1 00:00:00,430 --> 00:00:10,530 I think it's sort of like. 2 00:00:10,530 --> 00:00:19,710 So good morning, everyone. Thank you very much for coming. Yes, and we continue basically our journey to go from here to here. 3 00:00:19,710 --> 00:00:27,270 So Lucy, I'm just told you that's roughly speaking now that I see we have this snapshot of protons after the protons, 4 00:00:27,270 --> 00:00:32,040 we get out of gluons and we collide balloons, OK? And then the question is, 5 00:00:32,040 --> 00:00:37,800 how do gluons and quirk and gentle particles interact with each other to give us the Higgs or to 6 00:00:37,800 --> 00:00:43,710 give us any kind of complicated interaction that we measure at the LHC and this guy was discussing, 7 00:00:43,710 --> 00:00:49,170 So how does this work? Now let me start from the very beginning. 8 00:00:49,170 --> 00:00:53,940 So what do we want to discuss? So which kind of system we are talking about now? 9 00:00:53,940 --> 00:00:59,030 We're talking about subatomic particles at very, very high energy. 10 00:00:59,030 --> 00:01:05,820 OK, so you are know that if you talk about something which is very small subatomic, 11 00:01:05,820 --> 00:01:12,210 you need quantum mechanics and you know that if you want something, it is very, very highly energetic. 12 00:01:12,210 --> 00:01:16,270 You cannot use nuclear dynamics. You need to use special relativity like this. 13 00:01:16,270 --> 00:01:21,790 You know, what you may not know is that is what happens when you have to combine the two. 14 00:01:21,790 --> 00:01:27,540 Now you can start to say, OK, I want the theory that respects the laws of quantum mechanics and special reality. 15 00:01:27,540 --> 00:01:34,950 Now, one of the big achievements scientific achievements of the last century is that if you ask for theory which behaves like this, 16 00:01:34,950 --> 00:01:40,620 then there's only one theory that works. So you cannot just combine them randomly. 17 00:01:40,620 --> 00:01:45,510 If you have a theory with respect to the laws of quantum mechanics and special relativity, 18 00:01:45,510 --> 00:01:53,040 at least as a case of energy scale that we're interested in, there's only one way to put them together coherently. 19 00:01:53,040 --> 00:01:58,980 So this way, it's called one theory was discussed already with myself, already by Lucien. 20 00:01:58,980 --> 00:02:05,520 And the interesting thing of this theory is that it's really constrained by the principle of quantum mechanics overactivity. 21 00:02:05,520 --> 00:02:09,790 So they're not theories that we can tweak according to our wishes. 22 00:02:09,790 --> 00:02:17,920 So are completely fixed. So if I have a particle content of my theory, for example, I know that my theory works once a week. 23 00:02:17,920 --> 00:02:21,580 So and I know the symmetry. So Gavin was mentioning, this gets at this. 24 00:02:21,580 --> 00:02:27,870 I know how which kind of. Basically, charge is going south in this theory. 25 00:02:27,870 --> 00:02:31,780 Then this completely fixes to what I what I can get them. 26 00:02:31,780 --> 00:02:38,340 She's extremely nice. Because this allows TSA to do calculation for four percent from first principles. 27 00:02:38,340 --> 00:02:45,930 So we do not model stuff. We really do compute them starting from the basic laws of quantum mechanics and special relativity. 28 00:02:45,930 --> 00:02:50,000 So in order to understand what how quarks and gluons interact and how they interact with a Higgs, 29 00:02:50,000 --> 00:02:55,350 so we need to understand the quantum theory of the strong force. 30 00:02:55,350 --> 00:03:01,410 And this was already introduced up is called quantum dynamics. So it's what that. 31 00:03:01,410 --> 00:03:08,430 How what's influence interact together? And going back to Gavin's T-shirt them is the upper part of the T-shirt. 32 00:03:08,430 --> 00:03:12,450 So this is what the government was saying, that this part is very well established. 33 00:03:12,450 --> 00:03:16,650 So we know that is the right theory. We do not need to check whether this is correct. 34 00:03:16,650 --> 00:03:21,990 We know what is correct. It is well-defined theory. So it then I hear no ambiguities. 35 00:03:21,990 --> 00:03:27,180 Everything is here. It is very, very well established. So is it good news? 36 00:03:27,180 --> 00:03:32,370 Yes, it is good news. Unfortunately, he's also extremely, extremely difficult. 37 00:03:32,370 --> 00:03:38,550 So we cannot really do much with it in general, even with the largest supercomputers, 38 00:03:38,550 --> 00:03:44,950 we can not just to put this theory on a computer and predict LHC rates doesn't work. 39 00:03:44,950 --> 00:03:50,560 So then what can we do? Well, Suzanne was mentioning it already that there is a very, 40 00:03:50,560 --> 00:03:58,720 very nice feature about the wonderful tourism, which is that they behave differently at different case. 41 00:03:58,720 --> 00:04:02,920 And the theory that describes strong interaction is a very, very, very interesting feature. 42 00:04:02,920 --> 00:04:08,360 So at loss case. So the Protoss case, let's say. 43 00:04:08,360 --> 00:04:12,560 It is very strongly interacting. We cannot do much with them from first principles. 44 00:04:12,560 --> 00:04:18,020 We need to go through all the machinery that Alison was discussing mattered very high energy. 45 00:04:18,020 --> 00:04:23,420 So for example, here around the Higgs Mathur, then this year becomes very, very weakly. 46 00:04:23,420 --> 00:04:29,210 Carports in this plot just show you the strength of the coupling of strong interaction goes very, 47 00:04:29,210 --> 00:04:33,980 very large at low scale and becomes very small at high scale. 48 00:04:33,980 --> 00:04:41,150 So that loss gets very large. You cannot do anything from first principles, almost anything from first principles at large energies. 49 00:04:41,150 --> 00:04:48,120 It becomes quite small. So why is it nice? Well, if you're which is weakly coupled is much easier to deal with, and I say what? 50 00:04:48,120 --> 00:04:54,150 You strongly Typekit why? Well, because if the theory is weakly cupholder in the first approximation, 51 00:04:54,150 --> 00:05:00,480 we can imagine that interactions are actually not really there so that we have a theory of free quarks and gluons, 52 00:05:00,480 --> 00:05:08,640 and the interaction is only slightly changing this picture. So in other words, if we have a small parameter, we can compute that this better. 53 00:05:08,640 --> 00:05:12,780 But if expansions that Gavin Anderson were mentioning before, 54 00:05:12,780 --> 00:05:20,440 so I want to compute some observable in a sphere which is with a couple the first I switch off Rick optioning that I can see the first correction. 55 00:05:20,440 --> 00:05:24,600 A second correction is also fourth as much as as I need. Why is this nice square? 56 00:05:24,600 --> 00:05:28,560 Because while one capital is very difficult, we don't know how to deal with them in general. 57 00:05:28,560 --> 00:05:34,500 We have very good techniques, at least in principle, to compute the coefficients and do this function. 58 00:05:34,500 --> 00:05:40,410 These are what we call Feynman diagrams. I am pretty sure you heard the name some, at least at some point. 59 00:05:40,410 --> 00:05:44,890 But let me go through a little bit of more detail for what these objects are because. 60 00:05:44,890 --> 00:05:49,200 This hour, I will need this in the following. So what on the items? 61 00:05:49,200 --> 00:05:55,320 Well, just imagine I want to computer some theoretical prediction for scattering reactions at the collider. 62 00:05:55,320 --> 00:05:56,970 I have some initial state, for example, 63 00:05:56,970 --> 00:06:06,960 to glue on some miniature state and this some interaction happens how to get to some final stage for a couple of weeks up with many other particles. 64 00:06:06,960 --> 00:06:10,040 And I'm interested in this. I mean, see what I can do with this. 65 00:06:10,040 --> 00:06:19,170 This calculation in and if I thought about this expansion now already more than 50 years ago, five month old, I have to do this. 66 00:06:19,170 --> 00:06:21,540 So I said, look for any given theory. 67 00:06:21,540 --> 00:06:28,710 There are only a few set of basic building blocks, for example, for QCT that building blocks, which involve the glue ones, which are this one. 68 00:06:28,710 --> 00:06:32,970 And thus similar ones for wasn't. And he will show me some of that. 69 00:06:32,970 --> 00:06:40,050 Now, why is this important this building block? What do we do with them? Well, just imagine I want to compute the first time in this expansion. 70 00:06:40,050 --> 00:06:46,590 OK, now what? My mentality is that you have to do the following. So take up your initial state and take your final state. 71 00:06:46,590 --> 00:06:49,230 Now, just to make a very simple example, I don't even discuss that. 72 00:06:49,230 --> 00:06:56,890 He's just imagine we want to consider what happens if I have to laws that scatter into Tougaloo so that one of the simplest processes you can imagine. 73 00:06:56,890 --> 00:07:00,410 OK, so I have to glue on in to go to close out. 74 00:07:00,410 --> 00:07:03,450 OK, fine. So what if you are interested in this stem? 75 00:07:03,450 --> 00:07:12,900 What you need to do is to use this building block to connect the initial and the final state in all possible ways, avoiding close close loops. 76 00:07:12,900 --> 00:07:17,850 And I would come back to this one. I think meanwhile, I have this two building blocks. 77 00:07:17,850 --> 00:07:25,410 How can I connect this with this in all possible ways? What I can do with like this, like this, like this crossing and like this. 78 00:07:25,410 --> 00:07:28,740 And that's it. So I have this four different objects. 79 00:07:28,740 --> 00:07:37,050 And the interesting part is that the five months also tell us that each of these objects has a unique expression associated with them. 80 00:07:37,050 --> 00:07:40,710 So if I sum up all this object that we call Feynman diagram, 81 00:07:40,710 --> 00:07:47,890 I get an object that we call scattering amplitude that contains all the non-trivial dynamical information about the theory. 82 00:07:47,890 --> 00:07:53,370 So all the dynamics can be computed in perturbation theory just by summing this bunch of objects. 83 00:07:53,370 --> 00:07:58,470 OK, now this is the first step. What happens if I won the Hyatte, then what? 84 00:07:58,470 --> 00:08:02,220 The punch line is absolutely identical. That's what happens. 85 00:08:02,220 --> 00:08:09,990 Is that every time I move one of them apart, I have to take my original object them and drive them with extra particles. 86 00:08:09,990 --> 00:08:16,710 So either real particles. So for example, I take this object here and emit areal particle, or I can form loops. 87 00:08:16,710 --> 00:08:22,710 So I have this object here. I can create a virtual particle that connects this to and get something like this. 88 00:08:22,710 --> 00:08:32,430 And the rule is that every time I jump one order, I have to add one extra factor five particles, either here or taught in all possible ways. 89 00:08:32,430 --> 00:08:36,960 Now this is what Feynman said Larson told us a long, long time ago. 90 00:08:36,960 --> 00:08:42,120 And as I said, so the interesting part is that this is not just cartoons. 91 00:08:42,120 --> 00:08:47,050 So there are well-defined sets of rules to associate to each diagram in a lengthy form. 92 00:08:47,050 --> 00:08:51,790 And these are my take form when I encodes all the properties of the dynamics of your reaction. 93 00:08:51,790 --> 00:08:57,510 OK? There are two kind of picture that I can draw picture that don't have closed loops up. 94 00:08:57,510 --> 00:09:01,900 So these are called tresa. Because they branch out like a tree. 95 00:09:01,900 --> 00:09:08,140 And they're very nice, because if I use this rule that turned out to be very simple function, a simple, rational function of you off momentum. 96 00:09:08,140 --> 00:09:17,080 And I feel polarisation. So we don't have polarised like photos. So rational functional propositions that if I have close loops is more complicated 97 00:09:17,080 --> 00:09:20,950 because I also have to do something in the grass and I got more complicated functions. 98 00:09:20,950 --> 00:09:25,990 This is a punch line, and he's absolutely not new. So this was very well understood in the sixties. 99 00:09:25,990 --> 00:09:30,580 It's chapter one of every book in almost every book on quantum theory. 100 00:09:30,580 --> 00:09:41,560 And the interesting part is that it is fully algorithmic. So I want to compute the Higgs boson decaying sorry produce a Higgs boson with two tops. 101 00:09:41,560 --> 00:09:46,140 I, like Gavin, was showing you at the seventh saw. Then perturbation theory just drove a bunch of times. 102 00:09:46,140 --> 00:09:51,510 I'm so happy with them. That's it. And I know in principle how to do it. OK. 103 00:09:51,510 --> 00:10:00,070 The question is, how many times do I need in this series to do physics and then we see how many diagnoses to compute? 104 00:10:00,070 --> 00:10:04,680 Now. Just imagine we want to do this expansion. 105 00:10:04,680 --> 00:10:12,660 And I told you that the strong coupling had the Higgs at the scale of elements like physics is more or less point one, 106 00:10:12,660 --> 00:10:19,200 which means that if I only take the first time, I'm not going to get a very precise result. 107 00:10:19,200 --> 00:10:25,560 If I get the second time in Visa, I get something which is more or less 10 percent corrections. 108 00:10:25,560 --> 00:10:32,370 OK. So we cannot neglect these kinds of corrections with showing you we want to go to one percent. 109 00:10:32,370 --> 00:10:37,200 So this is not enough. This is not enough. And we really need to go through very, very, 110 00:10:37,200 --> 00:10:48,930 very high orders in this expansion to get them to be actually able to proper peaks physics at the fundamental level without saying a more or less OK. 111 00:10:48,930 --> 00:10:52,290 So we need to go to very high orders the same principle. We know how to do it. 112 00:10:52,290 --> 00:10:57,680 I thought, you know, we compute a bunch of diagrams with extra some and extra looks. 113 00:10:57,680 --> 00:11:02,390 OK, I'll do this or we need to do. Can we do it, sir? 114 00:11:02,390 --> 00:11:08,120 Well, let's again forget about the Higgs for it for the time being and focus on this very simple example. 115 00:11:08,120 --> 00:11:13,280 I have two choices and two balance out. OK, I want to compute one x doesn't one. 116 00:11:13,280 --> 00:11:16,310 I want to compute this. OK, so add one x w one. 117 00:11:16,310 --> 00:11:23,210 Now, if you just try to draw it on a piece of paper, you will find that that's not so nice because we have that quite a lot of diagrams. 118 00:11:23,210 --> 00:11:27,170 One X doesn't, and you've got at the beginning, we had four. 119 00:11:27,170 --> 00:11:34,340 Glad for you dressed that we want to warn you that 22 and the expression I you get out of I'm on time is not particularly nice, 120 00:11:34,340 --> 00:11:38,180 so it's a rational function, so I want you to read it, but it's rational function. 121 00:11:38,180 --> 00:11:42,320 So it's relatively simple, but it's long, and that's not the end of the story. 122 00:11:42,320 --> 00:11:49,380 So this is a piece of the answer so that it is pretty. 123 00:11:49,380 --> 00:11:57,250 So the simplest possible process to getting one of the most you can imagine you got to take formal notice was the 98 page long. 124 00:11:57,250 --> 00:12:03,590 OK. And then you can imagine if you start adding the Higgs stands at the heart of the particles, how this can behave? 125 00:12:03,590 --> 00:12:10,860 OK. So for example, we want to add one or two hire one to add one more, one more glue on how they look like. 126 00:12:10,860 --> 00:12:17,550 When I was trying to plot this, but my computer kept crashing when I was trying to print, it cannot do it. 127 00:12:17,550 --> 00:12:20,280 But what I can tell you is how many Feynman diagrams contribute. 128 00:12:20,280 --> 00:12:24,720 So if I have two balloons and if I stay three sites for three, I told you twenty five, 129 00:12:24,720 --> 00:12:29,310 if I have two hundred twenty two thousand thirty four thousand and so on, so forth. 130 00:12:29,310 --> 00:12:37,740 And each of these diagrams come with more and more complicated. So if you have twenty five diagrams of 90 pages, you can imagine what happened here. 131 00:12:37,740 --> 00:12:45,540 Okay. So for a long time, this was thought to be a showstopper. So this is a report that was written. 132 00:12:45,540 --> 00:12:50,250 Is that describing the fees potential of future colliders more or less 30 years ago? 133 00:12:50,250 --> 00:12:57,420 And is this my sense? This is the conclusion to say the cross section four elementary two to four processes have not been calculated, 134 00:12:57,420 --> 00:13:02,550 and that complexity is such that they may not be evaluated in the feasible and foreseeable future. 135 00:13:02,550 --> 00:13:08,070 And we're not talking about the precision of cross-sections here, but talk about the most simple, rough estimate of what these are. 136 00:13:08,070 --> 00:13:13,480 OK. Now you can say, OK, great, we cannot even think about doing this. 137 00:13:13,480 --> 00:13:21,370 Can you at least finish these calculations as of yet? We have to add the one real articles and one the other one. 138 00:13:21,370 --> 00:13:25,720 So how does it look? We are told why don't let you got something similar. There's a problem. 139 00:13:25,720 --> 00:13:32,230 I told you that the one you have loops, you have to compute integers, so you have this object integrated over. 140 00:13:32,230 --> 00:13:36,700 So good luck with that. So you get very difficult to integrate. 141 00:13:36,700 --> 00:13:39,250 And just imagine that you are extremely good in doing integral. 142 00:13:39,250 --> 00:13:45,070 So you sit down, you spend three years your computer's integrator and there's not that you find is infinity. 143 00:13:45,070 --> 00:13:57,400 OK. So it's not particularly nice. So in principle, we know everything so five-month-old that you don't get everything we want in practise, basically. 144 00:13:57,400 --> 00:14:05,830 We cannot go very far. OK. And that is why, for a long time, people thought that doing precision physics that it is impossible in principle. 145 00:14:05,830 --> 00:14:10,060 We know what to do with them in practise. Nothing works. OK, now understand your story. 146 00:14:10,060 --> 00:14:15,160 So this was my very first interaction with the Nobel prise winner, so I was a fresh out of Ph.D. 147 00:14:15,160 --> 00:14:22,090 I just left Italy for the first time in my life. I was in the USA, was first week of my postdoc and this very, 148 00:14:22,090 --> 00:14:28,060 very famous Nobel prise comes home and want to talk with all the young people about physics. 149 00:14:28,060 --> 00:14:32,080 And then most of my friends say, What are you working on? I work on X and Y on X and Y. 150 00:14:32,080 --> 00:14:35,830 At that time was a permutation of supersymmetry or extra dimensions. OK. 151 00:14:35,830 --> 00:14:39,890 And he was super happy. Very fascinating. Very, very nice. I super happy. 152 00:14:39,890 --> 00:14:43,240 I want it up with this guy. Then I go in and what are you thinking? 153 00:14:43,240 --> 00:14:50,140 What I'm trying to do? Positional fidelity. And I only became blank. And he was really worried to say, You cannot do it. 154 00:14:50,140 --> 00:14:53,770 I mean, there is no point. So don't don't waste your life doing this. 155 00:14:53,770 --> 00:14:59,710 So and it is messy. Well, yes, you are going to find supersymmetry and we are going to find that sentimental. 156 00:14:59,710 --> 00:15:03,610 But we were never will never be able to do precision physics. OK? 157 00:15:03,610 --> 00:15:10,270 And he was far from stupid. OK, so now he had to point to some extent because of what I just told you. 158 00:15:10,270 --> 00:15:19,720 So if we kept using this Feynman diagrams and whatever the techniques that we use in the 70s, then yes, it was a it was hopeless. 159 00:15:19,720 --> 00:15:28,000 But in the meantime, people actually didn't lose hope and start looking at this horrible formula as more entities. 160 00:15:28,000 --> 00:15:34,390 And they found something which was, on the one hand, the missing and extremely without a hand in the fighting longer. 161 00:15:34,390 --> 00:15:42,700 So you think 96 98 pages of formula, some you spent the two ESM simplifying it them and the result that you've got is one time. 162 00:15:42,700 --> 00:15:52,300 So this ninety eight pages collapse to either zero or two times, according to how you select whatever edition. 163 00:15:52,300 --> 00:15:56,050 It's not that I'm doing something else. I mean, this is the same identical formula. 164 00:15:56,050 --> 00:16:00,160 So again, so this formula here is absolutely identical. 165 00:16:00,160 --> 00:16:05,440 So it's literally I mean, is it simplification? Get get get to this one. 166 00:16:05,440 --> 00:16:07,900 And this is fantastic, but it's also very annoying, right? 167 00:16:07,900 --> 00:16:13,680 I mean, you spent three years of in this and then you find this OK, so it's not particularly nice. 168 00:16:13,680 --> 00:16:18,810 And then people say, what can we try to do it with more armed with more particles? 169 00:16:18,810 --> 00:16:25,830 So, for example, six particle technologies at one time, 20 Feynman diagrams impossible to computer back then. 170 00:16:25,830 --> 00:16:31,800 And actually, they computed it and they found again want them or a few times, according to how you select. 171 00:16:31,800 --> 00:16:37,170 But this is very simple. And they even tried to say, Well, what happens if I have infinite number of particles? 172 00:16:37,170 --> 00:16:41,490 Can I get the same kind of simplicity? You say this from what I hear, and this number here are very similar. 173 00:16:41,490 --> 00:16:45,620 I don't they didn't tell you what these objects are, but basically it's just simple. 174 00:16:45,620 --> 00:16:50,330 Simple point is that that's how the momentum is flowing into diamond. OK. 175 00:16:50,330 --> 00:16:54,110 So it's very nice the final result is good, but what is going on? 176 00:16:54,110 --> 00:17:00,890 I mean, I don't want to spend three years to get the results, which is one line, right? And this is for a long time not understood. 177 00:17:00,890 --> 00:17:05,330 For a long time we saw this, that people saw this. These are this this simplification. 178 00:17:05,330 --> 00:17:09,590 But you understand why this happened. She's got it bad because if you don't ask them what is happening, you cannot use it. 179 00:17:09,590 --> 00:17:14,990 So you have to compute the horrible results and then simplify. You start now. 180 00:17:14,990 --> 00:17:21,590 At the beginning, I was telling you all the story about quantum mechanics, special relativity, what happens in the past decade or so? 181 00:17:21,590 --> 00:17:26,150 Let's people actually took what I said before very, very seriously. 182 00:17:26,150 --> 00:17:29,480 So what happens, I told you that the structure of one of these here is extremely rigid them. 183 00:17:29,480 --> 00:17:35,900 It's very much constrained by specialising in quantum mechanics and to, it seems, just thwarts. 184 00:17:35,900 --> 00:17:40,190 But if you look, if you walk out the consequences, these are not just words. 185 00:17:40,190 --> 00:17:45,290 So if you look at special relativity, what is the underlying core concept of special activity? 186 00:17:45,290 --> 00:17:51,190 Why does everything has to happen locally in space and time? Because I do not want to violate causality. 187 00:17:51,190 --> 00:17:53,260 And this is nice once again, 188 00:17:53,260 --> 00:18:04,720 but it's very easy to work out that this has an extremely interesting consequence on which kind of singularities your your family values, 189 00:18:04,720 --> 00:18:08,690 your amplitudes can happen to some of them and that can. 190 00:18:08,690 --> 00:18:15,490 It turns out that at least a three level there are the final results can have only a very simple set of singularities. 191 00:18:15,490 --> 00:18:21,560 Well, if I just copy that off the spelling diagrams, I find all kind of messy singularities at the end. 192 00:18:21,560 --> 00:18:26,000 I can only have very, very few of them and very, very simple. 193 00:18:26,000 --> 00:18:30,050 OK, it's nice also, especially if it me that they have only some kind of sunglasses. 194 00:18:30,050 --> 00:18:37,160 But if I don't tell you what happens on this singularities, this is not particularly useful and this is what quantum mechanics comes into in. 195 00:18:37,160 --> 00:18:38,660 So I don't know if you remember quantum mechanics, 196 00:18:38,660 --> 00:18:44,660 as this principle of unity to quantum mechanics takes probability and then evolves capability in a deterministic way. 197 00:18:44,660 --> 00:18:56,270 OK. This has also extremely important consequences because it can, but it can be used to tell you what happens to close to this single point. 198 00:18:56,270 --> 00:18:59,750 And what happens is something which is almost a miracle. 199 00:18:59,750 --> 00:19:08,300 So it happens that the if you go close to a single point of an amplitude with, for example, six final state gluon, 200 00:19:08,300 --> 00:19:17,210 you'll find that these amplitude breaks down into pieces, which are exactly the same kind of complex with less number of schools. 201 00:19:17,210 --> 00:19:25,700 Why is this useful? Well, because if I can use this breakdown systematically, I can build the amplitudes recursively, so I have a complicated. 202 00:19:25,700 --> 00:19:34,100 Either that or not, I look at all the singularities and I see that in all the singularities, this becomes an umbrella with less rules. 203 00:19:34,100 --> 00:19:37,100 So if I start from the more simple amplitude, which is actually simple, 204 00:19:37,100 --> 00:19:43,850 then I can use it as a seed to do recursion and I can get the basically almost for free. 205 00:19:43,850 --> 00:19:54,330 I can add legs almost for free. If I do, if I'm a lighter, I'm sorry, I h legs cost me a lot of a lot of effort. 206 00:19:54,330 --> 00:20:01,140 For example, this 220 Feynman diagrams that give this a two to four scattering. 207 00:20:01,140 --> 00:20:03,960 How many times do I need in the recession? 208 00:20:03,960 --> 00:20:10,050 You don't even need a computer to do this calculations in your head because there are two thousand so to have two hundred and twenty diagrams. 209 00:20:10,050 --> 00:20:15,690 Thanks to this, symmetries collapses into two taps that you can complete in your head and you 210 00:20:15,690 --> 00:20:20,730 can use in this kind of principle computer all kind of the level that you want. 211 00:20:20,730 --> 00:20:24,060 So now we understand this very well and we can use it. 212 00:20:24,060 --> 00:20:33,250 And so three level computations is a problem solver so you can take your phone download and not that it is online compute. 213 00:20:33,250 --> 00:20:37,480 And amplitude for four protons to suffer for four gluons. 214 00:20:37,480 --> 00:20:44,230 That could not be done by Supercomputer 30, I think that's improved, but still OK. 215 00:20:44,230 --> 00:20:49,660 So this is a done. What about loops? My look is much more complicated. 216 00:20:49,660 --> 00:20:54,900 But on the other hand, you can imagine applying similar ideas. So what is a loop at the end and the loop? 217 00:20:54,900 --> 00:21:01,060 But you can always think it as I have a bunch of three that I joined together. 218 00:21:01,060 --> 00:21:04,840 OK? And again, this is more or less water. 219 00:21:04,840 --> 00:21:17,940 But if you take this water deeply, you can try to use the same tricks that allow to get very nice sea level amplitudes to get look one. 220 00:21:17,940 --> 00:21:20,830 I need it work now. I don't want to show the details, 221 00:21:20,830 --> 00:21:29,950 but it is possible to cut open a loop using a game principle of quantum mechanics that simplifies dramatically and then put it back together. 222 00:21:29,950 --> 00:21:34,990 And at the end, you end up with much simpler expression, which are also simpler to integrate at one loop, 223 00:21:34,990 --> 00:21:40,470 the expression becomes so simple at the end, and no matter what the process, you have the computer, you just need to compete for intercourse. 224 00:21:40,470 --> 00:21:44,950 So no matter how complicated the problem is. So this is completely solved them so. 225 00:21:44,950 --> 00:21:48,610 Same same app on your phone can also give you one look, maybe not on your phone or your laptop. 226 00:21:48,610 --> 00:21:54,940 OK, but still high a loop is much more delicate than this nice simplification doesn't happen. 227 00:21:54,940 --> 00:22:01,540 This is where we're stuck more or less now. So we do not really know how to do them, but we find this a long time ago. 228 00:22:01,540 --> 00:22:04,420 We just computed them. We find all kinds of horrible functions. 229 00:22:04,420 --> 00:22:11,290 Now we have a much better understanding of which kind of function happens to appear in amplitudes. 230 00:22:11,290 --> 00:22:24,460 We see, for example, that all the complicated integers that lead to higher loop computations are live in very, very nice space. 231 00:22:24,460 --> 00:22:29,830 So all the one loop amplitude leaves on a sphere, so you can only think them of doing this. 232 00:22:29,830 --> 00:22:35,620 Interact is moving around on the sphere. And if you add loops, this fee become more and more complicated. 233 00:22:35,620 --> 00:22:42,370 The first thing you can do, you can punch the sphere and get it done later, and then you can get more complicated picture. 234 00:22:42,370 --> 00:22:46,510 Probably if you if you ever want to somehow string some string theory tarka, 235 00:22:46,510 --> 00:22:53,950 you saw similar features when people say you need to compact DeFi from the time dimension of string theory to the fourth dimension, as we see. 236 00:22:53,950 --> 00:23:01,450 And it is just not. The pictures look the same, so it seems that we find exactly the same structure and we don't understand it the better. 237 00:23:01,450 --> 00:23:08,860 We start the seeing structure appearing, and there is a hope that we can get a breakthrough also in this kind of calculation. 238 00:23:08,860 --> 00:23:13,750 So I cannot say that this is problem solved, but I can say that there is a lot of progress. 239 00:23:13,750 --> 00:23:24,260 OK. So we have the new understanding and you're thinking of how we deal with petabytes of quantum theory that allows us, 240 00:23:24,260 --> 00:23:29,150 that allows us to do stuff which are unimaginable only a few years ago. 241 00:23:29,150 --> 00:23:38,750 And the question is, OK, what can we do with that? So this is a plot that I think I took from Gavin that tells you, well, how, 242 00:23:38,750 --> 00:23:44,650 how long, how many calculations and this order in perturbations here are available. 243 00:23:44,650 --> 00:23:51,420 So remember, we want to get to a few percent of our fastest point one. So a few percent we need at least the first two steps. 244 00:23:51,420 --> 00:23:56,310 OK, so long time ago, it was very difficult. Do these calculations? 245 00:23:56,310 --> 00:23:59,400 Because we do not know how to compute amplitudes are complicated, 246 00:23:59,400 --> 00:24:04,630 we got infinity and indeed going from one calculation to the other took significant amount of time. 247 00:24:04,630 --> 00:24:12,720 Everything was scattered. And as the processes we can see that became more and more difficult, we had to wait more and more time. 248 00:24:12,720 --> 00:24:16,680 So at some point, there was a couple of years when nothing happened. It was just too difficult. 249 00:24:16,680 --> 00:24:22,410 You could not do it. OK, but then something happened around this time. 250 00:24:22,410 --> 00:24:29,700 So what happened here? What I told you is infinities in the in the in the amplitudes I didn't tell you. 251 00:24:29,700 --> 00:24:38,100 Why do they come from? What happens is that around this time, we started understanding exactly how to deal with them. 252 00:24:38,100 --> 00:24:45,460 And then all these ideas that I was just mentioning about the higher latitudes started moderating. 253 00:24:45,460 --> 00:24:49,770 Yeah, OK. So there was some kind of better understanding. 254 00:24:49,770 --> 00:24:55,230 And then the question is, was it useful? Or we could keep getting one calculation every 10 years? 255 00:24:55,230 --> 00:25:08,820 So after this happened? So this is the situation now. OK, so now we can basically computer a lot of processes to extremely high precision. 256 00:25:08,820 --> 00:25:12,990 So these are many, many processes done by very different people. 257 00:25:12,990 --> 00:25:19,770 Many of them involve either the Higgs or the background. So now we really can do precision physics for the Higgs. 258 00:25:19,770 --> 00:25:30,180 The LHC and getting from colliding protons gluons collected working laws and get actual precision studies of the Higgs. 259 00:25:30,180 --> 00:25:36,600 Now you may wonder, is it all necessary? I was giving you this argument about the, well, strong coupling at this point one. 260 00:25:36,600 --> 00:25:41,460 So I need another for the stuff that is the computer that one can check whether it is useful to compute them or not. 261 00:25:41,460 --> 00:25:49,770 OK. So what can we look at what we can look at? The simplest possible observable, which is roughly speaking, how many things we produce, 262 00:25:49,770 --> 00:25:56,100 isn't going what we call the total cross-section something we can measure. So already now, so this is the measurement that we have. 263 00:25:56,100 --> 00:26:04,110 Now, how can you be better than this now? But so you can count how many weeks you have and say, OK, experimentally, 264 00:26:04,110 --> 00:26:08,280 I see this many things and then you want to predict this number in theory from the 265 00:26:08,280 --> 00:26:12,880 tactical side to see whether your standard model prediction agrees with your data or not. 266 00:26:12,880 --> 00:26:16,650 Because if it's not, it means that the Higgs is not the standard model. It's not like the standard model. 267 00:26:16,650 --> 00:26:24,240 We found something. As I said, go on and the computer perturbation theory, First Order is what you get. 268 00:26:24,240 --> 00:26:28,590 So this is experimental value. OK. This is a theoretical prediction. 269 00:26:28,590 --> 00:26:37,650 OK. So if we believe that this is a reliable approximation of reality, it means that the Higgs that we measure is not the standard model for sure. 270 00:26:37,650 --> 00:26:42,130 OK, but then we know that this is not a reliable way to have with the higher the higher order. 271 00:26:42,130 --> 00:26:48,550 So what happens if we do it? Wow. Next order. And getting closer. 272 00:26:48,550 --> 00:26:52,960 Next door, there we are basically there, but there is a problem. 273 00:26:52,960 --> 00:26:59,260 So if I tell you that this is a battle of ideas serious about what you should tell me that the outlook is not converging. 274 00:26:59,260 --> 00:27:04,210 OK, so that that dam could be here or could be here so we can just overshoot. 275 00:27:04,210 --> 00:27:08,080 And then because of this, even if this looks kind of OK, people do that. 276 00:27:08,080 --> 00:27:15,850 A hairy calculation that was completed only last year and could be that even one more than you do with them and you get exactly here. 277 00:27:15,850 --> 00:27:22,150 So you see that everything converge very nicely and you are absolutely. 278 00:27:22,150 --> 00:27:27,700 Compatibility doesn't mean that Hicks is asking the standard model error of the larger, 279 00:27:27,700 --> 00:27:33,340 but at least it means that can be found on one file or as far as we know. 280 00:27:33,340 --> 00:27:37,420 But it also tells you that in order to do this study, understand this actually makes for real. 281 00:27:37,420 --> 00:27:45,430 You really need to control by sesion feet. You have a very large, a very good approximation. 282 00:27:45,430 --> 00:27:50,290 Now these are the total cross-section. What can you do when you have this kind of procedure in the last few minutes? 283 00:27:50,290 --> 00:27:56,710 I want to discuss just one example of how you can use this procedure to do something that for a long time was thought to be impossible. 284 00:27:56,710 --> 00:28:05,560 Now, Gavin was telling you that we have established to some extent the coupling of the hexa to the third generation of feminism. 285 00:28:05,560 --> 00:28:09,400 But it is impossible that it's to directly test the Coppins to second generations, 286 00:28:09,400 --> 00:28:14,200 because that's too difficult to imagine, the impossible to measure too many Americans. 287 00:28:14,200 --> 00:28:22,270 Now what you can imagine doing is, OK, I cannot measure it directly. But Gavin was also telling you that you can have an indirect process of coupling. 288 00:28:22,270 --> 00:28:27,070 So if you remember he was showing you this virtual Thompson or real stops, 289 00:28:27,070 --> 00:28:32,590 and so you want to indirect constraints and that'll give you direct constraints. Now you can get. 290 00:28:32,590 --> 00:28:41,700 Can we get direct, indirect constraints about. Flavour you can accomplish for the second generation, you can imagine. 291 00:28:41,700 --> 00:28:45,660 But in the same game that Gavin played with Tulsa, with the Champ Walk. 292 00:28:45,660 --> 00:28:51,420 Okay. We cannot do it. We cannot measure peaks and charm directly. 293 00:28:51,420 --> 00:29:01,740 But there is a negligible probability for two balloons to become a couple of virtual charms that he lays back into the Higgs. 294 00:29:01,740 --> 00:29:09,630 OK. And if we now think a gluon and use it as a problem solution was telling you that the NDIS, 295 00:29:09,630 --> 00:29:14,640 what you're doing is take a photon and you use it as a probe to look inside the proton. 296 00:29:14,640 --> 00:29:25,020 Yeah, we can do exactly the same. Only we can use a gluon to loop inside to look inside this loop here and see if we can probe the structure of that, 297 00:29:25,020 --> 00:29:29,280 at least indirectly, the structure of the interaction to the second generation. 298 00:29:29,280 --> 00:29:34,860 OK, now people studied this and this is what they found. So in this a plot, 299 00:29:34,860 --> 00:29:42,480 what they show is how the Higgs behaves either in the standard model or if it's coupled 300 00:29:42,480 --> 00:29:47,370 with time is different from someone a more because not like the standard model. So one is a standard model. 301 00:29:47,370 --> 00:29:49,680 So if you have a standard model, see this. This is some of the Higgs. 302 00:29:49,680 --> 00:29:56,160 It's not important what it is, but it's a property of the Higgs that you can measure. And if they exist on some the money, you should measure this. 303 00:29:56,160 --> 00:30:03,480 And then they studied some theories to see me as a son of a mother, but not quite the same and see which kind of deviations you get. 304 00:30:03,480 --> 00:30:07,200 Now, if you get more or less crazy theory, you get large deviations fine. 305 00:30:07,200 --> 00:30:11,220 But this capacity for serious of zoonotic. So what happens? 306 00:30:11,220 --> 00:30:14,880 You have theories which are similar to the standard model, but not quite. 307 00:30:14,880 --> 00:30:19,890 Then you'll get kind of deviations that if you look here, which are the two percent level, 308 00:30:19,890 --> 00:30:23,910 but there is no way to distinguish standard model from these kind of theories 309 00:30:23,910 --> 00:30:29,670 if we cannot control these properties at this kind of precision at the LHC. 310 00:30:29,670 --> 00:30:35,670 But I just told you that fortunately we can. And then. 311 00:30:35,670 --> 00:30:39,600 People use this technique, and actually it's not just in theory is actually measured. 312 00:30:39,600 --> 00:30:45,780 So this is what the experimental collaboration's measures right now for that this is called kappa, 313 00:30:45,780 --> 00:30:49,740 but is roughly speaking is what Gavin was telling you. 314 00:30:49,740 --> 00:30:53,210 Basically, what Gavin was putting that carbon at the bottom more or less? 315 00:30:53,210 --> 00:31:00,950 So how this deviates from the standard model and this then you come with the champ, look now this deviation from a standard model, right? 316 00:31:00,950 --> 00:31:10,490 This that's worse than the model is and what the order are inside this circle is what experimental measurements allow right now. 317 00:31:10,490 --> 00:31:13,580 Now, right now, it's not particularly constraining. 318 00:31:13,580 --> 00:31:23,000 So right now it's telling you that we can measure deviation from the charm and bottom of what the 40 and 60, 319 00:31:23,000 --> 00:31:26,450 so eventually want to see whether these are the standard model or not. 320 00:31:26,450 --> 00:31:33,920 So 60 times on the models, not a great measurement them. But I also show you showing you are telling you that and it is just the beginning of the 321 00:31:33,920 --> 00:31:38,750 full programme going on in the future and already had this high luminosity that they'd see, 322 00:31:38,750 --> 00:31:41,270 which is a proof that this is going to happen no matter what. 323 00:31:41,270 --> 00:31:51,950 This is the kind of constraint that you can get on the time you have a copy and you can really look at the at. 324 00:31:51,950 --> 00:31:58,340 Valuation close to the standard model and constrain them and use this procedure in direct measurements 325 00:31:58,340 --> 00:32:05,480 and precision predictions to try to pin down something which is impossible to look at directly. 326 00:32:05,480 --> 00:32:11,420 Now why there are different costs and different Corazza. Why does it seem that what Gavin was showing with this onSaturday plaza? 327 00:32:11,420 --> 00:32:14,390 So when you do this, you assume that your error. 328 00:32:14,390 --> 00:32:21,950 So I think our error will go down by significant fraction and different culture means a different assumption of what is going to happen to the error. 329 00:32:21,950 --> 00:32:32,630 So really, we need to work harder to make by season's precision predictions to fully use this, this, this, this kind of potential. 330 00:32:32,630 --> 00:32:36,710 That added, see, this is just an example of plenty of them. 331 00:32:36,710 --> 00:32:38,270 But let me conclude that now. 332 00:32:38,270 --> 00:32:46,010 So I hope to have convinced him that we have convinced that it's very important to study the Higgs and to do this at the LHC. 333 00:32:46,010 --> 00:32:51,980 Really, we need very good control on UCD because it is a very well known theory in principle. 334 00:32:51,980 --> 00:32:55,600 We know how to do it in practise is very difficult to barter. 335 00:32:55,600 --> 00:33:03,290 And there's been a lot of research on your progress and a lot of your theoretical developments in how we understand the combination 336 00:33:03,290 --> 00:33:13,010 of quantum mechanics and special activity that allow us to to really create a new generation of theoretical predictions. 337 00:33:13,010 --> 00:33:14,870 And now in this talk, 338 00:33:14,870 --> 00:33:20,990 I cover a tiny fraction of what actually is going on in the field and the tiny fraction of what is actually needed to go to precision physics. 339 00:33:20,990 --> 00:33:27,980 There are many other interesting avenues. But the interesting part is that no matter what we do, we keep looking at UCD. 340 00:33:27,980 --> 00:33:31,260 And it's not just that we compete with a bunch of more, 341 00:33:31,260 --> 00:33:42,450 have a more accurate prediction that we keep learning about the new structures in one theory and how to apply them for real life, real life physics. 342 00:33:42,450 --> 00:33:48,390 Already now we can do a lot better the season programme, the more data you have, the better you can go. 343 00:33:48,390 --> 00:33:57,120 So the best is yet to come. We'll have more data, better your understanding. And that it's, as Gavin said, is only the beginning of this story. 344 00:33:57,120 --> 00:34:03,330 And with precision, we can really explore the new hicks interactions at the very core. 345 00:34:03,330 --> 00:34:09,910 Now was there a time in place in time when people said, OK? 346 00:34:09,910 --> 00:34:13,630 Doing physical as an act, this is not particularly interesting, that's it. 347 00:34:13,630 --> 00:34:22,120 So if we succeed over work, yes, at the beginning of the of the last century, so what not, Calvin said, basically is complete. 348 00:34:22,120 --> 00:34:28,030 That's it. So all we need to do is to measure some long quantities to a great degree of precision. 349 00:34:28,030 --> 00:34:38,180 This is the kind of prediction, to be fair, educated in Cambridge. So I don't know that five years later, there was special activity at less than 30. 350 00:34:38,180 --> 00:34:48,670 At least that's where quantum mechanics activity. So sometimes go into a great detail of investigation is what is required to move forward. 351 00:34:48,670 --> 00:35:01,754 So let's keep exploring. And thank you very much.