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MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we talk about nuclear fusion. And what we mean by fusion is the energy production by two light nuclei fusing together to produce a heavier one which is more tightly bound. And again, we can understand this from the empirical mass formula, OK? So the difficulty in nuclear fusion is that we now have to overcome the Coulomb barrier from the other side. So we have to bring two light nuclei together, have to overcome the Coulomb barrier in order to form this heavier and more tightly bound state. You might think that you can just take a two beams of protons like we do at the LHC, bombard them, and create heavier nuclei. But the problem is that most of the nuclei will scatter elastically, and will not lead to a new-bound state. So the practical way to overcome the Coulomb barrier is by creating a confined mixture and supplying heat, such that the thermal energy is enough to overcome the Coulomb barrier. You can estimate ho...

MARKUS KLUTE: Welcome back to 8.701. So we continue our discussion of nuclear physics. And in this lecture, we talk about the nuclear force. Now, in the last lecture we saw that nuclei are bound together, and we were able to calculate using an empirical model the binding energy of various nuclei. Now, the question remains, what is actually binding those nuclei together? If you remember, I mean, in the first weeks and months of this lecture, we looked and discussed various interactions between elementary particles. We saw the electromagnetic interactions, the weak interaction, and the strong interactions. There was no discussion of the nuclear interaction or the nuclear force. Now, what is this? We have seen that the strong force acts between quarks and hadrons. For example, we have discussed at length the pion, the pion, which is made up of an up quark and a down quark. And those are held together or bound together via the strong force. And we looked also at the structure...

MARKUS KLUTE: Welcome back to 8.701. In this video, we talk about nuclear binding energies. But before we get started on this topic, I would like you to have a look at this table or this diagram, which shows nuclear abundances in our solar system, so how many atoms of the various types are present in our solar system. And you see this super interesting structure. Most of it is hydrogen here. And then there seems to be some sort of an excess of iron. And, you know, this table goes all the way to lead and beyond. There's a little bit of a gap here. So how is this possible? How did this particle get there in the first place? Why is there some which are more frequent than others? A very interesting question which we will be able to answer at the end of the discussion of nuclear physics. And the first starting point is to understand why nuclei are stable in the first place, what holds them together. And that's the discussion of binding energies. So we can very simply w...

MARKUS KLUTE: Welcome back to 8.701. So this is our last video in the chapter on neutrino physics. And we'll talk about mass scales and the nature of the neutrino particle very briefly. When we think about how we can measure the neutrino masses, there's a number of methods which come to mind. The first one is to just look out into the universe and try to understand how much matter in total could come from as a source of neutrinos. And one has to make assumptions about the model, the cosmological models at hand. But if I accept those potential biases or model dependencies, one finds that there's a potential reach of this kind of measurements of 20 to 50 MeV, millielectron volts. And the current best limits are in the order of 0.1 to 1 electron volt. A second source, and I'll talk more about this later, is the study of neutrinoless beta decay-- double beta decays. Here, the current best limits are on the order of 0.2 to 0.4 electron volts. And there's a ...

MARKUS KLUTE: Welcome back to 8.701. So in this video, we want to look at experimental studies of neutrino oscillations. The first question is, where do we get the neutrinos? How do we produce the neutrinos? The answer is, there's numerous sources for neutrinos. You might be lucky and find them in supernova explosions. Or if we're really trying hard, we can observe them as relics of the Big Bang. There is a lot of neutrinos as a relic of the Big Bang around us. Problem is that they have very low energies and are difficult to observe. Easier-- so is the use of neutrinos in the-- generated in cosmic ray showers. There's a lot of neutrinos coming from the sun. Beams, beamlines-- accelerators can be used to smash particles into a material, and then in the decay product, produce also neutrinos. And also, reactors. Nuclear reactors can be used as neutrino sources. By the way, neutrinos can also be used in order to monitor the nuclear activity around the globe. OK. S...

MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we have a very brief view at the current status of Higgs boson research. And I have to tell you that we could spend an entire week discussing this. I just give you the high-level overview, maybe the 30,000 feet kind of overview of what we know about the Higgs boson. On the Canvas page, you'll find a reference to a summary report, which gives you a little bit more information than I give you here. But I do think that there's a few things to highlight. And those are the ones which I'm going to talk about. The first part is that we have discovered the Higgs boson in decays to photons and also in decays to the Z bosons. Where the Z boson itself decays into a pair of leptons, electrons and muons. And the detectors we have available-- and here is an example for ATLAS and for CMS-- they are very good in measuring with precision the energy or momenta of photons, electrons, and muons. So this allows us to then re...

MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we look at the interaction of W bosons with quarks, or the charged weak interaction of quarks. Let's just make a number of observations. Now, we observe that the weak interaction respects the lepton generation, meaning that a W couples to an electron and an electron neutrino, but not an electron muon neutrino. But in the case of the quarks, there is violation of this. So there is a disrespect of the quark generation when it comes to the interaction with Ws. So when you investigate these two diagrams here, you find that the W couples to the V quark and the U quark, but it also couples to the S quark. S quark and the U quark, all right? In order to encapsulate this, we have to make a correction. And the corrections are typically called cosine theta C and sine theta C. Theta C is the Cabibbo angle, so theta Cabibbo. Turns out this is rather small, so it's a decrease. So it is a correction, a small correction. W...

MARKUS KLUTE: Welcome back to 8.701. So now after we introduced the weak interaction and the Feynman rules for weak interaction, we can now look at decays of muons, and in this case, the decay of a pion. Decay of the pion is specifically interesting. And we discussed the decay of the pion before when it came to the discussion of helicity states. Now, let's look at this again with the information we have and what we learned. Now, if you look at the pion decay, the two or three leading decay modes are given here. The one is where the pion, in this case a negatively charged pion, decays into an anti-electron neutrino and an electron, or V or the W in a muon and an antimuon neutrino. If you look at this in the rest frame of the pion, we can see that the neutrino and the lepton, charged lepton, are produced back-to-back. Now, the spin of the pion is 0, which means that the opposite-direction outgoing leptons have to have the same helicity states. Since the neutrino is mass...

MARKUS KLUTE: Welcome back to 8.701. So in this section, we look at electroweak unification. So the aim is to combine the weak and the electromagnetic interactions. The issues we can see here are first, the strength of the interactions are very different. This can be mitigated by the fact that we have heavy gauge bosons involved, and we have seen our heavy particles as being used as mediators to kind of change the strength of the interaction. So this might not be a big issue. The second problem is that the structure of the coupling is very different. We have seen for QED that they are the vector coupling and for weak interaction that they are the vector-axial coupling. This 1 minus gamma 5 is vector minus axial coupling. So one way to mitigate this problem is to simply absorb this 1 minus gamma 5 term in the definition of the particle spinors. And I have to warn you, this is a little misleading. And I think that led also to some of the confusion we had in the class before...

[SQUEAKING] [RUSTLING] [CLICKING] MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we open a new chapter of weak interaction. So we are one by one adding together the components we need in order to describe all elementary particles and their interactions. And I'll be adding the third form of interaction. After the QED and QCD, we enter into the discussion of the weak interaction. So let's have a look at the standard model. So we discussed gluons and QCD. And we saw that gluons couple to themselves and also to all quarks. Because they carry a charge under the-- on the QCD, a color charge. We have also discussed the photon, and seen that the photon, they do not couple to themselves, but they couple to all charged elementary particles. Those are the meta particles, the fermions. The photon also couples to the W boson. We call it the electrical charge. So now what we want to do in this next chapter. We want to fully understand the W and the Z boson. And we wil...

MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we want to talk about asymptotic freedom, about confinement, and also the running of the strength of the strong force. In the recitation, we already talked about vacuum polarization, QED, and how it relates to QCD. So here we're just going to remind ourselves again about what has been discussed here. So loop contributions in QED, they make the effective charge a function of the momentum transferred q. So the coupling strength increases with larger values of q squared. So a leading order, you have to consider this diagram. And you find that there is a correction coming from this kind of diagram. m here is the mass of the particle involved in this correction. But as you know, in perturbation theory, you have to consider all possible diagrams. And this is being done here. So if you consider those higher-order diagrams, you can rewrite the running of the QED coupling as the coupling at q squared of 0 divided by 1 mi...

MARKUS KLUTE: Welcome back to 8.701. So we continue our discussion now of electron and proton scattering. And we dive deep into the structure using deep inelastic scattering. Inelastic here means that we are destroying the structure of the proton in the scattering process. But we have a way to look at the remnant of the proton and also of the scattered electron, and then compare our theoretic expectation for the cross-sections with the finding in experiments. Let me just talk about this in more general terms. The energy of the probing electron or the photon in the scattering process allows us to look at the proton with varying resolution. So at very low energies, we basically see a point-like particle. And then the scattering process looks very much like the scattering of an electron with a muon. If we increase the energy of the electron, we can see that there's an extended charge distribution in the proton. Further increase allows us to resolve the fact that the prot...

MARKUS KLUTE: Welcome back to 8.701. So again, we have now all tools in place to do a next round of cross-section calculations. We have seen how to set up a matrix element. We have seen how to build spin average or to treat the spin, and then specifically to calculate spin average amplitudes using [INAUDIBLE].. All right, I'm not saying that this is all easy now, but you have seen all necessarily elements to calculate a cross-section for QED process. So let's summarize. So we have seen that we can set up some matrix element using Feynman rules for QED. We have seen how to set up the spin average matrix element squared using the traces. Now we would have to evaluate the traces in order to derive this formula here. So I'll spare you a precise discussion of this step here, but you can actually follow this quite straightforwardly. Let me just step back a little bit before we proceed. My goal for the class is not to have you calculate all kinds of cross-section pro...

MARKUS KLUTE: Welcome back to 8.701. So the name of this plan is called Casimir's trick. But what we're actually going to do is we're going to evaluate or learn how to deal with spin information in the calculation of our matrix elements. So now what is it we're trying to do? So the first problem we might have is that we have polarized particles. So we have here again our example of electron muon scattering. And if you assume that the electron and the muons are polarized, you will find as we discussed in the previous lecture that our matrix element is proportional to the adjoined vector of mu 1 times some sort of gamma matrix times the spinor. And we probably have a polarization that is as well included here to give the polarization of the photon involved at the propagating. Good. Now in order to now get a number for M, we actually have to be explicit about the base function of the external particles. And you can do this-- you can just write this down. Howe...

MARKUS KLUTE: Welcome back to 8.701. So we continue our discussion, our development of QED as a discussion of the photon. We have already seen how we can describe electrons and positrons, anti-electrons. And now it's time to actually look at the quantum of electromagnetic fields. A few general remarks first, quantum electrodynamic is a quantum field theory-- the quantum field theory of electrodynamic processes describing how light interacts with matter. Specifically, all processes where a photon is used as an exchange particle involving electrically-charged particles can be described by QED. The photon is in the limit theory particle. And it's a quantum of the electromagnetic field. But the real power in QED lies in the fact that we can describe it as a perturbation theory. We'll see that we can write down Feynman diagrams, calculate them, and use those calculations to describe processes we can observe in experiment. And since we can do this with a very high p...