacting particles they could find, all the different hadrons they could find, they noticed the important fact that they always came in one of two varieties. Either they were made of three quarks, or one quark and one anti-quark. You never found a collection that was made of only two quarks, or two quarks and one anti-quark. It was always either three quarks or one quarks and one anti-quark. Of course three anti-quarks would work just as well as three quarks.

So they gave names to these particles, a baryon for those with three quarks, such as protons and neutrons as the classic examples. Both are made of three quarks each, so both are baryons. If something was made of one quark and one anti-quark, they called it a meson. The pion is the meson that carries the force between protons and neutrons inside the atomic nucleus, is a classic example of a meson.

So people started to wonder why we only found these two combinations of quarks in nature. Why is it that we only find particles with three quarks, or with one quark and one anti-quark? The answer is that you can assign to quarks a quality called the color. Since quarks come in three kinds, they will be either red, green, or blue. These colors act in the strong interacting world, like electric charge acts in the world of electricity and magnetism. The color of a quark is the source of its gluons, just like the electric charge of the electron is the source of its interactions with photons.

So the reason why it's very clever to assign colors to quarks, is because then you can then explain why you only get three quarks, or one quark and one anti-quark, by saying that you ever see colorless combinations of quarks as free particles! If you think about it, from how your tv works, if you have red, green, and blue shining, they appear as white light. You can combine them together to make white. You could also combine red and anti-red together to make a colorless combination. If you like, you can think of anti-red as cyan, anti-green ad magenta, and anti-blue as yellow. Yet most physicists forget that and just call them anti-red, anti-green, and anti-blue.

So a quark and anti-quark make a colorless combination, a red and anti-red, or a green and anti-green. That's why you get only these two kinds of visible particles made out of quarks and gluons. You must combine quarks and gluons together into combinations that have no net color. Those combinations are either baryons or mesons.

Gluons, sadly, are funny. They're a little bit difficult to explain, and every gluon carries simultaneously a color and anti-color. So you'll have a gluon that is labeled as green and anti-red, or blue and anti-blue, and so forth. So if you count in your head how many different possibilities, there should be nine:

red and anti-red
green and anti-green
blue and anti-blue

red and anti-green
red and anti-blue

green and anti-red
green and anti-blue

blue and anti-red
blue and anti-green

Yet one of these is missing. There turn out to be only eight gluons in nature, and this is one time in these lectures where we have to say, "You just have to trust me on this one." There are complicated mathematical reasons why that ninth gluon isn't there, the one combination that doesn't exist in the real strong interactions. Yet roughly speaking you can get pretty far thinking of the gluons that exist, as combinations of color and anti-color. So if you're going to join them together, you're going to still have to stick to that rule that we only see colorless combinations.

So those are the bosons we know, the photon and gluon, but what about the weak nuclear force? We mentioned it was carried by W and Z bosons. The Z is all by itself as a neutral particle, sort of like the photon, but it has a huge mass. The photon has zero mass, being massless and moving at the speed of light, while the Z boson is also electrically neutral all by itself, but very heavy. The W bosons are also very heavy, one positively charged and one negatively charged. Together these three kinds of particles carry the weak nuclear force.

In fact, the reason why the weak nuclear force is weak, is because these W and Z bosons are so very heavy. If you think of forces as being manifestations of bosons traveling back and forth, photons and gravitons, which are massless do so very easily. Gluons are also massless and travel only a short range, yet still travel back and forth very easily. Therefor all of these things can stretch over distances and still be very strong. Weak bosons, the Ws and Zs, are very massive, so it's hard to get them to travel from one particle to another. That's the reason why the weak nuclear force just doesn't seem very strong. It takes a lot of "umph" to make a W or Z boson.

In particular, lets think of an example of the weak nuclear force at work. There is one classic example, the decay of the neutron. One of the reasons why that neutrons last so long, is that the interaction which helps it decay is the weak interaction, which happens very infrequently. Neutrons last about 10 minutes, which might not seem long to us, yet to an elementary particle, it's incredibly long.

All these other particles of the standard model, which seem to be unstable to us, like the top or charm quark, decay away very quickly. The neutron lasts relatively long, because that decay of a neutron into a proton, electron, and anti-neutrino, is actually a manifestation of the weak interaction. So we saw a little picture of a decay of a neutron, into an electron, proton, and anti-neutrino, yet here is a magnified view of that picture. What is really going on is that one of the quarks inside the neutron, emits a negatively charged W boson, and in the process it converts from being a down quark into an up quark.

In other words, the neutron that was two downs and one up, becomes a proton of two ups and one down. The W that gets spit off, then decays into an electron and an electron anti-neutrino. So we have a better understanding of what happens when that neutron is decaying. It's really first emitting a W boson, which then decays itself. This is very paradigmatic of how modern particle physics works. We take an interaction that we see, that makes sense to us, yet to understand it better we zoom in on it and see other more complicated interactions going on inside. So those are the bosons that carry the weak nuclear force, the W+, the W-, and the Z boson.

There's also of course the graviton which carries the gravitational force that's so very obvious to us, keeping us on the ground. We ordinarily think of it, as Isaac Newton would, as some force traveling between massive bodies, or if we're Albert Einstein, as some manifestation of the curvature of spacetime. Yet if we're good quantum mechanists, we think of it as the exchange between us and the earth, of a whole huge number of gravitons. We're all certain that there exist such things as gravitons, which are just the quantum mechanical version of gravitational waves. Yet each individual graviton interacts so very rarely, it's almost impossible to detect it. So in fact, there's no plans in the immediate future, or what we should call the foreseeable future, to build a detector that would be sensitive to individual gravitons, even though we're sure that they are there.

Finally we have the Higgs boson, a little bit different from the others. The photons, gluons, and weak bosons, all have the same amount on intrinsic angular momentum. The graviton spins twice as fast as any of them, yet still is the same basic kind of idea. The Higgs doesn't spin at all, an absolutely spinless boson. Of course, it's purely hypothetical, and we haven't detected it yet. So sometimes we'll talk as if we know what the Higgs boson is like, yet what we really have is just a really good theory that predicts it's properties, but we're still trying to test that theory. We're very hopeful that the large hadron collider at CERN outside Geneva will find the Higgs boson explicitly, so then we'll be talking about their measured properties rather than just the hypothetical.

Why do we think there are Higgs bosons there? It's due to the story told earlier on the secret symmetry of the standard model. The secret symmetry between leptons, the electrons and their neutrinos, etc, and between the quarks, up, down, etc. We can understand all the interactions of the particles in the standard model if we promote the rough similarity between electrons and neutrinos and up and down quarks, into an absolutely true symmetry of nature. To do that, we have to explain why we don't see that symmetry, why the electron looks like it has a different electric charge than the neutrino.

The answer is because there is some particle, some field that exists and has a non-zero value, even in empty space. We call that field the Higgs field. It's almost like the Higgs is filling empty space with a kind of molasses through which these particles that would want to move at the speed of light, are slowed down from moving through this medium. The particles we have in mind are the W and Z bosons, as well as every single fermion in the standard model. All of these particles have mass, yet if it weren't for the Higgs boson, they would all be massless!

In yet other words, the understanding according to modern particle physics, of the origin of mass for all the fermions and the W and Z bosons in the standard model, is a hypothetical field called the Higgs field, which we haven't yet detected. Yet you can get an idea of why we're so very interested in detecting the boson associated with this field. It plays an incredibly important role in our understanding of particle physics.

So that's it. That's the standard model of particle physics. We have 12 different kinds of fermions, and 5 different kinds of bosons. So by now we can recall our mission throughout this whole project, which is to try and understand the dark matter and dark energy of the universe. Dark energy we don't think is even made of particles, but is a smoothly distributed energy density, about the same amount in space and time. We'll get to it in great detail of course.

Yet dark matter is made of particles. Could it be any of the particles we listed in the standard model? The answer is no. The thing we'd need to have to make a dark matter particle, is something that has a mass, yet is neutral and stable. The only stable and neutral particles in the standard model are the neutrinos. For a long time, people were hopeful we could understand dark matter as neutrinos. Yet the fact is that even though they do have a mass, it's still too small to be the dark matter. It's not so small that you can't get enough energy density to be the dark matter, but if you do, you have particles that are very light, yet moving close to the speed of light. That's not what you want in a good dark matter particle!

If the neutrinos were the dark matter, they wouldn't form galaxies and clusters of galaxies. They would come together as if they were going to do so, yet then just keep on going, close to the speed of light. You would not see in our universe, the galaxies and large-scale structure that we know to be there, if neutrinos were the dark matter.

So that's bad news in the sense that we don't know what the dark matter is, yet it's good news in the sense that 25% of the universe is something we haven't yet discovered. We will discover it as we look more closely, so in subsequent lectures we'll go into details about what that dark matter might be.

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