So superset that we've talked about a bit procedural studies of the Higgs at the LHC.
So what I have here, my first life is one of the Higgs events where the Higgs kicks into two units, into leptons.
Sort of one of the very clean signatures. So one of the beautiful events.
On the other hand, you also see that things are not that simple.
They are complicated because you have often a huge amount of collisions that happen at the same time.
So understanding this physics is interesting, but also very challenging.
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.
So as one told you already, what we have now is a standard model of particle physics.
And this has been remarkably successful for you in describing essentially everything that we see in all collider experiments that we have,
we don't have so far yet. We really know that it is not the fundamental theory.
It has some theoretical issues. So I will discuss some of them.
But more seriously, the important unexplained phenomena. For instance, gravity does not fit in the standard model.
The amount of symmetry that we observe where the presence of dark matter, dark energy that we we'll talk about later.
Now, the other experiment was designed to explain essentially the origin of mass in the standard model for the Higgs mechanism,
what goes under the name of Electroweak symmetry breaking, and to find physics beyond the standard model.
As you all know, the Higgs has been discovered. In fact, well known physics has been seen.
Now, these two are statements that you probably heard already many times.
Also in one stalker, I thought that I would like to start with the store who is really addressing what is really means.
So what is really the problem with particles having a mass in the standard model?
Why Easter problem and how does the Higgs mechanism solve this problem?
And also, why do we believe that the LHC is exploring the right energy scale to really find new physics?
And so to do this, I will take now a big step back and forgive me for being a little bit maybe simplistic here,
but we all know here that there is a duality in quantum field theory.
So to every way, to every particle, we associate duality between ways and particles.
So to the electromagnetic wave, we associate the particle difficult to a no.
I want the fourth on this wave propagate. So that's only one direction.
We know that this has to physical polarisation state so this is if you want just an empirical effect,
it starts as an empirical fact that there is no longitudinal polarisation and now it is a sounds like an accidental effect or so,
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?
So what you find is that you find scattering because the proportion to the energy which is getting pincer.
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.
Now, this is of course, not physical probabilities can't be doubted.
And one what this is telling you is that your field theory is striking down at some higher energies.
Now, in quantum electrodynamics, this does not hit,
but we know there is no field polarisation and this is related to a symmetry of the theory that we call gauge symmetry.
So they gauge symmetry. If you want to act like a filter,
it features a way this longitudinal polarisation and you're left with the physical photon in a quantum electrodynamics.
So the symmetry then is really, really, really crucial to related to keeping your theory sensible when you go to high energy some.
The other thing that everybody here knows very well is that when you look at the light propagating,
the speed of light is the same in any reference frame.
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.
But this is not the case, of course, for objects.
It's heavy mass when a massive particle propagates. So the speed it has is different according to your thinking.
But in particular, what you can always do is to find the reference frame where your particle is not moving anymore.
Now, in this reference framework, there is no distinction anymore between transverse and longitudinal polarisation
slider because this would break the rotational symbol of your feeling.
So the trick that works nicely for photons that are much less does not work.
As soon as the particles head in loss. On the other hand,
we heard from one and we know very well for many experiments now that the electroweak interactions are mediated by particle said
to have been lost w in desert force so and so and the masses break these electroweak symmetry so they feel it breaks down.
It's high energy. That's the problem. And then you can sit down and look at what energy does for energy.
Would you find probabilities that become larger than one idea?
Has it which this happens is about one tree. So this is the energy scale solved by the LHC.
And this is why the LHC was designed to sort of investigate, to test this mass generation.
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?
So. So the most popular solution is what goes under the name of Higgs mechanism or Electroweak symmetry breaking.
So when you say that Electroweak symmetry is spontaneously broken,
so spontaneous symmetry breaking means essentially a very simple thing that you have equations said to have a symmetry,
for instance, of rotational symmetry.
But then once you pick a solution to this, the solution the most energetic and convenient solution has, it breaks this rotational symmetry.
So your laws of physics are have the symmetry, but the solutions do not.
And something that is typical of spontaneous symmetry breaking is that if you have laws that are invariant under some symmetries,
you can have solutions that do not respect symmetry.
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.
So typically in general of spontaneous symmetry breaking you having a sort of degenerate solution.
So. All right. So here you see, for instance, here all the solutions are sort of, you know,
and these are sort of called zero energy excitations, essentially, because moving around the circle costs to energy.
But this corresponds with the presence of a massless particle. What goes on the name of massless goes simple.
So no. And now you have sort of a second problem that we don't observe physically.
This goes on wasn't is not there. So the Higgs mechanism essentially source these two problems.
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.
So from to polarisation to get in this free physical polarisation.
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,
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.
So the Higgs has loosened down. They have a speed that is slower than the speed of light, meaning they have lost them.
So that in this simple picture, the mass added particles have always proportional to the amount of interaction, the shape of the Higgs.
So now. So the problem was that if you have master's particles, you have gene variants and everything is fine,
but with massive particles, you have unique calculations.
So the way the Higgs mechanism works, in a way, you said it's small energies, meaning large distances.
You see the effect of this medium. So you have massive particles.
But once you go to China changes. You don't see this anymore. And so you have no problems with unitary isolation.
So. So of course, once you have a field, you also have excitations of this field.
So you know that that must be the Higgs boson associated to this.
And again, for the Higgs boson, like for whatever particles, the Higgs interacts with itself.
So the Higgs also hasn't lost that it's proportional to the coupling of the Higgs to itself.
So the nice thing about these six mechanism in the standard mode, it is really very flexible.
So once you find the Higgs, once you know the mass of the Higgs, you know everything.
So you can predict all other couplings and masses.
And now so before the discovery, we really didn't know whether to fix it.
It's been an open question for really many years, and it was believed to be extremely hard to figure out.
And the reason is that the way you see the Higgs is by looking at some distribution.
For instance, this could be some energy spectrum or invariant mass distribution of two photons.
When the Higgs raced through the photons and what you see, you have a huge default on background and the really little bump here.
So of course, once you collect data, data are not perfect.
This is how data look like. So it's very difficult to discriminate between these two possibilities.
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.
So let me tell you just briefly the history of this discovery,
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.
But what happened in 2011, the LHC experiment was able to sort of exclude some massive regions for the Higgs boson.
So let me explain a little bit what is shown in this plot.
You have a green band and these are different confidence levels that you have and you have a black line here.
This is what you what what you expect. And another line here, that is what you observe.
So once this green band moves below this red line, you are allowed to you are excluding a cross-section.
So. So if they give in, they would be here.
Then you are you can exclude something like two or ten times the standard material section,
but once you below here, then you can exclude the Higgs boson with some given mass.
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.
Because what you have here is different from what you would expect under the hypothesis that there is no Hexham.
So if the first in the centre were on a heavier Higgs boson, states could be excluded.
And then very shortly afterwards you see, oh, this band goes down.
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.
So this is shown here. You can look at the probability that this so you see this thing here.
If that this is in fact, that he was on it and all these results were presented at the conferences.
People were really excited at the time. It was an exciting time because before those conferences,
people that were not working in this collaboration certainly did not know what would happen I thought would be presented.
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.
And this is for instance, this is the plot I was telling you before.
This is the invariant must be to offer the photons Higgs field.
And as you see really they speak here like a peak or them in the background muscle for
electrons when the Higgs decays due to the physical decay in to follow on 60 peak.
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.
Of course it's a standard model. But then a few months later, it was in fact identified as a standard ordered the Higgs.
And how do you do that? Is what I told you.
The sentiment is very predictive, you know that masses and couplings have to be proportional to the Higgs mass.
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.
And everything is really aligned. It's a on a straight line.
Yeah. I think that you can look at for instance is the speed of this object now found the
fact that the Higgs decays into two photons you already know it can't have spin one,
but it could have spin too. But here you see that this is the policy of spin zero and this has been true.
So data really seem to immediately spin two.
And this is again sort of a summary plot where you look at fair Munich versus Bosonic coupling.
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.
So you see that everything is really compatible C with large areas but compatible with being a Higgs boson.
And that's why then the Nobel Prizes was awarded really just one year after the discovery.
So what we have now are sort of what we call legacy results.
And so essentially all data have already been analysed in all possible ways.
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.
And I will discuss this a little bit later.
Let me stress that, at least for me, these three years have been really remarkably intense and very exciting.
So here you see this is for the original people was a spokesperson of collaboration at the time and will
become DG of Director General of TIL next year when she announces the evidence for the Higgs boson.
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.
Now, having found the Higgs is of course, it's something really very positive, is very satisfying.
On the other hand, it also leaves some open questions and some open problems.
One is the fact that the Higgs mass, the Higgs being a scalar, is not protected by any symmetry.
So the Higgs maskin essentially gets the corrections, quantum corrections from vacuum fluctuations.
And because there is no symmetry to protect this, the mass of the Higgs can be the corrections can be arbitrarily.
So it should be proportional to the maximum allowed energy that you have.
So something like a plank mass.
So the fact that we observe a very light centre requires, I say fine tuning of to really many digits or some new physics.
So to take an analogy, if you think about like thermal fluctuations,
if you take a particle and put it in a thermal buffer and wait long enough to do a few,
you would expect that the right particle has about the average energy of all available particles.
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.
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.
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.
There is some screening mechanism. So the threat simply does not see the presence of blue.
And this is essentially the same as so what happened to the Higgs case?
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.
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.
And and of course,
all these models are all speculations and all experimental data can sort of discriminate between different in order to constrain this order some.
So where are we now? See? Has been looking for particles predicted in this model.
One of the most popular class of minutes are supersymmetric models.
And what you see here sort of plots, again, I don't expect you to follow what is in here,
but what you see, a bounce on the masses that are predicted in these models.
And very roughly the number to keep in mind is that the LHC can be around one tree energy
scales for these objects and so particles have to be triggered and then some scale.
Otherwise we would have seen them already. And for more exotic, more response, I even saw one go about maybe to TV or so.
So this is what the Galaxy could do so far. Could put constrain.
It could excluded at the promoters, but not really see anything yet.
Now what will happen next? As one told you, Iran two is about to start this summer.
It will has essentially twice the energy that the previous Iran had and also much higher luminosity.
On the other hand, it is true this effect of twin energy is not that much.
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,
simply because the energy is not enough. Maybe you would need 50 TV or hundred.
So one of the focus of the two would also be indirect to just precision this.
So there is an indirect filters, imprecision tests help in this case when when the energy because.
For Diana to adjust, you always have to have their identity to produce a C directly for indirectly through virtual loops.
So you can you're sensitive to the presence of particles we have without producing genetically.
This is the same as, for instance, what happened with the top.
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.
One of the sectors that has not been investigated much yet is, of course, the Higgs sector.
And as I told you, this is particularly interesting because everything is predicted in the centre.
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.
So I think and this is different from sort of direct searches.
So in the Higgs digesting, that is my spectrum that I showed you.
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.
But when you talk about indirect searches, you really have to control all your harmonisation, your sections precisely.
If you want to say that the cross section is a little bit larger than what you expect.
That's why for this type of searches, theoretical predictions are really more important.
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,
your coupling constants or the way particles in the coupling contents are smaller.
So all you do afterwards, you fix punch holes in the coupling constants.
So for instance, you want to compute an equal section that you compute it at lowest order,
and then you can compute the correction suite that are essentially expansions in this constant.
Thank you. So for the strong interaction, the capping content is around 0.1.
So when you compute what we call it next to reading order correction,
you can expect something of the order of a 10% correction next to the next leading order.
So Alpha squared something of the order of 1%.
So this is a bit now if I will show you for the Electroweak interaction because it is of the order of 1%.
So when you do an x two leading order conclusion, you you could have a very good position.
The other thing to keep in mind is that when your measurement is very inclusive, this works nicely.
But once your measurement is less inclusive, typically when you're sensitive to two different energy scales,
for instance, a hard scattering of the forces enters of the scalar.
What happens is that in your code section you will have large log of the ratio of these two scales.
So when the logs are larger, they compensate the fact that the coupling is smaller.
And so you have to change the way you do this expansion and sort of talk about
the result calculations and you talk about leading log next leading logs.
And so these are essentially different ways of doing better with the fixed functions way.
So now when we go back to the Higgs at the LHC,
what this graph shows is how the Higgs is actually produced under different production modes as a function of the Higgs mass here.
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.
So you have to know what's coming from your post on that. And so a top loop, they produce a Higgs.
So, so this is a process that is loop induced already.
So the gluons don't copula to the Higgs because if you want some lesser, but the top four has a very large mass.
So even if this is looping, you said this is the dominant process.
Then you have other processes like vector fusion production where you have two balls.
Once they cancel each from important, they together they build the Higgs in the final state or processes where the Higgs is
isolated from the bottom and so also insensitive Higgs produce associated with T-bar.
Now here the coupling is also very large the Higgs to to back out.
On the other hand, you pay a price because you have to produce also two tops in the finance.
So you need a lot more energy to produce this. That's why this is so much smaller than these forces here.
So these are the ways the Higgs can be produced, you see.
And the other thing to keep in mind is that we never really see the Higgs,
because the Higgs has a very the case essentially immediately propagates fuel from two metres and then decays.
So you never see the Higgs. What you see is the decay modes of the Higgs.
And this is again flawed, showing the different branching ratios of the Higgs.
And this is where we are, where we did discover the Higgs.
And you see that somehow it's a very nice place to be, because if the Higgs had been much heavier,
essentially you would have seen only the Higgs decay in 2006.
So you would have never been able to see those moments.
And if the Higgs would have been much like that, you would see essentially on your TV there, but never those modes here.
But in the place where we are, we can essentially see all those two key to look at.
For instance, Gamma. Gamma is in fact very small, was one of the discovery channels.
And this is because the signature here is very clear. So we already could see all of this.
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.
So you can look at those sections so different that you can always look at the ratio to the prediction from the standard model.
And you see that essentially there is no deviation. So this looks really like a Higgs boson.
On the other hand, you see that this was actually really quite large here.
There is a little tension, but not too much.
And this is the plot that already showed once. But you see somehow this nice fixture mass aligned with the coupling.
Right. Now there are two we now restart and essentially we redo this test.
So trying to decrease to zero as much as possible.
That's now I want to discuss only one of these calculations.
I mean, behind the all these production modes and the key modes, there are difficult calculations.
And I want to focus only one, which is the simplest one here.
So he filled out this team list, but dominant.
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.
One nice thing about the hicks is that being a skater, you can always forget about the key and include it later.
For instance, Viktor goes on to cancel it. So here, let's focus only on the production.
This is loop induced. This makes things difficult.
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.
This loop essentially shrinks to a point. So let's say that that leading or this is your production where this is an.
I think so. And then once you're in this limit, you can do loop corrections to this.
So if you talk about next to an actual leading order, what you do is you have diagrams, for instance,
where you have to we want to exchange this where you have one loop and one area or two areas.
So these are called features, the ones this is real. And this calculation was done over the 12, 15 years ago now.
And this is what comes out when we do this calculation. So let me explain a little bit this plot.
So as one said, and everybody knows that you said, when you do custody corrections, you have to normalise the CD.
And this introduces a normalisation scheme. And typically what we do is we choose the normalisation scale to a physical scale of the process.
Here we are looking at Higgs field action. So a natural choice is to fix it to the mass of the Higgs.
So, in fact, in this plot, it's set for some reason, which I can explain,
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.
And conventionally we're always very effective sector up and down.
And this gives you a bend. So this is how right is your leading order prediction here to centre value?
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.
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.
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.
So the way we sort of use, the way we estimate the fear,
uncertainty here for the leading order completely fails to sort of tell you what is the size of the next reading.
So these two bands don't even overlap.
These bands now overlap a little bit, but still the centre value is really at the edge of this bend.
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,
but this is not converging very when your next two leading order Quebec decides now easily could be 10%.
Here it's a factor two. And then next to the next leading order, that could be 1%, very naively.
Here is, in fact, another 20, 50%. And this is what makes things really very difficult in the case of Higgs production.
Right now. So this is a picture that we had essentially a few years ago to a few years ago.
So what people have been doing now is. So there are two ways in which you can feel.
You can say, okay, it's time to go. And you tire of all the teams approximately with this type of resolution.
So identifying if there is a large log and trying to resolve those was something that is more brute force.
You compute the next two, I mean the six punch or the entry and or two and took it.
Can this be so difficult? You are expanding your computing, the field or the team in this expansion.
Is it that difficult? Well, so some facts about this calculations.
So I told you this involves really accurate interference, diagnose and so on.
If you count a diagnosis, a hundred thousand interference diagnosis, you have to compute that at the next to next leading order.
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.
So this custom. So this is the face, this integration, these are the particles that counted in this calculation.
So you have this integrals plus another 68 reasons and so on.
And in comparison, this is the number that you have at next to the next leading order.
And so the way these integrals are computed is you write down the expression for the interval and then you have some reduction mechanism.
So the way you relate this integral to a set of simple scalar mastering to go.
And so this is the process. You find a way to reduce simplicity of simply indigo.
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.
You have to see that, you know, 26 such integrals.
So things are effectively much more complicated and these calculations are possible because there are new technologies which are used to do this.
Integrals, in fact. So this is one of the most up to date plots now of the season.
So this group did not finish the calculation yet, but could do it in some approximation sort of a threshold expansion.
So there is enough proximity expression now for these calculations.
And different groups now took their results and put it in the calculation as well.
And what this plot shows here, this is this one number, one simple number for the cross section.
These are different groups. And this is the old recommendation that we had essentially before this calculation.
And this is how numbers change. From different groups, the oldest to colours, light blue and dark blue.
These correspond to different choices of your normalisation, scale and peaks over two or three weeks even.
This is sort of debated what should one choose?
But the most sort of striking thing I think about this plot is that if you look at what these people say,
they believe that better because we learn from what happens at next, the next leading role that what is important and what is not.
They sort of believe that they have a very precise number and the really very small level.
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.
Things can change a lot once they finish the calculation.
So they claim that, in fact, the central values should go down and the uncertainties is really very large.
So these are the things that are really now hotly debated.
And let me conclude by showing one of the slides that was presented in January now about essentially both these results.
So the question is a little bit easier, wiser when you try to learn from what you learned next,
the next leading goal, and you try to apply that, then Cubillo or whoever you have.
Why is that? If you admit that you don't have this full calculation yet and you should have a very conservative variable,
and these are the things that are really now a bit open and under discussion.
So let me conclude by saying we had fantastic data from on one end.
I think we perform even better. There is a lot of expectation it starts this summer.
It will be very exciting. The Higgs discovery was really my SO it was a remarkable success.
On the other hand, it leaves many open questions, the hierarchy problem and thinks about naturalness.
And so now we're want to will focus on these precision studies.
And as I said, I mean, procedural studies. You can't go on just with experimental data.
You really need to futurists and experimentalists to work together.
So what is shown here is, again, this is this Higgs cross-section where can go.
This is an image of a tool from this meeting in Germany, where fear and experiments go hand-in-hand together.