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So superset that we've talked about a bit procedural studies of the Higgs at the LHC.

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So what I have here, my first life is one of the Higgs events where the Higgs kicks into two units, into leptons.

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Sort of one of the very clean signatures. So one of the beautiful events.

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On the other hand, you also see that things are not that simple.

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They are complicated because you have often a huge amount of collisions that happen at the same time.

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So understanding this physics is interesting, but also very challenging.

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Now, this is one of the images of the Atlas attack. So one of the detectors that people here really had for building at the now exploiting.

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So as one told you already, what we have now is a standard model of particle physics.

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And this has been remarkably successful for you in describing essentially everything that we see in all collider experiments that we have,

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we don't have so far yet. We really know that it is not the fundamental theory.

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It has some theoretical issues. So I will discuss some of them.

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But more seriously, the important unexplained phenomena. For instance, gravity does not fit in the standard model.

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The amount of symmetry that we observe where the presence of dark matter, dark energy that we we'll talk about later.

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Now, the other experiment was designed to explain essentially the origin of mass in the standard model for the Higgs mechanism,

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what goes under the name of Electroweak symmetry breaking, and to find physics beyond the standard model.

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As you all know, the Higgs has been discovered. In fact, well known physics has been seen.

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Now, these two are statements that you probably heard already many times.

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Also in one stalker, I thought that I would like to start with the store who is really addressing what is really means.

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So what is really the problem with particles having a mass in the standard model?

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Why Easter problem and how does the Higgs mechanism solve this problem?

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And also, why do we believe that the LHC is exploring the right energy scale to really find new physics?

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And so to do this, I will take now a big step back and forgive me for being a little bit maybe simplistic here,

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but we all know here that there is a duality in quantum field theory.

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So to every way, to every particle, we associate duality between ways and particles.

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So to the electromagnetic wave, we associate the particle difficult to a no.

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I want the fourth on this wave propagate. So that's only one direction.

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We know that this has to physical polarisation state so this is if you want just an empirical effect,

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it starts as an empirical fact that there is no longitudinal polarisation and now it is a sounds like an accidental effect or so,

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but it has some deep consequences. Why so? Why is it if this further polarisation existed and you sit down and try to compute scattering amplitude?

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So what you find is that you find scattering because the proportion to the energy which is getting pincer.

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So what this means is that if you perform this getting a very high energy, you will find at some point probabilities that are larger than one.

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Now, this is of course, not physical probabilities can't be doubted.

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And one what this is telling you is that your field theory is striking down at some higher energies.

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Now, in quantum electrodynamics, this does not hit,

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but we know there is no field polarisation and this is related to a symmetry of the theory that we call gauge symmetry.

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So they gauge symmetry. If you want to act like a filter,

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it features a way this longitudinal polarisation and you're left with the physical photon in a quantum electrodynamics.

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So the symmetry then is really, really, really crucial to related to keeping your theory sensible when you go to high energy some.

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The other thing that everybody here knows very well is that when you look at the light propagating,

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the speed of light is the same in any reference frame.

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So it doesn't matter if you're not moving. If you're moving slowly or faster, you ought to see the same speed of light.

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But this is not the case, of course, for objects.

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It's heavy mass when a massive particle propagates. So the speed it has is different according to your thinking.

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But in particular, what you can always do is to find the reference frame where your particle is not moving anymore.

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Now, in this reference framework, there is no distinction anymore between transverse and longitudinal polarisation

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slider because this would break the rotational symbol of your feeling.

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So the trick that works nicely for photons that are much less does not work.

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As soon as the particles head in loss. On the other hand,

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we heard from one and we know very well for many experiments now that the electroweak interactions are mediated by particle said

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to have been lost w in desert force so and so and the masses break these electroweak symmetry so they feel it breaks down.

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It's high energy. That's the problem. And then you can sit down and look at what energy does for energy.

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Would you find probabilities that become larger than one idea?

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Has it which this happens is about one tree. So this is the energy scale solved by the LHC.

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And this is why the LHC was designed to sort of investigate, to test this mass generation.

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So how do particles have mass in the standard model? But at the same time, how do we keep the theory sensible when we go to this energy scale?

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So. So the most popular solution is what goes under the name of Higgs mechanism or Electroweak symmetry breaking.

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So when you say that Electroweak symmetry is spontaneously broken,

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so spontaneous symmetry breaking means essentially a very simple thing that you have equations said to have a symmetry,

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for instance, of rotational symmetry.

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But then once you pick a solution to this, the solution the most energetic and convenient solution has, it breaks this rotational symmetry.

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So your laws of physics are have the symmetry, but the solutions do not.

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And something that is typical of spontaneous symmetry breaking is that if you have laws that are invariant under some symmetries,

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you can have solutions that do not respect symmetry.

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For instance, you have a particle that is more massive, then you have a one as long as so also the other solution is allowed that exists.

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So typically in general of spontaneous symmetry breaking you having a sort of degenerate solution.

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So. All right. So here you see, for instance, here all the solutions are sort of, you know,

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and these are sort of called zero energy excitations, essentially, because moving around the circle costs to energy.

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But this corresponds with the presence of a massless particle. What goes on the name of massless goes simple.

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So no. And now you have sort of a second problem that we don't observe physically.

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This goes on wasn't is not there. So the Higgs mechanism essentially source these two problems.

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It's your what you do is you absorb a decent degree of freedom from the massless from the ghost on boson into a massive particle.

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So from to polarisation to get in this free physical polarisation.

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So. So in a way. One way to think about this a bit naive is that the Higgs field is sort of like instead of having a vacuum,

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you've had a vacuum, you have a Higgs field vacuum. And when particles propagate to this vacuum, they sort of interact with the Higgs field.

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So the Higgs has loosened down. They have a speed that is slower than the speed of light, meaning they have lost them.

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So that in this simple picture, the mass added particles have always proportional to the amount of interaction, the shape of the Higgs.

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So now. So the problem was that if you have master's particles, you have gene variants and everything is fine,

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but with massive particles, you have unique calculations.

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So the way the Higgs mechanism works, in a way, you said it's small energies, meaning large distances.

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You see the effect of this medium. So you have massive particles.

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But once you go to China changes. You don't see this anymore. And so you have no problems with unitary isolation.

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So. So of course, once you have a field, you also have excitations of this field.

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So you know that that must be the Higgs boson associated to this.

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And again, for the Higgs boson, like for whatever particles, the Higgs interacts with itself.

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So the Higgs also hasn't lost that it's proportional to the coupling of the Higgs to itself.

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So the nice thing about these six mechanism in the standard mode, it is really very flexible.

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So once you find the Higgs, once you know the mass of the Higgs, you know everything.

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So you can predict all other couplings and masses.

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And now so before the discovery, we really didn't know whether to fix it.

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It's been an open question for really many years, and it was believed to be extremely hard to figure out.

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And the reason is that the way you see the Higgs is by looking at some distribution.

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For instance, this could be some energy spectrum or invariant mass distribution of two photons.

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When the Higgs raced through the photons and what you see, you have a huge default on background and the really little bump here.

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So of course, once you collect data, data are not perfect.

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This is how data look like. So it's very difficult to discriminate between these two possibilities.

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So this is why they did it easy, as one described earlier, really collected, needed to collect a huge amount of data to discover this, the Higgs.

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So let me tell you just briefly the history of this discovery,

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which I think is sort of an amazing it's quite amazing because people really thought that it would take much longer and it did.

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But what happened in 2011, the LHC experiment was able to sort of exclude some massive regions for the Higgs boson.

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So let me explain a little bit what is shown in this plot.

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You have a green band and these are different confidence levels that you have and you have a black line here.

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This is what you what what you expect. And another line here, that is what you observe.

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So once this green band moves below this red line, you are allowed to you are excluding a cross-section.

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So. So if they give in, they would be here.

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Then you are you can exclude something like two or ten times the standard material section,

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but once you below here, then you can exclude the Higgs boson with some given mass.

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And this is what happened here. And once this points to somehow go outside these things, then you sort of have a hint that something is there.

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Because what you have here is different from what you would expect under the hypothesis that there is no Hexham.

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So if the first in the centre were on a heavier Higgs boson, states could be excluded.

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And then very shortly afterwards you see, oh, this band goes down.

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So we could exclude much more. But then you started having a hint of something of a life the Higgs falls on at around 220 725.

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So this is shown here. You can look at the probability that this so you see this thing here.

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If that this is in fact, that he was on it and all these results were presented at the conferences.

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People were really excited at the time. It was an exciting time because before those conferences,

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people that were not working in this collaboration certainly did not know what would happen I thought would be presented.

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So it was really very exciting. And then now you are now in 4th of July 2012 for the evidence of renewables and suppose in data.

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And this is for instance, this is the plot I was telling you before.

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This is the invariant must be to offer the photons Higgs field.

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And as you see really they speak here like a peak or them in the background muscle for

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electrons when the Higgs decays due to the physical decay in to follow on 60 peak.

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This is the standard mode is a peak that you have and so this was one newborn so and it was clear what it is what people believed.

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Of course it's a standard model. But then a few months later, it was in fact identified as a standard ordered the Higgs.

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And how do you do that? Is what I told you.

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The sentiment is very predictive, you know that masses and couplings have to be proportional to the Higgs mass.

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So so in this plot here, for instance, you show this pathway, you see the mass of the particle and the coupling of the particle to the Higgs boson.

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And everything is really aligned. It's a on a straight line.

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Yeah. I think that you can look at for instance is the speed of this object now found the

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fact that the Higgs decays into two photons you already know it can't have spin one,

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but it could have spin too. But here you see that this is the policy of spin zero and this has been true.

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So data really seem to immediately spin two.

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And this is again sort of a summary plot where you look at fair Munich versus Bosonic coupling.

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So so Hickson coupling to vector goes on so the Higgs coupling to fair and where is this one one is the standard model hypothesis.

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So you see that everything is really compatible C with large areas but compatible with being a Higgs boson.

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And that's why then the Nobel Prizes was awarded really just one year after the discovery.

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So what we have now are sort of what we call legacy results.

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And so essentially all data have already been analysed in all possible ways.

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And look, I don't expect you to follow all this. But really, this has been studied in all possible ways and all changes that we know of.

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And I will discuss this a little bit later.

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Let me stress that, at least for me, these three years have been really remarkably intense and very exciting.

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So here you see this is for the original people was a spokesperson of collaboration at the time and will

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become DG of Director General of TIL next year when she announces the evidence for the Higgs boson.

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And this is I don't know if you heard about it. This is a movie that sort of tells this story from some point of view.

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Now, having found the Higgs is of course, it's something really very positive, is very satisfying.

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On the other hand, it also leaves some open questions and some open problems.

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One is the fact that the Higgs mass, the Higgs being a scalar, is not protected by any symmetry.

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So the Higgs maskin essentially gets the corrections, quantum corrections from vacuum fluctuations.

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And because there is no symmetry to protect this, the mass of the Higgs can be the corrections can be arbitrarily.

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So it should be proportional to the maximum allowed energy that you have.

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So something like a plank mass.

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So the fact that we observe a very light centre requires, I say fine tuning of to really many digits or some new physics.

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So to take an analogy, if you think about like thermal fluctuations,

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if you take a particle and put it in a thermal buffer and wait long enough to do a few,

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you would expect that the right particle has about the average energy of all available particles.

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Divide that by what we observe. Is that our right particle, the Higgs has really an energy transition much, much, much smaller than a blue particle.

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So it's not inconsistent, but it's really hard to believe that something like this happens without there being a deep reason for it.

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So in this analogy, the reason, of course, could be that right thus does not acquire the energy of blue because red does not interact with blue.

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There is some screening mechanism. So the threat simply does not see the presence of blue.

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And this is essentially the same as so what happened to the Higgs case?

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So you could say that, well, the mass of the Higgs is protected or screened by some new forces or new particles that we don't know about.

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And that's why the masses so light. And there are, in fact, many new physics models that sort of try to explain why the Higgs mass is solar.

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And and of course,

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all these models are all speculations and all experimental data can sort of discriminate between different in order to constrain this order some.

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So where are we now? See? Has been looking for particles predicted in this model.

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One of the most popular class of minutes are supersymmetric models.

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And what you see here sort of plots, again, I don't expect you to follow what is in here,

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but what you see, a bounce on the masses that are predicted in these models.

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And very roughly the number to keep in mind is that the LHC can be around one tree energy

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scales for these objects and so particles have to be triggered and then some scale.

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Otherwise we would have seen them already. And for more exotic, more response, I even saw one go about maybe to TV or so.

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So this is what the Galaxy could do so far. Could put constrain.

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It could excluded at the promoters, but not really see anything yet.

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Now what will happen next? As one told you, Iran two is about to start this summer.

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It will has essentially twice the energy that the previous Iran had and also much higher luminosity.

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On the other hand, it is true this effect of twin energy is not that much.

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So why should give in? I mean to take into account the possibility that even in round two we will not see the production of new states directly,

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simply because the energy is not enough. Maybe you would need 50 TV or hundred.

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So one of the focus of the two would also be indirect to just precision this.

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So there is an indirect filters, imprecision tests help in this case when when the energy because.

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For Diana to adjust, you always have to have their identity to produce a C directly for indirectly through virtual loops.

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So you can you're sensitive to the presence of particles we have without producing genetically.

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This is the same as, for instance, what happened with the top.

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The top was discovered at the table, but there was already evidence from the left whether the top should be data from the loop collection simply so.

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One of the sectors that has not been investigated much yet is, of course, the Higgs sector.

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And as I told you, this is particularly interesting because everything is predicted in the centre.

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So to do this procedure in the in position tests, what you need of course is the most accurate measurements but also very precise prediction.

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So I think and this is different from sort of direct searches.

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So in the Higgs digesting, that is my spectrum that I showed you.

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You really didn't need any fear at all to see about if you collect enough data and there is a but, that's all.

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But when you talk about indirect searches, you really have to control all your harmonisation, your sections precisely.

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If you want to say that the cross section is a little bit larger than what you expect.

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That's why for this type of searches, theoretical predictions are really more important.

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Now how do we do theoretical predictions? So as one said already, everything is based on the fact that when you go to high energy,

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your coupling constants or the way particles in the coupling contents are smaller.

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So all you do afterwards, you fix punch holes in the coupling constants.

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So for instance, you want to compute an equal section that you compute it at lowest order,

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and then you can compute the correction suite that are essentially expansions in this constant.

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Thank you. So for the strong interaction, the capping content is around 0.1.

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So when you compute what we call it next to reading order correction,

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you can expect something of the order of a 10% correction next to the next leading order.

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So Alpha squared something of the order of 1%.

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So this is a bit now if I will show you for the Electroweak interaction because it is of the order of 1%.

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So when you do an x two leading order conclusion, you you could have a very good position.

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The other thing to keep in mind is that when your measurement is very inclusive, this works nicely.

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But once your measurement is less inclusive, typically when you're sensitive to two different energy scales,

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for instance, a hard scattering of the forces enters of the scalar.

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What happens is that in your code section you will have large log of the ratio of these two scales.

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So when the logs are larger, they compensate the fact that the coupling is smaller.

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And so you have to change the way you do this expansion and sort of talk about

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the result calculations and you talk about leading log next leading logs.

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And so these are essentially different ways of doing better with the fixed functions way.

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So now when we go back to the Higgs at the LHC,

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what this graph shows is how the Higgs is actually produced under different production modes as a function of the Higgs mass here.

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So we are in fact about here. Right? So you see that by far the dominant production mode is school and fusion to Higgs production.

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So you have to know what's coming from your post on that. And so a top loop, they produce a Higgs.

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So, so this is a process that is loop induced already.

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So the gluons don't copula to the Higgs because if you want some lesser, but the top four has a very large mass.

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So even if this is looping, you said this is the dominant process.

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Then you have other processes like vector fusion production where you have two balls.

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Once they cancel each from important, they together they build the Higgs in the final state or processes where the Higgs is

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isolated from the bottom and so also insensitive Higgs produce associated with T-bar.

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Now here the coupling is also very large the Higgs to to back out.

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On the other hand, you pay a price because you have to produce also two tops in the finance.

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So you need a lot more energy to produce this. That's why this is so much smaller than these forces here.

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So these are the ways the Higgs can be produced, you see.

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And the other thing to keep in mind is that we never really see the Higgs,

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because the Higgs has a very the case essentially immediately propagates fuel from two metres and then decays.

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So you never see the Higgs. What you see is the decay modes of the Higgs.

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And this is again flawed, showing the different branching ratios of the Higgs.

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And this is where we are, where we did discover the Higgs.

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And you see that somehow it's a very nice place to be, because if the Higgs had been much heavier,

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essentially you would have seen only the Higgs decay in 2006.

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So you would have never been able to see those moments.

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And if the Higgs would have been much like that, you would see essentially on your TV there, but never those modes here.

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But in the place where we are, we can essentially see all those two key to look at.

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For instance, Gamma. Gamma is in fact very small, was one of the discovery channels.

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And this is because the signature here is very clear. So we already could see all of this.

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So and this is something I said a bit already, but that this is where we are now in terms of precision studies of the Higgs.

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So you can look at those sections so different that you can always look at the ratio to the prediction from the standard model.

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And you see that essentially there is no deviation. So this looks really like a Higgs boson.

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On the other hand, you see that this was actually really quite large here.

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There is a little tension, but not too much.

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And this is the plot that already showed once. But you see somehow this nice fixture mass aligned with the coupling.

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Right. Now there are two we now restart and essentially we redo this test.

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So trying to decrease to zero as much as possible.

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That's now I want to discuss only one of these calculations.

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I mean, behind the all these production modes and the key modes, there are difficult calculations.

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And I want to focus only one, which is the simplest one here.

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So he filled out this team list, but dominant.

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But the Higgs is produced via global fusion, so this is the lowest order diagram to use them and we can even forget about the decay of the hicks.

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One nice thing about the hicks is that being a skater, you can always forget about the key and include it later.

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For instance, Viktor goes on to cancel it. So here, let's focus only on the production.

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This is loop induced. This makes things difficult.

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So what the people have been doing in the past is to go into sort of an effective limiting the limit where the top is very heavy in that limit.

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This loop essentially shrinks to a point. So let's say that that leading or this is your production where this is an.

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I think so. And then once you're in this limit, you can do loop corrections to this.

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So if you talk about next to an actual leading order, what you do is you have diagrams, for instance,

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where you have to we want to exchange this where you have one loop and one area or two areas.

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So these are called features, the ones this is real. And this calculation was done over the 12, 15 years ago now.

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And this is what comes out when we do this calculation. So let me explain a little bit this plot.

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So as one said, and everybody knows that you said, when you do custody corrections, you have to normalise the CD.

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And this introduces a normalisation scheme. And typically what we do is we choose the normalisation scale to a physical scale of the process.

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Here we are looking at Higgs field action. So a natural choice is to fix it to the mass of the Higgs.

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So, in fact, in this plot, it's set for some reason, which I can explain,

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but it turns the mass of the Higgs over to once you fix this scalar, you try to what you can do is you can vary your normalisation scale.

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And conventionally we're always very effective sector up and down.

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And this gives you a bend. So this is how right is your leading order prediction here to centre value?

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You want me to scale up and down by 4 to 2 and you get something that this type of thing do you do a next leading order calculation.

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And what you see is that you get this centre value in this type of bent here and the next, the next leading order and you are up here.

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So what you see from this plot is, first of all, in the case of Higgs field action, this procedure doesn't seem to work very well.

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So the way we sort of use, the way we estimate the fear,

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uncertainty here for the leading order completely fails to sort of tell you what is the size of the next reading.

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So these two bands don't even overlap.

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These bands now overlap a little bit, but still the centre value is really at the edge of this bend.

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So it would have been much better if the blue band would have been here. And so what this says is you're doing it for theoretical expansion,

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but this is not converging very when your next two leading order Quebec decides now easily could be 10%.

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Here it's a factor two. And then next to the next leading order, that could be 1%, very naively.

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Here is, in fact, another 20, 50%. And this is what makes things really very difficult in the case of Higgs production.

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Right now. So this is a picture that we had essentially a few years ago to a few years ago.

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So what people have been doing now is. So there are two ways in which you can feel.

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You can say, okay, it's time to go. And you tire of all the teams approximately with this type of resolution.

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So identifying if there is a large log and trying to resolve those was something that is more brute force.

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You compute the next two, I mean the six punch or the entry and or two and took it.

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Can this be so difficult? You are expanding your computing, the field or the team in this expansion.

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Is it that difficult? Well, so some facts about this calculations.

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So I told you this involves really accurate interference, diagnose and so on.

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If you count a diagnosis, a hundred thousand interference diagnosis, you have to compute that at the next to next leading order.

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You hit thousand when you go to looping to get on to fit between signals, this is the numbers you have to compute so you have four integral.

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So this custom. So this is the face, this integration, these are the particles that counted in this calculation.

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So you have this integrals plus another 68 reasons and so on.

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And in comparison, this is the number that you have at next to the next leading order.

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And so the way these integrals are computed is you write down the expression for the interval and then you have some reduction mechanism.

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So the way you relate this integral to a set of simple scalar mastering to go.

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And so this is the process. You find a way to reduce simplicity of simply indigo.

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And what happens here at this set of simple integrated about 2000 mastering the goals of this type of what is next the next leading order.

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You have to see that, you know, 26 such integrals.

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So things are effectively much more complicated and these calculations are possible because there are new technologies which are used to do this.

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Integrals, in fact. So this is one of the most up to date plots now of the season.

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So this group did not finish the calculation yet, but could do it in some approximation sort of a threshold expansion.

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So there is enough proximity expression now for these calculations.

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And different groups now took their results and put it in the calculation as well.

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And what this plot shows here, this is this one number, one simple number for the cross section.

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These are different groups. And this is the old recommendation that we had essentially before this calculation.

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And this is how numbers change. From different groups, the oldest to colours, light blue and dark blue.

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These correspond to different choices of your normalisation, scale and peaks over two or three weeks even.

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This is sort of debated what should one choose?

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But the most sort of striking thing I think about this plot is that if you look at what these people say,

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they believe that better because we learn from what happens at next, the next leading role that what is important and what is not.

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They sort of believe that they have a very precise number and the really very small level.

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This group of people, on the other hand, which are in fact, those that did this calculation, sort of claim that this is still a partial resolve.

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Things can change a lot once they finish the calculation.

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So they claim that, in fact, the central values should go down and the uncertainties is really very large.

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So these are the things that are really now hotly debated.

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And let me conclude by showing one of the slides that was presented in January now about essentially both these results.

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So the question is a little bit easier, wiser when you try to learn from what you learned next,

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the next leading goal, and you try to apply that, then Cubillo or whoever you have.

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Why is that? If you admit that you don't have this full calculation yet and you should have a very conservative variable,

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and these are the things that are really now a bit open and under discussion.

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So let me conclude by saying we had fantastic data from on one end.

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I think we perform even better. There is a lot of expectation it starts this summer.

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It will be very exciting. The Higgs discovery was really my SO it was a remarkable success.

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On the other hand, it leaves many open questions, the hierarchy problem and thinks about naturalness.

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And so now we're want to will focus on these precision studies.

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And as I said, I mean, procedural studies. You can't go on just with experimental data.

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You really need to futurists and experimentalists to work together.

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So what is shown here is, again, this is this Higgs cross-section where can go.

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This is an image of a tool from this meeting in Germany, where fear and experiments go hand-in-hand together.