 Welcome back everybody to the ICTP summer school. Now we have the second lecture of the day, the first lecture of the QCD and Collider Physics series by Matteo Cacciari from the University of Paris, LPTHE. He is an expert of perturbative QCD, Collider Physics, and I hope you will enjoy his lectures just before the start. Let me remind you that if you want to ask a question, if you are free to ask questions during the lectures, by just raising your hand with the zoom option, and then I will allow you to ask the question directly. At the end of the lecture, we will have a Q&A session in case you want to ask a more in-depth and long question. So that's all. Okay, so I leave the floor to Matteo. Please, thank you. Okay, thank you Giovanni. Thank you for the invitation to deliver these lectures and thank you everybody for being here, even if virtually. I would have loved all of you to be able to be interested as well as I would have loved myself to be able to be interested this week. Unfortunately, it's not going to be the case. We have to leave this and I will still try to make the lectures as similar as I would probably have delivered them in person over a Blackboard, meaning I will deliver them by writing over my iPad, my writing notes. This means that you have to live through my handwriting, which is not necessarily great, but hopefully it will be enough to understand. So that's QCD and Collider Physics. So I will talk about QCD and Colliders. I'm not necessarily in this order, meaning that, of course, each of the two components has an impact on the way we use or we actually attack the other. Since the format is a bit unusual, even if now it's been a year we have been living through this, it's still not something that one has been used to do for 30 years, like regular lectures. So it's never very clear how much time it will take and also I'm not very clear yet about what is your background. There may be a lot of difference between what you know of QCD and Colliders among you. So I'll try to be very basic, at least in the very beginning. And then we may pick up some speed later, but this means that since I'm not sure exactly how much ground I would be able to cover or how quickly, I'll rather not commit myself to a precise schedule lecture by lecture. I'll rather give you some sort of, how can I say, a cloud of topics I will work with. So of course we have Colliders, we have QCD, of course. That's the idea. And then what do we do with this? We are going to look, of course, on QCD calculation. It could be tree level, but also especially higher orders, which will lead us to something like infrared and collinear safety, which is one of the key characteristics that will actually allow us to do calculations in QCD. But then more generally, let's say, pattern distribution functions, what we can extract from protons, deep in elastic scattering, which is historically the way we led, we went to pattern distribution functions, Monte Carlos, pattern showers, jets, perhaps too. So I'm hoping to be able to at least touch upon most of these topics. We'll see exactly with what depth and with what kind of order. The idea, of course, is that all these things represent ingredients for predictions. At the end of the day, what you want to do is to be able to use QCD to calculate predictions for collider physics, for the kind of physics that is now being done at the Large Hadron Collider at CERN, but not just there. I mean, in general, some of these things can be used at any colliders in the past or in the future. But today, it's mainly LHC. In terms of what you need to know to follow, hopefully not too much, in the sense that at least at the very beginning, it will probably enough to just be at least a bit familiar with QD and the way you go about and calculate, plus quantum field theory. Quantum field theory meaning not that I will perform very complicated multi-loop randomization on these kind of things, but just to know a little bit how calculations are performed in high energy physics. So if you've taken master courses in particle physics, quantum field theory, and QD, you should be able to follow most of this. This also means that, unfortunately, I will not be able to show you many nice pictures like Celine did this morning. It's a different level. It's much more hands-on in a sense, but that's what you get when your experiment is underground and not up there in the sky. The surprise you have to pay, in the sense it's the other infinity. Sometimes when you talk about fundamental physics, you talk about the physics of two infinities, the infinitely large when you look at cosmology and the universe and the infinitely small when you go down to the fundamental constituents of matter. So this morning, you saw the infinitely large with very nice pictures and very nice, how can I say, big pictures about the universe. And now we look at the infinitely small and we look at the other way that we have to try to understand something about the fundamental forces in the universe. Again, either you look at the universe and you look how it structured, how it evolves, and you try to deduce what kind of interaction or kind of forces shaped it. Or you go and you directly try to get the particles and the fundamental interactions, what interact indeed and see in a controlled experiment how it works. So this is the other side of the mirror in a sense. It's the two ways we go about trying to understand something about fundamental forces. Let me give you some bibliography perhaps before we start. So there are really plenty of lectures online and in particular, even just YouTube is your friend. It's your friend because there are many of these lectures that have been recorded like those of today and this week and have been put on YouTube. And it's a very, very nice collection of different lectures sometimes on the same topic, but by different people that allows you to really get a general idea. So for instance, from this very school over the year, this is some names that gave the lectures in the past few years. And all these lectures, again, are on YouTube. And you can look them up. If you just search on YouTube, ICTP, the name of the person, the year, you immediately find it. And I think you can also find the links from the web pages of the ICTP itself and also with additional materials, light and stuff. And of course, since I'm not reinventing the wheel or the hot water or anything, you will find many elements of my lectures, of course, borrowed and taken from these other lectures. And we all end up doing similar things, each of us with our own style and focus, of course. Another nice set of lectures is instead, the one that you get from the Galileo Galileo Institute in Florence, GGI for short. Again, they do put their lectures online. And in particular about, and I'm here showing, of course, QCD lectures. In particular, on QCD, there is this list of lectures, which again, they span through five days. So they are quite in-depth lectures. And they give you many of the details, you know, you need. And if you don't like to sit through 10 hours of YouTube lecture, even though you may, of course, have realized that you can play them at almost twice the speed. And actually, you can still follow, especially if you already know a little. So I have actually found that it's quite efficient to look through a YouTube lecture at twice the speed or 1.5, 1.75. It's usually enough to understand and really allows you to get in a lot of lectures in half your time. But I'm sure you know this better than I did better than I did. Anyway, so these are the lectures. But then in some cases, there are also written printed materials. So for instance, for Michael Peskin, there is a very nice book on particle physics. I'm not talking about a quantum field theory book. There is a more recent particle physics book, which is more at the level of phenomenology. So you have both the quantum field theory book, of course, Peskin Schroeder, you might know it. But there is also much more recent particle physics book with many details. And then from both Maltoni, Swaye, and Jesse Taylor, there are essentially lecture notes. Lecture notes that, again, are available on the website of the DJI. Then there are a couple, at least a couple, but there are many more, in fact. So Gavin Salam, again, this archive preprint, again, lectures on QCDN colliders, and somebody else, Peter Scantz, also, again, a nice set of lecture notes. Once again, there are many more. I've picked out the ones perhaps I know. What happened there? It stopped. Sorry, I was writing, but it stopped writing for some reason. This is not nice. I don't know what... Do you see the... No, you don't see the number for Peter Scantz. I've written it, so I'm not understanding what's happening. Okay, this is where a real blackboard is still better than an iPad. Let me try. Let me try. Okay, now there is a problem here. Something is really... I'll try to... I'll just try to stop the sharing and set it up again to see if it works. I'm sorry about that. Let's see what happens. I've thought all year this way, and now, of course, let's try again. That seems okay. Yep. Okay, let's see if it repeats itself. So as I was saying, there is Peter Scantz, of course, many more. I've written down the two I know better, the style perhaps that's closest to what I'm doing, but again, there are very many other lectures that you can find on the web. Okay, so we said QCD and colliders. Let's start with colliders. And then you can ask yourself, why do we use colliders? We use colliders because as it happens, breaking things is still the best way to look what's inside. And so if you want to understand what's inside the particles, meaning what is the interaction at the most fundamental level that you can actually reach, the best way to actually find out in a controlled experiment is to smash particles against each other and see what comes out. On the other hand, why QCD? Well, the why QCD is that because especially at hard on colliders, you want to be able to control the environment. You want to be able to make predictions, quantitative predictions, in order to then control what comes out. Because as we will see, the what we actually want to measure, meaning the new fundamental physics, ideally physics beyond the standard model and stuff like this, it's actually quite rare. And it is actually very difficult, if not outright impossible to actually discover something in all the mess, if you allow me the word that you produce when you collide at high energy to protons. It's very difficult to extract meaningful and understandable signals of new physics, unless you control the standard physics very well. So in a hard on collider, the meaning of why study QCD there is not so much to understand QCD. We do understand fairly well at this point. The meaning of understanding QCD is actually to set the stage and to be able to really analyze what we have produced in a reasonable way. And all the more so that today, when we say colliders collider today, actually means the LHC. So which is a hard on collider PP collisions. In the future, things may change a little bit. For instance, people are planning the ILC, the international linear collider that should ideally, and should ideally meaning if it will ever be built, but it should collide E plus E minus, so leptons, an easier collider to work with, but don't be fooled. Even E plus E minus collisions, especially at very high energy, still produce a lot of strongly interacting particles in the form of hard runs. Hard runs eventually will come out at every collider. And so even in an in an E plus E minus collider, QCD will always be one of the important tools that we need to use in order to make sense of the of the collisions. And then in the future, of course, we may have the future circular collider in the electron positon version first, and then eventually, perhaps 50 or 60 years from now, who knows, it's still a machine very, very much far in the future, but we will have a new hard on collider, which will eventually be the successor of the LHC if we'll ever need or want to go too much higher energy. So the reason why we want to study colliders, we want to use colliders is that we want to break things and see what's inside at very small energy scales. And the reason why we want to use the QCD is to actually understand better and make sense of what we will be able to to look at. Mind you, even using QCD in this context won't allow you to calculate everything. We will see that will actually QCD today only allows us to answer only some of the questions. And still these questions have to be framed in an appropriate way so that we can actually calculate things. So it's not like we say, oh, we have a PP collision. Let us calculate how many pions I'm finding in the final state. No, it doesn't work. I mean, would be nice if it worked that way. Perhaps in principle QCD could answer the question, but today we cannot actually answer that question quantitatively. And so we will actually, especially in these lectures, only work with a subset of QCD, which is perturbative QCD or P QCD for short. And P QCD is only applicable in a certain regime will make that more detail later on. And then and it also has to pick appropriately the kind of questions that it can answer. So we are limited by our ability to actually calculate in a theory that potentially we do we do know we do have. So eventually we will we want to be able to calculate again with the restrictions that I'm just mentioning something like sorry, initial state going to some final state. That's what you do in collider phenomenology. You have an initial state set by the machine that has been built. You can't usually escape that, even if the LHC for instance allows you to collide the different kinds of beams, you can collide protons, you can even collide heavy ions. We won't talk about heavy ions today, but it would be a very nice topic for a full week of lectures, of course. So with the answer we want to rather answer in terms of fundamental physics at the level of, let's say fundamental interactions are things like the initial state is PP proton proton, and your final state could be for instance, a hex particle, or you could have some again, PP that goes to let's say jets will make sure to explain later what we mean by jets in the context of QCD. Or again, at the deeper level, perhaps you want to know how often you produce a Higgs that then decays into virtual Z that then gives four leptons for leptons being one of the olala. What's going on again for leptons being come on. This could be a problem. This could be a problem if it does this too often. Try again. These are, I've done this plenty of time without any problem now. Sorry. Okay, let's try again. So these are four examples of a final state that you may want to study at the LHC. And of course, all these final states, you want them to be on one hand, experimentally measurable, and also physically, of course, relevant and useful to study what you want to study. So you look at the Higgs into four leptons because it is a particularly background free process. Other processes like Higgs in, let's say gamma gamma, which is another nice signature of the Higgs. It's good. It's nice, but it has a larger background. So again, this is the kind of trade off that you also have to take into account when you do collider physics. It's not enough to have a nice signal. It's not enough to be able to calculate perhaps that signal quite well. You also need that signal to be reasonably background free. Or at least you need to be able to calculate that background very accurately, something which is not always the case. So again, when you do colliders on one hand, again, with respect to cosmological observation, it is a controlled experiment. You can make choices. On the other hand, some of these choices are quite constrained. And so you have to work around what you can actually do. QCD helps a lot in doing these things. We can do many of these calculations. But again, we cannot calculate everything. So we'll have to choose, in a sense. So let us give a few figures, perhaps. Oh, no, it's not possible. Giovanni, I think I have a problem here. If I have to restart my screen every two minutes, this gets complicated. My mind is fine. It's just that from time to time, what I write here is not, I know I'm writing new things on this page, and I don't see them there. I don't see them in the screen that is shared. You don't see anything under PP24 leptons right now. No. Yeah. And that's the problem. I've been writing something below. And I don't know what happens. Your iPad is connected. My iPad is connected. And I've taught this way all year. But something now is not so... I'm not understanding. Let's try again. But if I have to do this every two minutes, it gets complicated. So we want to give some... Let's try. Yeah, it works. Let's see how long. We want to give some numbers about colliders. So a relevant question are how often we collide things. A related question, which is actually the one that interests us, is how often we observe a given final state. The reason why we are interested in connecting these two questions is that in between there is the dynamics, of course. Something goes in. Something goes out. And in between something happens. And it is exactly that something happens that we want to study and to probe. And so in order to study it quantitatively, we must first establish something. So we have, let's say, a number of events in final state, what we actually measure. And then we have something which is called the integrated luminosity, which is how often we collide things. And then the dynamics I was talking about is actually encoded into a quantity which is called the cross-section. And it is exactly in the cross-section that resides the dynamics of the process. And it is exactly in the cross-section that we must calculate to have a quantitative control of what happens in this particular process. Eventually, what we will do will be to calculate things cross-sections of the following form. So the cross-section for A and B, let's say, A and B could be two protons colliding, giving a final state. This will have the form one over flux, which is a sanctioned normalization factor. The sum over final state of some matrix elements squared, this is where the dynamics will reside, of course, times d-lips, which is the Lorentz invariant phase space. These are all the elements of a typical cross-section that we will eventually calculate. Once again, even if ideally we would like to be able to calculate the cross-section for proton-proton, giving 137 pions in the final state, we actually are not able to do that in QCD, at least not yet. And so we will have to make approximations. So inevitably, we will be able to calculate this kind of process only in certain cases and after having made the appropriate approximations and after having chosen the appropriate observables. Again, there will be a trade-off, there will be a compromise. We will not be able to measure everything, and so we will have to pick the observables that will, at the same time, most teach us something while at the same time being calculable. Okay, so let's some facts about LHC. Now, this is what eventually we will do, but let us see first. This is now a sort of introduction to the introduction. Since we will be dealing mainly with LHC physics, let's see something about the collider itself. As I was saying, we collide Pp at a center of mass energy that I write as root of s of eventually 14 terelectron volt. Just a reminder, a proton is one gv mass. We are accelerating this proton to seven Tv, so more than 7,000 times its mass, so it's a very ultra relativistic proton, very energetic. So the machine, I'm sure you must have seen it, the machine is something like this. Underground near Geneva, actually crossing the border between Switzerland and France, the machine is this ring down here, about 100 meters underground, and the particles are about 27 kilometers in circumference, and then the particles collide at four experiments, LHCb, CMS, ATLAS, and again, I don't believe it, something is really, sorry again, no, we are on it. In the break, I will try to figure out what happens. You can connect independently to devices. Okay, so as I was saying, four colliders, sorry, four detectors, where particles do collide while traveling and crossing themselves over the over the ring, and I'm sure you have seen plenty of time this picture here. Okay, now even the iPad doesn't work anymore. This picture here, which you don't see, if it's something, so a picture of the tunnel of the LHC with the beam pipe, the big cryostats that contain all the cryogenic that then contain the superconducting magnetic field, the superconducting magnets that produce the magnetic fields that actually bend the particles around the ring. So this is how over 27 kilometers you accelerate your particles and then you bring them to collide in the detectors. An interesting fact is perhaps that beams are organized in bunches. So for instance, protons travel in bunches of a certain length in one direction. Other protons travel again in bunches in the other direction, and eventually they meet somewhere, actually in four positions, but let me draw here one in the detector. Detectors that, again, I'm sure you have seen have this kind of aspect. And so this is, for instance, the CMS. They are big cylinders, essentially, across the beam pipe, well along the beam pipe, the beam pipe goes in here and the other way, and then the particle collides at the center. And then once again, this is stopped working. I will have to try to, I will, how long do we have to pause? Giovanni, let's do, again, five minutes. I try five minutes more and then we take a break and I try to reboot everything. In the meantime, let me hoping I will be able to come out of the reboot at all. There's always a bit like rebooting the helicopter in Mars, over Mars. You never know what's coming out of our reboot. Okay, let's do it again. Okay. So I was saying the particles go, the beam pipe here, the beam pipe there, they collide at the center and then you have plenty of things going out and then eventually hitting your detector. The detector is like a multi-layer. You even see the layers here. They are sometimes different detectors sensitive to different types of particles, different energies and so on and so forth. And then eventually you record all the elements of the collision. And just to, let me also show for another detector, which is actually very similar. The idea is always the same. This is actually Atlas here and it has the same kind of structure as you can see. Alice also has the same structure. LHCB is a bit different because it actually collides the proton from the beam onto a target because it wants to see boosted BDKs, but this is a different issue. It doesn't really matter. These four detectors work roughly with the same principle. You collide particles at their center and then they are structured around the place where you want to record and register the results of the collision. And then remember, this is of course the ring of 27 kilometers that I was mentioning earlier. So let's see how many actually, or perhaps, yeah, I think it could be a good idea to take a break now. And then we will talk, once I get my iPad in working order, hopefully, talk about how many particles we actually do get around the LHC and how often they collide and what kind of cross-section or kind of rates we can actually expect. Okay. Yes. It was proposed that you try connecting your iPad as a new participant independently of your video, if you can. Instead of using the shared screen. Yeah, I guess I can try that. Except, yeah, the only problem is that you want, yeah, I can try. Okay, I'll try that. And yes, in one of the two devices, please keep the audio closed, avoid feedback. Okay, I'll try. See you in five minutes, hopefully. Okay, then we take a five-minute space. All right. Actually, I have not connected directly the iPad because I'm not sure if I can then use the note sharing, the note taking app in presenter mode. And I needed to be able to actually shift things from one window to another, but I've connected it differently. So let's see how it goes now. Okay, so let's hope for the best and then see how it goes. Okay, so again, the LHC, big tunnel, big beam pipe, big superconducting magnets, you put a lot of protons inside it and you collide them in certain parts of your detector. So now let's see how many of these things actually, so the beams are in branches, as I said, with a crossing. I want to give you some feeling for how much stuff there is in the LHC, crossing frequency 40 megahertz, meaning that 40 million times a second, once again. Once again, this doesn't work. The other option could be instead of rewriting my notes, I show you directly my notes. It's less pedagogical than as if I were writing on a blackboard, but it could be an option at least until I figure this out. Yes, I think maybe it's, let's try that and see if it works. No, it's really blocked. No, not even that works. Not even that works. Or I can, yeah, let's do, I'll do this. I'll do a PDF of my notes and then I use that. I don't see any other way, just a second. It's not I was planning to do, but let's do this. Let's do this. I'll try to see if I can do something different tomorrow. Okay, can you see this? Yes, I try to put the full screen. Okay, you know something is long here. There are two pages, sorry, just a second. Do it again. Marfield's rule, if something can go wrong, of course it will go wrong. I've literally taught all year this way without a glitch. I missed it. So the possibility of connecting the two devices independently did not work? No, I didn't try because I need to be able to use good notes in presenter mode. And if I directly connect my iPad, I'm not sure I can do that, because I need to have two parallel, two simultaneous windows. Okay, so let's try this way. Should not bother writing 100 notes at this point. Okay, can you see it? Yes. Okay, so again, as I was saying, you're crossing beams made of bunches, almost 3,000 of them per beam, and they cross every 25 nanoseconds, so 40 megahertz, and there are 10 to 11 protons per bunch. And of course, as you see that in a second, you get plenty of protons that eventually see each other. Still, you can realize quickly that that doesn't mean they always collide. Even if 10 to the 20, 10 to the 30 protons see each other every second, that doesn't mean that they always crash into each other. For instance, take the volume of a bunch. While traveling over the LHC, a bunch is about one millimeter across 30 centimeters long, so you can easily get its volume. It's squeezed at the interaction point. It's actually only about 16 micrometers wide, so the density is higher. But still, even if it has a very small volume, 10 to the minus 11 cubic meters at interaction point, the volume of 10 to the 11 protons is still much, much smaller yet. A proton is about the size of 10 to the minus 15 meters. And even if you sum up the volume, so for these protons, you still see that they constitute a very minute fraction of the volume of the beams. So there is a lot of empty space, even if the beams are so much squeezed when they do meet each other. So how often they do collide? That's the first question that we can ask. You collide protons, how often the protons collide? It's not so much the proton collision that we are, I mean, it's not so much every proton collision that we are interested in, but to get a feeling for how often something happens in the LHC, we can do this exercise. So geometrically, and we are looking here just at how often two particles that have a certain size collide each other, you take the luminosity and you multiply it by the cross-section. So the luminosity is given by this formula here. It's called the instantaneous luminosity at the LHC. It's the number of protons in a bunch, the number of protons in another bunch, their crossing frequency divided by the beam cross size, which is, as I was saying, 17 micrometers squared. And you end up with this number here in fairly bizarre units of tuition, centimeters minus two seconds minus one, which tells you essentially how often protons, how many protons collide. And then there is the cross-section of a proton that you express here in, take its diameter roughly 10 to the minus 15 meters. So square it and you get a cross-section of 10 to the minus 30. Of course, you are not interested so much in the instantaneous luminosity, but in how much luminosity accumulate by running the collider all year round or almost all year round. And that's the integral of the instantaneous luminosity times the time. The typical time you end up being able to run a collider is something like a third of a year in an year that are about pi 10 to the seven seconds. As you know, that's not because it has anything to do with pi. It's purely an accident, but it's a nice number to remember. So pi 10 to the second is the number of seconds in a year, divide by three, you get something like 10 to the seven, you multiply by this, and you get this integrated luminosity, 10 to the 41 centimeters minus two. And then you multiply it by the cross-section, the one that you have here, and you end up with about 10 to the 15 events per year. So this is how many proton-proton collisions you get by running one year of the LHC. It seems a lot, it actually is a lot, but it's not the lot we are interested in, because, well, we know protocol lesions since seven years, and it's not really why we build a 10 billion machine for. We want to do something different. The first thing I do, because I will then use the units later on, is to rewrite everything using a new unit, which is the barn. The barn, as you know, if you've already done particle physics, is a unit off surface, and one barn is 10 to the minus 28 meters squared, or 10 to the minus 24 centimeters squared. And so if you rewrite the proton-proton cross-section that we had calculated earlier using the proton size 10 to the minus 30, you get something like 10 to the minus two barn. In practice, what you do the experiment is more like, here we are really estimating the back of the envelope and order of magnitude. If you try to actually measure it in practice, it's more like a tenth of a barn, the proton-proton total cross-section. And also the integrated luminosity, the 10 to the 45 meters minus two per year that we calculated earlier, can be re-expressed in this inverse femtobar per year amount, which is a fairly bizarre unit, but it's something that then allows very quickly to the calculation. So using these units, you can again estimate the number of PP collisions, and you get the same thing, give or take one order of magnitude. Again, we are not really at plus or minus one order of magnitude, 10 inverse femtobar per year times a tenth of a barn. And you end up with 10 to the 16. Well, it was 10 to the 15 earlier because we had used 10 to the minus two. Now it's 10 to the minus one. It doesn't matter. So 10 to the nine seconds, collisions per seconds. Again, it seems a lot. It is a lot, but it is not a lot. We are interested in. In fact, these are even too many to actually record on disk. We cannot record all these collisions on a disk if you wanted to. It's 10 to the nine per second. At the end of the day, if you sum the data for all the channels in a detector, one event is, well, it's smaller than a picture. It's one megabyte. Today's cameras actually do much better than that, but it doesn't matter. If you wanted to write down all the information that the detector gathers from a single collision, you would need to write down one megabyte. But if you have 10 to the nine collisions per second, this wouldn't mean having to write one terabyte per second. There's no technological way to do this today, or at least there's no technological way at a decent cost that allows you to write down one terabyte per second. You have to reduce this by at least a factor of three, 10 so that you can write something like one gigabyte per second. One gigabyte per second is doable with cost-effective technology. So you might say, fine, what's the problem? We have so many collisions. Just take one every 1000 and we're done. Well, it's not so easy because those so many collisions were collisions that were not really interesting. We are interested in something that is actually much rarer. And if you start throwing away if you start throwing away 999 collisions every 1000, you end up being left with very few of the interesting collisions you are actually interested in. And I'll give you an example. So let's estimate cross sections using a different unit that will then help us calculating different kinds of cross sections. So we said the cross section is either centimeter squared or barns. Now we want to use a third unit to write down a cross section. And this is inverse energy squared. Why we can use inverse energy squared? Because there is this combination of fundamental constants h bar and c, which can be written in MeV, so energy unit times femtobar distance unit. When you go to natural units, h bar equal c equal one, then you can just convert quickly something like the proton radius 10 to the minus 15 meters. So one femtometer, sorry, in one over about 200 MeV. Remember this number because it will also come out again later when we do QCD. For the moment, just remember this thing. Proton size equal one over 200 meters, 200 mega electron volt. Remember this unit. Remember this number. We'll meet it again. So the sigma pp cross section, we estimate it again using these different units, one over 200 MeV squared. And then you can convert these two barns using h bar c squared. This will give you the conversion, but you can go back to what we had before. But remember this one over 200 MeV squared. Now consider now a cross section instead for weak interactions. Proton-proton is, again, things from the 50s. Now we want to do more modern stuff. We want to go towards weak interactions and then eventually beyond standard model, Higgs or beyond standard model. A cross section for weak interactions is in first approximation proportional to G Fermi, the Fermi constant, which controls in the Fermi model the weak interactions. Even I don't even need to go to W and Z bosons. Just use weak interactions from the 50s. GF is something like 110 to the minus 5, GeV to the minus 2. Very conveniently, it already has units of energy minus 2, so it's directly an estimate for a cross section. I could have used one over 100 GeV squared, the mass of the W boson, but it doesn't matter. It's the same thing. So this tells me that if I compare now Sigma weak, any weak process roughly, with Sigma PP, I get 10 to the minus 7. So I get a weak event only once every 10 million PP events. And now you see that if you start throwing away indiscriminately PP events, you're not left with so many weak collisions. This gives you an idea of the different sizes. Here is the total Sigma PP. Here is the 0.1 barn we were mentioning earlier. Down here is our estimate for the typical weak cross section. So at least six orders of magnitude. We estimated seven, but again, it's order of magnitude calculations plus or minus one doesn't really matter. But if you want to do even rarer processes like Higgs, for instance, look at Higgs. Higgs is down here. Another something like five, six orders of magnitude. Double Higgs, which is fundamental to actually get this Higgs self-coupling measured, something we cannot do yet at the LHC, is even lower. So you see, this is something like 13 orders of magnitude with respect to the total Sigma PP. So this tells you how rare the real interesting collisions are with respect to the total rate of collisions that we produce. And we have to produce so many because we want to extract the very rare ones that then are the interesting ones. So this actually tells you, well, a couple of things. It tells you why you need to spend so much money in colliders because you need to have a large energy, but also a very large luminosity in order to produce sufficiently many collisions. And it also tells you why you need to perform quite detailed phenomenology calculations and predictions because you will have to control backgrounds that sometimes can obscure very, very rare events. So even if, as I was saying earlier, breaking things, it's still the best way to discover something. One usually gives the example of, well, colliding protons is like throwing two garbage cans and then seeing what flies out. Sure, fine. The problem is, most of the things that fly out from these two garbage can collisions are not the things we are interested in. We are interested in some details that we have to go and look in very rare cases that come out of these collisions. And here there are some numbers. So Higgs boson, for instance, has a cross-section of 10 to the 2 picobarga. So even in an LHC with full luminosity, 10 inverse femtobarga, you would still get only 10 to the 7 events per year. And they say only because then most of the decays of the Higgs would be buried in the background, you would never be able to see them. And you can only see some rarer decays that would further reduce the number of useful events. And this is an example here. The branching ratio of Higgs into gamma-gamma, which is one of the main discovery channels, is only about one in a thousand. So that 10 to the 7 actually already comes down to 10 to the 4th, and then you still have to detect all these things. Also, when we discovered the Higgs about 10 years ago, the LHC was not yet delivering 100 inverse femtobarga per year. The discovery was made with about five. So again, you cannot really afford throwing away things. And even rarer, but this time with less background at least, Higgs discovery channel is the one I was mentioning earlier. Higgs that goes to ZZ that goes to 4 leptons. And eventually the Higgs will discover with about 10 events per experiment in this channel. So again, if you had from the very beginning thrown away all, I mean, 999 events every 1,000, you would never have accumulated the 10 events you would have needed for discovery. These are the plots of the discovery. You see here this is the gamma-gamma channel. And you see here the little bump of the Higgs discovery over background in the gamma-gamma channel. And here is the discovery in the 4 lepton channel, where at least you see a nice peak and the background is a lot flatter. So this was easier in a sense. This is almost background free. But on the other hand, look at the number of events. These are events. So you have perhaps 10 events. You would never have seen these events if you had just thrown away all collisions, but one over 1,000. And so the way out of this is selective triggering, meaning that what the experiments do, they look very quickly at each collision and they decide whether the collision actually contains potentially interesting physics or not. And they throw away the others. Needless to say, in order to do this, you have to be able to tell, to predict how many collisions out of the interesting ones your trigger is keeping, because then you want to be able to measure the number of events and then measure across sections. So you cannot just do this without any idea of what you're doing. And this is where again, simulations and predictions come in. Triggers, various levels of triggers in the experiments are devised making use of predictions of production cross sections, both for backgrounds and for the signal. So this goes in the direction of what you want to discover these days in colliders is way too delicate, way too buried inside everything else to just do it without an accompanying phenomenology that calculates things and predicts things and actually allows you to prepare yourself for what is going to come. If, I mean, most of you are definitely too young to know this, but one of the incredible feats I would say of the LHC was that it went in two years, 2010, 2011, 12, from switching on the machine to Higgs Discovery. It was done in two years. 20, 30, 40 years ago, it would have taken two years just to understand the detectors. The LHC was able to actually start up and running immediately because all the simulation work that had been performed to prepare the experiments. So everything had been simulated properly, everything had been studied so that people knew how they, I mean, roughly knew what kind of behavior they detectors would have had thanks to even detector simulation and people knew what kind of events they would have expected with kind of topologies. They were able to prepare the analysis beforehand and so on and so forth. I say this to you because today you may take this as absolutely for granted. Of course, we can simulate, of course, we can run a Monte Carlo and get a full description of the events from the PP collision down to the hits in the calorimeter. Today we can do this. We can simulate everything. But once again, this is not something that was so obvious even only 20 or 30 years ago. It's really something that has been done in the past 20 or 30 years. Anyway, since today we do have all these things and of course things are still improving. We could prepare the analysis for the LHC. We could discover the Higgs and even today we are still using predictions and simulations to actually keep preparing these things further. So let me now actually say a few more things about what we actually observe in a detector. So far I've been very generic. Oh, yes, we do collide things. Oh, yes, we do measure things in a detector. But let's actually be a bit more precise because then we'll also have how can I say consequences about what we will ask QCD to do. What can we actually measure? Well, not too much in the end. With respect to the zoo of particles that you produce in elementary collision, there are, as you know, there are hundreds of particles. If you take the particle data group booklet, which is the list of all the particles that have ever been observed and measured in particle physics since, well, since almost a century ago, this booklet goes on hundreds of particles. Most of them are not fundamental particles, of course. Most of them are mesons and hydrons composed, of course, but it doesn't matter. You have literally hundreds of them. On the other hand, there are not so many particles that you actually observe in a detector. Because they decay before reaching the detector, remember the detector is something that has a macroscopic scale. The closest layer to the beam are a few centimeters. And that's still quite a technological feat. You can put something at a few centimeters from a beam that delivers quite a huge amount of radiation. But still, you can. The closest layers of the detector are at a few centimeters from the beam. And then these huge detectors actually go out a few meters. But still, the order of magnitude of the distance of a detector is one meter. On the other hand, remember the collisions happen at the level of a proton 10 to the minus 15 meters. So there are a lot of things in between. So the critical number is CtO. CtO is the distance that a particle travels before decaying. And this distance, of course, tells us whether a certain particle produced in the elementary collision, in the hard collision at the center of the detector, will travel enough to hit one of the elements of the detector. Of course, it's a particle decays before traveling far enough to hit the detector. You have no way of actually detecting it. So some particles are totally stable, or at least as far as we know. For instance, the proton, the electron, the photon, the neutrinos. Okay, forget about detecting neutrinos at the LHC, but still they travel far, way far enough. But let's say for the purpose of detecting them, proton, electron, positron, and gammas. In fact, they are so stable, these particles, that not only we can detect them in the detectors, but we can also make beams out of them. And of course, to make a beam, you need a fairly stable particle, not totally so. People are now exploring the possibility of actually building a muon collider. You can, you just have to be quick enough to actually circulate the beams and collide them before the muon decays. But if you are quick enough, you can even do a muon collider. But more generally, you can easily do colliders with particles that are stable, and therefore don't die too quickly. So other particles have a sufficiently long decay length. And so they easily reach a detector. And these particles are neutrons, muons, pions, cairns, cailons, a few hadrons. The lightest hadrons are typically long lived enough that they can reach the detector. And others actually, and so we can see these particles. This is the typical layout of an LHC detector. You have the tracker here. They are typically silicon elements that over which you can actually record the heats of the various particles and then reconstruct the track of the particle from the many heats that you can actually see over these detectors here. So these are the elements that are closest to the beam. And they are typically immersed in a big, strong magnetic field that bends the tracks. And this allows you to reconstruct the mass of the particle. Then you have an electromagnetic calorimeter. As the name says, it detects mainly the electromagnetic particles, so electrons and photons. You have a hadron calorimeter. This is where pions, neutrons, cairns, protons eventually deposit their energy and stop so that you can measure them. This is CMS. So this is the solenoid of CMS that generates the magnetic field that you have inside here. And then out here, you have the muon chambers. The muons are the particles that punch quickly, easily through all the detectors. So they traverse all these detectors here. They traverse the solenoid and eventually you detect them in the muon chamber far out. These are 10, 20 meters out from actually a bit less, sorry, seven meters solenoid. Yeah, sorry. CMS is compact muon solenoid. So seven meters radius is a compact detector. Atlas is much bigger. Atlas is something like 20, 20, 30 meters. So this is the compact one. So you detect eventually the muon sub. So these are the particles, as I was saying, that you easily see in the detector. Then there are other particles. This cannot be 10 meters. I cannot remember. This should have centimeters. I can't remember what I've written. This must be centimeters. These are particles that decay actually very quickly, but we can still somehow observe them. Either we reconstruct the invariant mass of their decays, the displaced vertex in the case of a bottom, for instance, its decay length is long enough that if it's even boosted by a Lorentz boost of the center mass frame of the collision, it gets to those few centimeters that allows us to actually see it when we reconstruct the track in a detector or other characteristics of the decay products, etc. So these are again particles that we can more or less easily pinpoint in a modern detector, like the ones of the LHC. We could not do this 20, 30 years ago, but we can do this in modern detectors. On the other hand, these are not the particles that we are interested in. These are particles that were all known since, I would say, the latest discovery is the bottom quirk in 1976-77. So these are particles that have been known for 50 years. That's not what we are about at the LHC. That's not why we have invested 10 billion years of dollars and 30 years of work from about a thousand people to actually find out. We want to measure weak interactions, we want to measure the Higgs, we want to measure whatever beyond standard model physics may actually or not be there. And everything else, all these other physics must be deduced exclusively from the measurement of these elements. And you see the difficulty, the challenge. The challenge is to measure something that is actually quite far from what we are interested in. We can only see things that at the detector level, we will identify as an electron as a positive on candidate. So a deposit in the electromagnetic calorimeter, and I think I missed the photon, or the photon again, a deposit in the electromagnetic calorimeter, a muon or anti-muon candidate, something in the big muon chambers that are far out from the detector, something that deposits energy in the electron, in the hydronic calorimeter, but also leaves tracks in the tracker. This will be a charged Hadron, something that deposits energy in the hydronic calorimeter, but does not show up as a track, which will be a neutral Hadron, or some missing transverse momentum that could have been carried away by some unseen particle like a neutrin or whatever else we don't, we cannot, a dark matter particle for instance, imagine we produce a dark matter particle in the LHC, it won't interact, probably, or at least not easily. And it may, or it is a long lived one, it may decay into something we don't see, I don't know, I mean, whatever we cannot see can show up as missing transverse momentum, so not seeing something in a detector is actually unobservable. This could be a bit counterintuitive, but that's the case. If you expect to have energy momentum conservation as you do, and something is missing, it means that a particle that you cannot detect was there. So missing transverse momentum is unobservable class, like the others I've listed here. And this is pretty much all you can actually see in a detector. So this is what you can see, what you can measure, and the challenge, as I was saying, is to calculate predictions at the fundamental physics scale, meaning something which is much, much smaller than a proton size, because we know what happens at the level of a proton size, now we want to go deeper and connect it through many other magnitudes to the observation that we can perform in the detector. And to give you an idea of the scales, so this is a very messy drawing that was not meant to be shown to you this way, because I was planning to actually draw it layer by layer at the blackboard on my iPad. Since I cannot do it, I can at least try to explain what happens. So you have here your proton and proton that come in and collide. They go and collide at this point here, and this point is actually at a scale, well, you see, at a scale that it is at the order of the one TV or less. This is the energy of the LHC. Inside here, especially if I go at a size smaller than this, smaller than one over TV, this is where beyond standard model physics has to be. Why? Because we already know, we have already explored what happens down until this distance scale. We know what happens at the scale of a proton, which is one over 100 mg, 10 to the minus 15. We know what happens at 10 g, sorry, at one over 100 gv. And we know what happens at one over one TV, because this is where the LHC has explored. So up until here, so from here to here, we know physics. Now we have to understand what is inside here. But what is inside here, we cannot probe directly. We only see what comes out and eventually reaches the detector. So there are various stages. So this is, as I was saying, a scale one over one TV. We know everything down to this scale, but we don't know anything below that scale. We don't know what happens in that black dot that I have here at the center of my diagram. Now let's start going out from the short distance, hard interaction. By hard interaction, I mean something that happens at a very large scale. At the LHC, very large scale is at least a few tens of gv up to one TV. And from these scale, I want to try to understand what is at even smaller scales. So this is where the hard interaction takes place. And then you produce, and how does this interaction take place? Well, let's first start with the beams. So you have a proton out here. And as you get here, so this is the size of the proton. This circle here is the size of the proton, 10 to the minus 15. A proton is still a proton a bit below the scale. But then eventually I know, I know from QCD, I know from the lectures I will do later on, that inside the protons there are constituents, gluons, that eventually collide in the hard interaction. What collides is not a proton. What collides are constituents of the proton itself. We know because in the past 30, 40 years, we have explored the scale distances below the proton size. We know physics down to about 10 to the minus 18 meters. We know what happens down to 10 to the minus 18. We do not know what happens below 10 to the minus 18, 19. So we do not know what happens inside here, but I do know what happens here. What happens here in this shell that I call the PQCD, pathological CD, and this is where I will be working in the next few days. I know that the proton is made of quarks and gluons. And so I've depicted here in my very bad drawing style something that is not any more a proton, but it is quarks and gluons that eventually collide. So they collide here and then something goes out. But what goes out will be a lot of things. Can be Higgs bosons, can be W bosons, Z bosons, can be supersymmetric particles, can be other BSM particles, I don't know. Or it can be simply quarks and gluons. And this will eventually propagate out from the short distance collision. And then what happens? Well, I know from perturbed QCD, calculate in this shell. Then there is another shell, which is still QCD. I called it hydronization, part on distribution functions and fragmentation functions. This shell here, which is still inside the proton radius, you see. I'm still inside the proton in this shell here. What happens here is that the quarks and the gluons eventually fragment, hydronize into the hydrons that we know. Once they are at 10 to the minus 15 from the hard interaction, once they are as far as a proton size, then they are hydrons. Everything has happened in a sense. From here on, what happens in the, this is not to scale on, this is 10 to the minus 15, this is one meter. So of course, this is the, at the particle level, these shells here, whereas the last shell here is simply at a macroscopic level. So once I've done that, the particle get out here, they may decay, they may just travel directly to the detector. And eventually I get to those sets of particles that I told you before, I can detect in a detector. So you see that, I mean, this drawing was meant to give you an idea of the complexity and of all the stages that one has to go through from the short interaction where things happen, where I can calculate what I know, but some things I do not know may also happen and that we'll have to infer them from the results if I see discrepancies between what I observe and what I calculate. But then a lot of things happen in order to get to the prediction of what happens out here. So you see that by talking about perturbative QCD in these lectures, and we will essentially only be addressing this shell here and a little bit of that one there when I'm dealing with standard processes. But of course, for instance, I will not be talking about this part because it would require a few more lectures just devoted to non-pertuative QCD. On this part here, it's still QCD because it is still something that happens inside a proton. You see, it happens inside the 10 to the minus 15 shell. So it's still inside a proton, but it is not something that I can calculate. The reason will be explained later on. Once you have produced your hydrons, then the hydrons will start to propagate. Now it's macroscopic physics. Now it's, well, it's electromagnetism is whatever you want happens. Its interaction between particles and matter is what happens in a detector. And then eventually you get the detector. But again, I want to stress it again. The challenge and the difficulty is to bridge this huge distance between where things happen, where beyond standard model physics may actually be produced. If you produce a supersymmetric particle, you produce it here and inside this very small black dot. And then you have to infer what has happened by just looking at a few pions, electrons, missing energy, perhaps the odd muon or proton out there. So you see the difficulty of doing these kind of things. So this is exactly what I wanted to say. So this page is essentially described what I've just said. We will use QCD to at least take care of the predictions in one particular shell, knowing that if you want to control the whole process, there will be many other stages that we'll have to take to be taken into account. So QCD is one of these stages, is one of the very important ones at the LHC. If anything, because it's protons that you collide. And so your initial state is made up of particles that are sensitive to the some interactions that QCD tries to describe. But then many other things will also be needed. So then there was a part on the kinematical variables. But since it's already, I think 1530, I think we may perhaps leave it, since it would take a bit, we may perhaps leave it for today. And in the meantime, we also try to fix my technological problem. I'm a theorist. I'm supposed to be technologically challenged. So apologies about that. And perhaps we go to some questions and then I can try to squeeze this into tomorrow's lecture. All right. Then thank you very much for the nice first lecture. And I guess we can move to the Q&A session. So if anybody I haven't followed the chat, so I have no idea what is being asked. I will. Yeah, I will. Okay, so there is the first raised hand. I'm going to unmute Max Varkentine. Please. Yeah. Hello. So thank you very much for this very nice talk. So I have one very particular question about, so you had this slide where you showed the detector and tracks of the particles. And yeah, I think like this one. I was just wondering, so why, so why does the track of the muon reverse its curvature when it is outside the magnetic field? Because the magnetic field changes. Inside you have one magnetic field generated by the solenoid and outside you have a different magnetic field. Okay, but because I would assume that since the so the magnetic field inside is probably homogenous, right? So but then I would assume that so right outside of the solenoid, there should be a very large region where there's no I confess, I cannot remember what shape a solenoidal magnetic field has inside there. You should ask an experimentalist, but the reason why the track is drawn that way is simply to to show that there is a different magnetic field inside and outside of solenoid. Okay, that's weird because it took me. I don't know who is a user. Oh, we have a couple of. Yes. Okay, hello. Hello. Okay. Thank you for the nice lecture. My question will be on this triggering. So you told that we cannot record everything, so we could we need to make a selective triggering. But for example, for Higgs, the gain into two photons, I think just the final particles specified as two photons is not enough selective. So is it always the case that we can find some further features to select enough as much processes that we can record or like how it goes on? I think it could be you should consider that first off one of the main signals that something interesting is happened that you have at least some activity at very large transfer at large transverse moment, because most of the times the protons will come in, will collide, and then whatever happens, we just go down the beam pipe with no big activity in the in the transverse direction. The only way to have activity in the transverse direction is that something very massive is produced or something very massive. I mean much, much more massive than the proton. A proton is one GV. And so the typical fragments will have a transverse momentum of the order of one GV at most, if nothing harder happens. So the only way to have something happening at very large transverse momentum, meaning several tens of GV, is that you produce something of higher mass, 100 GV or something like this. So the first, the probably most effective triggering variable is to make sure that you get something in the detector at large transverse momentum. Two photons or activity in the electromagnetic calorimeter in the transverse direction with a lot of momentum is probably a good trigger for the kind of thing. Then I'm not the person to ask detailed questions about the efficiency of the triggers and the sensitivity of these kind of things. These are really very specialized questions for, I mean, not even for the average experimentalist perhaps, but for the experimentalists that actually work on the trigger. But that's the main idea. The trigger are designed so as to tell you when something, let's say something more than the typical proton-proton collision happens. And one of the ways of actually telling that is if you have significant activity in the transverse direction, meaning a few GVs, and actually here would have been useful that the lecturer couldn't finish because I will talk about the observables, I mean the variables that we actually measure tomorrow, but that's the idea, to observe things in the transverse direction and to have something with at least several tens of GVs coming out. Okay, thank you. Thank you very much.