 Poziv even nekaj prišlišnjen, je še česnimi in odning, hovorim, je zelo ili svojeh. Jer jo v pred Tusu, ker mimo je se tako zelo počakamo, kjer voda za vsem mora. Tostanje leksoriraj, zelf je vsobrš Još. Tostanje leksoriraj je v kompostiji, The name Seys, ideas, in the idea that the位 could be composed particle with a compositive scale, which means with the geometric side not far from its mass. And the first reason to try to ask whether this could really be the case is a bit heuristic, but it sounds rather strong, Namely, smo vzelo, da vse zelo spindzirnega bozina, ki je vzelo, ki je nekaj, ki nekaj, je, da kompostivne partijegar. Sve spindzirne partijegar, ki smo vzelo, je hodronje KCD, ki pa jons, sigma, keons. Zelo, da je kompostivne partijegar, komposit partikor, ki je, da bi pripovorečili zelo sem vziv, ki bi se zainemno radi, što bi se vziv na vziv in neče, da so da vziv elektromagnetnji radu z vzivem, neč proton, neč z vzivem, ki je vziv vziv in in vziv na vziv. Kaj je vziv, ki se vziv vziv na vziv, a neč je z vziv vziv vziv na vziv, in se zgleda, če je za toga značnega共jačna kacidina in taj je biloapproprialo, ali je bilo drakovno, da to bilo.- Je to začetno nekaj, bo naželi se različno, da je zelo ta držena, in brzak je, da tega oblh�� ne pri funnel ne začel, ima neki, da je se značno, zelo je nekaj začetno, in je biti prijev, da je so ne bilo jez, ali je to način. Tudi tebe se način z vrštih bila. In je biti leža, da je to začin nezavrštih, ker je dolgoz to, in tudi se način zelo način. Vzelo, da je to najbolj uristivne motivacije, je to sekazne, da ne je površtik, in z占jati kompositih. The main motivation for studying compositih is the hierarchy problem, or naturalness problem, and so the fact that the presence of a geometric size of the hexes so a composiness scale of the hexes, not too far let's say from the TV scale, so composite hexes, solves the hierarchy problem. mislim, da se najbolj izvršen, in kompositivni soluzion v 10 minutih. Prepovo bomo se počasila, da sem nastavljena pristata, kaj je najbolji koncept in ideju, ki je zelo v kompositivni stadi. Tukaj bi pa se počasila, da tega naprejnaje. So composite X theories are charakterize by to main physical concepts or physical ideas that I will describe in turn. The first one is that so the the x is a composite state but not only that, the x is a specific composite state. The X is a composite Nambu Goldstone boson. Well, I forgot to say, but it's rather obvious. The X must be the bound state, but it cannot be the bound state of QCD. It will never make it to make a resonance of 125 gV. So if I want to study this possibility that the X is composite, I have to introduce a new confining strong force. An entire new sector, conceptually or, say, naively similar to the QCD theory that confines and delivers resonances among which the X. And furthermore, this composite sector theory must be endowed with a global symmetry. And this global symmetry must be spontaneously broken. And this is what makes a rise, as you know, I think very well, special particles, which are Nambu Goldstone bosons. And the X, these are composite states as well, like the pions of QCD, but they are different from the other bound states of the theory. In particular, they are naturally much more lighter, because of the spontaneously broken global symmetry. So the X is going to be a special hadron of this new strong sector, a Nambu Goldstone boson. Actually, the X is not exactly a Nambu Goldstone boson, because in particular it has a mass, and so it's actually going to be a pseudo Nambu Goldstone boson. So why we need this hypothesis to start with, I already anticipated. So we want a situation where the X has a geometric length, like the other composite states. The length of the X is now not set by lambda QCD, but it's set by another scale of confinement that I call M star. And this is the scale of confinement of the new strongly interactive sector. And the situation we want, we have in mind, is the following one. So a generic composite sector, like for instance if you open the particle data group, you discover that there are plenty of hadrons. And most of these hadrons, including proton, neutrons, and others, they share more or less a common mass, which is the lambda QCD scale. So the composite sector is going to behave in the same way, and so we are going to imagine to have a wide set of more or less narrow resonances, similari to the one that have been observed for ages in other spectroscopy physics, in the case of QCD, more or less all of them with the same mass. Perhaps not narrowly degenerate, but let's say this is mass 1, this is mass 2, 3, and 4. Already, please. Because the QCD scale is 300 MeV, 1 GV, and so you cannot have a particle that is 125 GV by QCD. Andrea, if you can repeat the question. Ah, sorry, sorry. The question was just that why not to consider the Higgs as a hadron, as a QCD hadron. And the answer is that QCD confinement is so low that it's impossible. If you want at 125 GV, QCD has already been confined. And so you know it's not going to produce resonances at that scale. So what I was saying is that our composite sector even without knowing anything about that is expected to give all a whole set of particles at the scale in star. These particles are called the resonances, the resonance bound states of the composite sector. Now, if the Higgs has to be one of these hadrons, we will be in deep phenomenological problems. Because if you pick randomly any of those hadrons, it will be surrounded by particles, all more or less with the same mass. Somebody above, somebody below. And of course we have already observed one resonance at the LAC. And we know that there is no other electro-wig charged or even colored resonances up to one TV or so. So what we really want is that the Higgs is not inside this grid of resonances, but it's detached, it's below. It has a lower mass. This is naturally what happens if the Higgs is a pseudonambu-Golston boson. Because a Golston boson is an exactly massless particle. If the Golston symmetry is exactly a symmetry, spontaneously broken, but with no sources of explicit breaking, it can acquire a little bit of mass, but its mass is not controlled directly by this m star, but it can be made, say, up and down. As much as you like if the perturbation that breaks spontaneously in the Golston symmetry is small. So the first reason why the Higgs should be a Golston boson and not a random resonance is that we want to explain why the Higgs mass is below the m star. It's below the confinement scale. This is why it's below the scale of these other resonances that I want to take more or less in the TV range or multi-TV. In spite of this, there is still people entertaining the possibility that the Higgs could actually just be one of these random guys. I know that I want to have m star at TV or multi-TV scale because sorry, again. The question was why I want to put m star at the TV scale. The reason is, of course, phenomenology. You see, the Higgs carries electro-week-one-two numbers. So electro-week-one-two numbers must be present in this sector. So the resonances of this sector will carry electro-week-one-two numbers. The most dangerous one are spin-one-electro-week-charged bosons for which the bound is of around two or something like this TV. Now I will repeat the question. Now I understood how it works. So if I understand the idea of composite net correctly and I draw an analogy with the standard QCD, then in QCD the scale of compositeness it will be 300 EV or so. And we know that proton is a composite object and its mass is higher than the QCD compositeness. It's 1G EV. So if I draw the analogy, then the Higgs mass should be higher than the compositeness scale. Because proton is a composite object and the... If I understand properly the question, in QCD you can quantify lambda QCD as the place where there is the pole. And this gives the 300 MeV that you are mentioning. However, aside from the Goldstone bosons from the pions, which are light for a reason, actually the resonances of QCD are more close to the 1GV. So if you average the other spectrum you should better read lambda QCD as 1GV rather than 300 MeV. But the important point is that whatever this... we are dealing with another sector which has nothing to do with QCD so we are free to place the scale where we like. Suppose we place it at the right place to reproduce the Higgs mass, 125GV then they all come down together. All the resonances. And you haven't seen them. In case of QCD suppose the constituent particles are very light. Proton mass is 938 MeV and the constituent coax are of the order of MeV. So the main source of proton mass comes from the binding energy. I guess if that is the scenario of the Higgs also with some other kind of strong interaction then the binding energy contribution should be much higher than that. If the compositeness scale is... sorry, this m star is the binding energy in analogy with QCD this m star is the binding energy contribution has nothing to do with the quark masses. The confining scale of QCD is what has 1GV or 300 MeV to give whatever you want which sets the mass of the addrons has nothing to do with the constituent quark masses. So that is kind of the binding energy of the Higgs boson. There should be a bilinear that breaks some symmetry and we will see it more. I was saying that I wanted to tell you that there is still some activity in trying to give up this hypothesis not to treat the Higgs as a boson but as one of these resonances. None of this proposal as far as I know I have a structural reason why the Higgs should be lighter because we are able to explain in a natural way why the spectrum looks like this and moreover this kind of proposal our intention with another important property we should ask to the Higgs to be physical. Namely the fact that by now we have measured the Higgs couplings not very precisely but we do have measured them. And also the Higgs couplings they enter indirectly in that physics there are very precise calculations in which you have also to include loops that involve the couplings for instance of the Higgs boson with the electrowig bosons. And so indirectly we know that these couplings have to be not too far from let's say 20% or 10% to what is predicted by the standard model and the standard model of course the Higgs is not composite it's an eminently elementary guy. The Higgs was just a random resonance lost here in the middle of the spectrum there would be no reason for this to happen. The couplings would be allowed all of them to deviate at order 1. Instead if the Higgs is a pseudonambugal stone boson by a mechanism due to Georgian Kaplan and collaborators which I will explain and it's called say vacuum misalignment. I will tell you which vacuum is. So it is a mechanism by which you can systematically recover a Higgs particle emerging as a pseudonambugal stone boson with couplings that are arbitrarily close to those of the elementary standard model. More precisely there is going to be one parameter which is called the misalignment angle that if you take it small enough you can make the Higgs look like an elementary particle as much as you like. Taking this parameter small as far as we understand there is not a consensus of a structural reason for taking this misalignment angle small so this could either be something that we should still invent or it could be the result of some little amount of cancellation where for this to make sense should not exceed say one into ten or something like this. Ok, so just keep in mind that inside vacuum misalignment there is one fine tuning taking place. Only one however that controls all the Higgs couplings and more than that and other observables as well. Ok Ok, so that's the first important physical idea the second important physical idea is more technical I will I will just tell you the name basically it's called partial fermion compositeness and this has to do with the way in which we couple the fermions, the matter fermions, the quarks and the leptons with the composite sector and since the composite sector contains the Higgs this is unavoidable, we want to couple the fermions with the Higgs in order to generate their mass ok, and to give rise to the Yukawas ok, all things that we start also having observed ok, the mass ok so we will see that there are two ways to do that one way is doesn't work and the way that works seems to be this one ok, just to well just to for you to keep in mind this hypothesis on the way in which we will make the fermions communicate with the composite sector seems to be really mandatory ok, not to run into inconsistency only actually for the top quark and perhaps also for the bottom so, just to say that we are sort of convinced that this is the right thing for the top, for the others, for the other quarks one may consider alternatives still it's an open model building activity on this ok so, this was the most important part the physical ideas, but there are also technical tools that perhaps are the main obstruction for people trying to understand this stuff so, the main technical tools we will need to study the implication of these physical ideas and that I will try to briefly summarize are first one, the physics of non linearly realized symmetries so, a non linearly realized symmetry is a spontaneously broken symmetry it's a synonymous we call it non linearly realized on purpose because a spontaneously broken symmetry is not broken is indeed realized on the physical fields in a complicated non linear way but the fact that it's doesn't mean at all that the symmetry still doesn't have a lot of predictive power in particular it has a lot of predictive power on the physics of the Pseudonambo-Golston bosons that is on the physics of the Higgs and we will use this to make predictions so, in particular we will compute the prediction for the leading order in a momentum expansion the leading order corrections of the couplings of the Higgs to standard model particles so, we will compute the Higgs coupling to vector bosons and the Higgs coupling to fermions the second tool is called power counting and it is needed for beyond what we can say only on the basis on symmetries power counting means that you have a low energy effective Lagrangian whose operators you can predict by symmetries but whose coefficient you cannot predict by symmetry it's a free parameter and power counting is in the first place a way to estimate the size of this coefficient it's not gonna give us a definite prediction only up to order one number but it is absolutely essential first of all to make sure that the leading order prediction that per x are fixed by symmetries like the Higgs coupling modification are actually robust because the corrections can be estimated to be small and furthermore the power counting rule that we will derive is gonna be important to describe the physics of resonances you know that resonances that I wanted to be heavy enough not to be seen still we hope them that they are light enough to be seen now at the LAC run 2 and so we would like to describe and parameterize in some useful way their phenomenology and also for this we need power counting just to mention a final 2 prime tool which I will just mention I will not discuss in any detail so so I will not discuss at all our phenomenological models so you may have heard about these models even though perhaps you are too young in particular the very popular models of composites where the 5 dimensional holographic models so which are interesting quantum field theory things also because of their possible connection with weak and strong coupling duality ok and they were used to be they are formulated as theories in 5 dimensional space typically with a war factor Alaranda Sundrum they were historically very important because they provided a first representative example of all these 2 k physical ideas x as a number goes to boson and partial fermion composites they are all inside these interesting kind of constructions but I'm not gonna discuss them because it's technically too much ok ok, this was the plan of the lectures if there are questions or special requests if not I go to the I start I want to start by the motivations ok, as one should do so by the motivations of the composites that is the hierarchy problem and the way in which composites solves the hierarchy problem and under which hypothesis so but even before that ok let me remind you I'm sure Marcus already explained this to you that the standard model of particle physics is for sure right, an effective an effective field theory so sometime people say let's interpret the standard model as an effective field theory like if it was say I think you can or cannot do the standard model is an effective field theory and we are sure that the standard model is an effective field theory because it has a cutoff which is it has a maximal energy which we call lambda standard model above which it is not applicable it doesn't give prediction it's wrong we don't know where this scale is we have an absolute upper bound on this scale which is provided by the Planck mass which is where the perturbative semi-classical description of gravity which is inside the standard model breaks down but this scale is very high 10 to the 18 gv so if the standard model cutoff was really that high in a certain sense we would be say tempted to regard it as a fundamental theory given that in practice it is difficult to reach such a big energy and I think you are all familiar with effective field theories and in particular with low energy effective field theories that is theories that are valid below a certain threshold of energy but I just want to recall you a couple of concepts taking from the simplest example of a low energy effective field theory which is of course the Fermi theory so the Fermi theory works as follows in the scale of energies at a certain point you hit the W mass and you have a complete description of physics of electro-wave interactions that goes from zero up to above the W mass quite above which is the electro-wave theory or if you want the standard model but here it only matters the electro-wave theory part of the standard model and below the critical threshold which is provided by the W boson mass you know that well the W's cannot be produced so we can compute we can define an effective field theory in which there is no W particles and there is only the fermions and the Fermi theory holds from the W mass below and the Fermi theory is an effective description of the electro-wave theory and we know we are sure about this because we can really compute the Fermi theory Lagrangian starting from the electro-wave theory by integrating out the W boson the thing you have seen in all textbooks so the Fermi Lagrangian now we know that is some parameter G Fermi psi bar psi square plus all possible higher order correction about the W and expand the propagator you know this gives a lot of higher derivative operators but the leading order contribution to GF comes from this diagram with the W in between and it is G W square over 4 square root of 2 and W square ok so conceptually we know that the Fermi constant is not a fundamental parameter is an effective field theory parameter we know that it is derived from the electro-wave theory because we are able to compute it and we input G W and M W we get the right value and so we know that the electro-wave theory is the microscopic UV completion of the Fermi theory which is the theory that stops down here now for the standard model one day we will be able to do the same operation one day we will know the equivalent of the electro-wave theory the one that holds at very high scales above the standard model cutoff and we will be able to be able to compute the standard model Lagrangian ok as an effective Lagrangian originating from a more fundamental theory and trying to guess what this fundamental theory is of course the job of BSM physics and is what compositing model building is done for ok so the picture is like this in the scale of energies there is the Planck mass or some other very high scale it doesn't matter much they are the same as infinity as far as this discussion well to some extent proceeds this is the gut scale of 10 to the 16 gv which could be also another critical scale in physics and at this scale you have some theory which we really don't know anything about it could be a string theory there could be gut or whatever else now below the Planck mass and perhaps also below and gut but well doesn't matter much we have the standard model cutoff and the only thing we know about the standard model cutoff is that it should be above the electric scale because this is where we have tested the standard model ok so as I told you the problem is that we don't know really where to place this thing in the range of energies so by knowing this fundamental theory which of course I don't know I will be able to obtain the standard model as an effective Lagrange so I will reduce myself to a low energy theory below the standard model cutoff which contains only the standard model particles and the standard model symmetries which are the Lorent symmetry and of course gauge invariance and I will integrate out all the heavy particles that arise at the standard model and above and I will obtain an effective standard model Lagrangian like for the Fermi theory so one day I will be able to compute the standard model Lagrangian compute these parameters in terms of this more fundamental theory so what I'm gonna get I'm simply gonna get as for the Fermi theory general possible Lagrangian which contains the standard model fields and is invariant under the standard model symmetries and what I can usefully do is to classify the possible terms that I get into the Lagrangian by their dimension in energy d so there will be the operators in the Lagrangian of dimension 4 the Lagrangian itself has dimension 4 so the pre-factor here is dimensionless number then there will be operators of dimension 5 since the Lagrangian must have dimension 4 this must be 1 over lambda standard model oh well this must have a negative energy dimension how do I estimate how do I estimate by just dimension analysis what is the number I have to put here it's obviously lambda standard model because it's the result of some physics taking place at this scale I can put for instance in the case of the Fermi theory the scale that controls higher derivative corrections when I expand the propagator is just p square the momentum which is derivative square over mw square and here is gonna be the same thing so dimension 5 and then of course I can continue there is dimension 6 which is weighted by 1 over lambda standard model square so that's what I'm gonna get now what I will try to argue or to discuss is what I can infer from observation concerning these various terms in the Lagrangian and concerning the expected size of this lambda standard model so when we say that perhaps there is only the standard model what we really mean is that so the so called standard model only option is that lambda standard model is huge and useful so a critical place where to put it just to fix the ideas more or less but suppose the standard model cut off is at the order of the god scale of 10 to the 15 gv this scale has a reason and I will briefly mention why in a second so this option of no new physics at colliders for instance there is new physics also here that matter this option here is strongly supported if you look at these at these operators here if you look at d equal 4 5, 6 d equal or larger than 4 operators this picture is very strongly supported because at d equal 4 the Lagrangian you get is just the say the Lagrangian of the standard model as it appears on the CERN t-shirt which is the normalizable standard model Lagrangian that was written down in the early days and we know that this works very well so this is the t-shirt standard model so this account for basically naively all what we have seen aside from important issues you know there is the strong cp problem the cp phase is equal to 0 but it is dimension 4 so it is not suppressed there is no dark matter there is no candidate for inflation biogenes but the point is that all these issues which are of course serious issues could be solved just by physics at say either very quickly coupled so that is relevant in this argument or very heavy which is exactly at the scale or above if you look at d equal 5 operator the evidence becomes even stronger because at d equal 5 you can see that there is only one more operator to be added to the standard model Lagrangian and this is the Weinberg operator which is 1 over lambda standard model the left-handed lepton doublet bar the Higgs the Higgs conjugate conjugate means high sigma 2 times the X star is the conjugate X doublet and then there is and this is SU2 indices which are contracted with each other and then there is the left-handed doublet again but the charge conjugate of it times the X conjugate once again so by this only operator which comes the only one at dimension 5 you can explain neutrino masses this gives Majorana neutrino masses if you check it and it gives Majorana neutrino masses of a side which is almost right if you take lambda standard model 10 to the 15 gv so d equal 4, d equal 5 roughly speaking explain what we have seen and also explains why neutrinos were so light because well because their mass doesn't come from some dimension 4 term like the Yukawa for the others but it comes from a dimension 5 so the mass of the neutrinos will be suppressed by this 1 over lambda standard model huge suppression d equal 6 operators are not so dangerous with this very high scale for instance if you look at, well they can induce proton decay this is the most dangerous effect they have but they induce proton decay of an amount so the width of the proton over the mass of the proton which is a good dimension less measure of how narrow the proton is predicted by d equal 6 operator of course it's not observed, there is a bound only on this 1 over 8 pi which I put just for fun mass of the proton over lambda uv so you see the d equal 6 operator are weighted by 1 over lambda standard model square so in the amplitude there is 1 over lambda standard model square everything goes again square because I have to make the model square so all this goes like 1 over lambda standard model to the fourth to make something dimensionless here and this estimate is still roughly compatible with observation which give for this an incredibly small number of 10 to the minus 64 ok now if you look closely to the numbers so the scale you need to do neutrino masses is in slight tension with the scale you need to do so to suppress enough proton decay or whether you should take into account that these are all estimates with 1 ok here ok 1 over lambda standard model 1 over lambda standard model square we have no idea whether this one is actually a product of couplings that can be very, that can be rather small in one case and larger in the other so qualitatively this is still perfectly compatible and perhaps the only sign of this could be if we are able to improve the bounds on proton decay by say 3 orders of magnitude then we don't see it this could be in tension otherwise it's perfectly ok ok ok so this is to tell you how important the hierarchy problem is because if was not for the hierarchy problem or if we discover that the hierarchy problem is not reflecting in new physics at the LHC to me well there would be no structural reason to destroy say the standard model to change the standard model in large way at the scale which is below around the gas scale ok of course there are all the issues I mentioned here which have to be solved but they could be done by some tiny deformations not with some radical change because you want to buy all these successes instead the hierarchy problem or the problem of naturalness is challenging this picture in a very radical way because here I just wrote operators of dimension 4, 5 and 6 but I forgot to write operator of dimension less than 4 and again there is only one such operator which is the Higgs mass term which has an energy dimension equal to 2 and so if I do dimensional analysis also for the Higgs mass term and not only for the large dimension guys which I think I should do for consistency at least then I find that this mass term has an estimated coefficient of some order one number the standard model cutoff square h dagger h ok so this would be the Higgs mass but of course the x is 125 gV so lambda standard model we took it 10 to the 15 there is a big mismatch which is the hierarchy problem the hierarchy problem is asking why the Higgs mass over the standard model cutoff is in this say MGAT physics scale is of around 10 to the minus 28 so which is much much much much much smaller than one ok so is asking why this is gonna happen ok ok Frerno origin question let me go on so the hierarchy problem the first thing you will say about the hierarchy problem is that maybe it requires new physics at the TV scale or at around the Higgs mass itself of course this is what we are gonna do keep in mind that this is a very dangerous game because if the new physics scale is rather than 10 to the 15 gV is say 10 to the 3 gV then all the higher dimensional operators become huge ok and so it's clear that they cannot just come with a generic order one coefficient they must be strongly suppressed and indeed model building at the TV scale is a dangerous and delicate business ok which comes from which has constrained from zillion of different places ok on one end also because of this there is an objection you may make to the hierarchy problem in the way I stated there which is the following so we actually seem to have found that the Higgs mass is not equal to the standard model cutoff but is proportional to the standard model cutoff with a proportionality factor C and and given that it looks so difficult to put the standard model cutoff light with respect to phenomenology then it could be better to make C very small ok so we could take lambda standard model at MGAT but just C of order 10 to the minus 28 ok trying to find some microscopic reason for this to happen in the UV theory ok this wouldn't help actually because there is another way in which you can better view the hierarchy problem which is connected with the solution offered by composites ok so this doesn't help and the reason why this doesn't help is that the Higgs mass parameter that we estimated down there is not the full answer for the Higgs mass is not the physical Higgs mass the physical Higgs mass receives other contribution in a Wilsonian approach to the normalizability this would be very clear here I just do a poor man version of the Wilson approach ok so let's read something in a slightly different now I'm interested in computing the Higgs mass ok because one day again I will know what is the fundamental theory that gives physical origin to the Higgs mass for instance it could be a composite theory and this calculation can be really done ok so what I'm gonna write you could put number inside and the prediction of this Higgs mass will be performed in terms of the fundamental new theory parameters that we are gonna call P-Fund and we'll have an algebraic form that we are not able to predict but we can write it we can parameterize it as follows so the Higgs mass prediction as computed in for instance your favorite composite theory ok is an integral over the energies which extends from all in all the energy range of some function which I don't know what it is so I just call it dmh2 over dE and this is something that after integrating becomes the Higgs mass which again depends on the energy scale and on the fundamental theory parameters ok this energy in say the Wilson language would mean the shell of momenta that contributes to the Higgs mass ok in our poor man approach this just means the energy of the virtual quanta into the loops that contribute to the Higgs mass indeed this formula is written having in mind loop contribution to the Higgs mass so diagrams like this with here standard model particles but also plenty of other new particles or those that come in the fundamental theory which I don't know and in this case it would be the energy of the virtual particle inside here and what this means is that a priori the Higgs mass receives contribution from all the energy scales that goes from zero to infinity the formula does not prevent to be used in case of three level contribution for instance in gut models there are three level contributions to the Higgs mass in gut models you can predict the Higgs mass as the difference of two masses of two triplet and doublet that break the SO5 the SO5 gut group and there is one place in which you see the fine tuning but in composites for instance is perfect like this you don't need to put any delta function here because there is not three level contribution it's only radiative contribution and the thing that is problematic is that again following Wilson I can split this integral the shallow momenta from low energy to high energy so I can just write this as the integral from zero to an intermediate scale that I will take to be around the standard model cutoff but just a little bit below because I want to live in a range of energies where the standard model is more or less valid so I have to be below its cutoff plus the integral from this intermediate scale up to infinity so again this is what Wilson would call infrared contribution and these are what we call UV contribution because it's really what they are it's basically the guy here we were estimating before it's the contribution from the physics above lambda standard model one we integrated out to get the X mass so actually the X mass is not only this piece it's this piece that I call which is the same as there which I call delta BSM MH2 so it's the contribution of beyond the standard model physics to the X mass but then there is also a contribution which comes from standard model physics so this contribution gets accumulated in a range of energies where we do know the theory so this other contribution delta SM of MH2 we can at least estimate it by our knowledge of the standard model what it would be simply it would be the usual say quadratic divergence calculation so the contribution of the X mass so these things here are associated with loops like the dominant one being the one of the top because it's the top is the guy with the largest calving to the X there are also other contributions I'm not gonna write which has to be integrated over a range of momenta which goes from zero to around the standard model so standard model cutoff so more or less is like taking this loop interpreted the energy that flows in the loop as this scale here and integrating only up to the standard model cutoff so this calculation happens to coincide with the quadratic divergence calculation let me insist that the quadratic divergence calculation is not the calculation because the quadratic divergence cannot be computed but the calculation makes sense as our estimate of this physical contribution to the X mass that will come in this fundamental theory that we still do not know and the result of the calculation you know very well is 3 y top square over 8 pi square lambda standard model square the fact that I get lambda standard model square again is due to the fact that this diagram is superficially quadratic divergence so now we start seeing the problem so I don't have to find a UV reason why this C parameter is to be tremendously small it's not what I need because the X mass is this contribution so delta BSM which is proportional to this C plus or minus, hopefully minus the contribution that comes from the standard model which is also huge so what I really need to do is to choose very peculiar value for C such that beyond the standard model contribution is almost equal and opposite to the standard model part they cancel, they fine tune and give us the X mass so the naturalness problem is a fine tuning problem which is to say that I have no conceptual obstruction sorry, no technical obstruction in getting the X mass light as light as I want if I just tune very precisely delta SM of MH square almost but really almost equal up to many digits to minus delta BSM square or vice versa I can tune, I probably want to tune delta SM MH square and I get the X mass that I want the amount of fine tuning I have to do means how much cancellation I have to do among these two terms to get the result is quantified by something that's called delta which is equal to let's say the standard model contribution one or the other doesn't matter given that they are almost equal delta SM MH square over the X mass square which turns out from that estimate and knowing also the value of the X mass is lambda standard model over 550 gb you see you see the sorry, sorry, sorry the usual problem yeah the question is whether the calculation is is gauging variant and whether it makes sense at all so I mean, if I wanted to do this precisely I would have I mean, I would have probably used the Wilson approach to resolve my zability which can be formulated not in the straightforward Wilson paper but it can be formulated in a gauging variant in a proper regulator way ok so here I want to give you the idea of what of what happens suppose for instance in the composites you can really compute the X potential and in particular the X mass and put it really in this form where this guy here is some say some two-point function some two-point function that results from a so it's a column by and by term that results from from an effective Lagrangian for the top for instance for the effective top and then what you really see there is that when you go to low energies below the standard model cutoff well the couplings in this effective Lagrangian are equal to the standard model coupling and so the contribution of this integral just becomes equal to the one of the standard model and so the contribution to the final integral that comes from energies below the standard model it's the one you expect from the standard model so if you want I could have done the full calculation in that gauge and in that gauge is completely gauging variant in Lorentz invariant and you would have found the C so the so what is the main there are still a couple of comments I wanted to I wanted to make because they are important for composities before going to explain why the composiness of the Higgs helps in this in this problem so first of all to the problem of naturalness you can give a quantitative sense so if you look at the fine tuning formula delta equal to lambda standard model over 550 gv square you may interpret this in different ways you may say well the amount the fine tuning is a strange thing it shouldn't happen so I expect delta to be of order one and so new physics at 400 gv 450 gv if you want a non quantitative interpretation that says that after you go above this kind of threshold in your search for new physics you should just give up you should accept that there is some fine tuning and at that point it would not matter if this fine tuning is large or small I mean that's just a way to estimate the place where new physics is expected to be or there is another more quantitative way to interpret this so which is as follows again taken from the experience in concrete models in gut or in composites so if you end up with a situation like this in which there is a formula for the Higgs mass that is written in this form and you find that this formula is made of two contributions which sum up and each of these two contributions is huge but the difference is very small then in practice it is like you don't have to start with any concrete prediction for the Higgs mass why? if I say that there is let's say new physics at the gut scale it means that there is 28 digits of cancellations between here and there and this means that well in my final physical formula for the Higgs mass you would have two unrelated terms one comes from the infrared the other comes from the UV they are both huge they have to be both huge but their difference has to be cancelled to 28 digits so if I want to predict the value of the Higgs mass only with one digit accuracy I need the 29 digit accuracy on this part and on this part of the story just for the same reason that 100 minus 99 is one but I have to know the 100 at one percent if I want to know that one is one and is not three so in concrete the fine tuning issue can be viewed as a predictability issue because I will never be able to compute these two pieces to this big accuracy and I will never be able to compute the fundamental new physics theory parameters so accurately to check that indeed this is consistent so in this sense the fine tuning can also have given a quantitative sense and this is what people try tends to do in the literature so for instance there is a fine tuning of around ten this means that my compositing theory happens to have this is equal to ten this is equal to nine to minus nine and the result is one I just have to work a little bit more to predict these two terms into the sum in order to check that the Higgs mass is what it is so tuning let's say equal to ten almost okay of course if the tuning is of the order ten to the three then well I will probably give up because at a certain point if it's too challenge to achieve a true prediction of the Higgs mass from the microscopic point of view then at a certain point it's like that the Higgs mass has not microscopic origin but it's a fundamental parameter and it will remain a fundamental parameter forever as it could be but you see this is an important information whether the Higgs mass and so in turn the electro-wiximary breaking scale a microscopic origin or it doesn't have it I think it's an interesting information that you can check because naturalness or unnatural are testable concepts as you see here so if the standard model cutoff is you can explore like now we are able to do with the LHC standard model cutoff of the order of the TV or multi TV you can access the region where this fine tuning becomes large and this is also the reason why in composite x we don't worry too much if we have to do a fine tuning of around 10 ok on something ok, what is that composite x does to address this this issue so in supersymmetry you have seen that you can really say check ok, that you cancel this guy by means of the new physics you can use powerful theorems here as well it's a bit more complicated to explain properly in particular because you don't have a model of these things strongly interacting new sector behaves in a way which we it's difficult to do at the blackboard example but you can understand qualitatively in a very simple in a very simple way so again in composite x the x mass is predicted in terms of the fundamental parameter and so you can imagine plotting the contribution to the x mass from different shells of momenta the one that enters into this formula ok, so dmh2 over de ok so first of all what you get in the standard model the usual quadratic divergence which means the usual linear behavior linear with the energy you integrate it up a certain cutoff you get e square, so that's what you get ok and this is what you're gonna get also in composite x at sufficiently low energies indeed there is this threshold which is the confinement scale m star that corresponds to the inverse of the sides of the x again lh1 over m star and this part of the plot here which is below m star corresponds to virtual quanta was wavelength given that energy is small the wavelength is large in comparison with the sides of the x ok, so this is like this and so, or even more and so the fact that the x has a size doesn't matter the x behaves like an elementary thing when instead you consider energies which are much above m star the wavelength of the wave of the virtual quantum you are studying the effect of is much smaller than the size of the x and so it starts to if you want to resolve the constituents of the x and what happens typically when you have a bound state and you eat it with a very high frequency sorry, short wavelength wave is that the guy becomes transparent to this wave the data in for proton electron proton scattering the ones from which it was discovered that the proton has a size it was because the interaction with the photon when you start reaching the proton size starts becoming weaker and so what you expect to see is that on this side of the curve the contribution for this kind of wavelength to the x mass is gonna go to zero in alternative way to see this is that if I go much above the confinement scale well there is no x there is no x physical x and so there is no say x master to worry about and so there is no expected to be any quadratic sensitivity to this kind of energies above much above the confinement scale and in between it will have a peak and so you will have you will gonna have a scenario where the generation the phenomenon of generation of the x mass of course is localized at the confinement scale so the microscopic origin of the x mass compatibly with the hierarchy problem is gonna take place at an energy m star which is not far from the TV scale or well the light is the better concerning the hierarchy problem and so the well the tension due to naturalness disappears and what is important is of course that much higher energies quanta will not give mass to the x because the x does not exist at very high energies so if you want you solve the problem of masses of scalars which is the hierarchy problem by avoiding having scalars by having scalars only at low energies clearly it's very important for this to make sense so basically what we did is that we attached the phenomenon of x mass generation to a scale which is m star, which is not too heavy that's what we did we made the thing happen at a place where we can still be natural but it's very important of course that the scale we attached the x mass generation 2 should not be itself pushed by naturalness to very high scale itself otherwise and you can easily cook models where this happens where you have a composite object which however is made of a theory whose confinement scale is itself set by a parameter m star which is not natural and this wouldn't help at all so the full picture that we have in mind is the following one and it really relies on some strongly interacting composite sector with the following property the thing we want is to have one day a big UV picture for the generation of the electric week scale so we want a story that starts at an energy scale which we call lambda UV which is perhaps of the very same order of the gut scale which is very high and at this scale you will generate perhaps by integrating out new physics even more heavy a sector, a new physics sector that we call composite sector and this composite sector have to have a special property which is called dimensional transmutation that is to say it must be capable to generate a confinement scale much below the UV theory where it is defined we don't have to look too much to exotic examples, QCD is one of such examples QCD is capable to naturally generate a big gap between the scale where QCD theory is defined where it is the scale it could be for instance an effective QCD Lagrangian could be defined when you integrate out the W and you end up only with quarks or even above QCD could be defined at very high scale and this would not be any problem and the way in which QCD behaves to do that is the following one QCD starts at a very high scale where it is weakly interacting being weakly interacting means that it is close to a fixed point of the normalization group evolution simply means that if it is close to being free then this theory doesn't run doesn't do anything, stays the same at all scales it is actually only close to this fixed point because it's not exactly free theory it has a coupling which is weak which makes it move a little bit from the fixed point this is the usual running coupling which goes from zero from small parameter but not zero it tends to become large and it has become large that it can deform the theory radically and make it exit from the fixed point and lead to violent phenomena such as confinement I say this in this complicated words in terms of fixed point and the formation around fixed points because it's likely that it's possible at least that the composite sector of composite fixed theory is actually not a plain QCD like theory in the sense it's not a theory it's a free fixed point in the UV it may be that it's a more general theory which has a fixed point of its say evolution but this fixed point is a strongly interactive fixed point and there is a certain activity in trying to in studying this kind of strongly interactive fixed point perhaps also for this kind of applications but if you just want to understand where this gap comes from just think to QCD and to the old textbook of dimensional transmutation so if you are sure that M star now is naturally much smaller than lambda UV then you can try to build some say potentially realistic physics around this scale so what you need let me tell you the ingredients in the composite sector we say that the X must be a gorshton boson and the first ingredient that you need is a global group I will take this group to be fully exact in the composite sector so by definition you may relax this assumption but for simplicity I'm gonna consider the composite sector to be exactly invariant under an exact global group ok it is exact and it's not even spontaneously broken in the UV like in QCD, chiral symmetry is not broken in the UV but then when you go in the infrared there could be there can be confinement and there can also be spontaneous breaking of this group actually we do expect this to happen generally speaking and so here you will have a spontaneous symmetry breakdown to H that occurs at M star, the infrared scale the confinement scale of the strong theory and in the breaking the sure thing you know is that you are gonna produce gorshton bosons and you want to choose the g and the H you want to find the theory where the g and the H are such that the Higgs belongs to this G over H, which means the Higgs is generated as one of the gorshton bosons associated with this breaking ok then you need another piece of the of the world which is the elementary sector so what is the elementary sector made of the elementary sector is made of all the particles that on one end we know they cannot be composite resonances by phenomenology and on the other end the particles that do not give us problems with naturalness so basically is made by all the standard model particles minus the Higgs so here you will have the fields that correspond to the standard model minus the Higgs doublet so here you can really have the most general Lagrangian at equal 4 with small corrections because there is no X master to worry about there is no naturalness problem there are not even Yukawa and so this will be because there is no Higgs so generating the Yukawa will require of course communication between this side and this other side and this sector then explicitly is made of the electrowig gauge bosons W mu B mu the gluon and these ones are gauge fields because we know that electrowig and gluon interactions are dictated by gauge invariance and nothing of degrees of freedom is not even phenomenology so these guys have to be gauge fields and there will be gauge fields associated with global symmetries that involve of course the elementary sector but also the composite sector in particular the Higgs has to be a doublet of the standard model group and so we know that this composite sector has to carry electrowig quantum numbers and the W mu and B mu and G mu will gauge part of these symmetries of electrowig symmetries that we have also on this side so this one will be coupled by gauging for sure then there is the fermions the only possible exception is the right-handed top which still could be a composite guy well and then of course you have to make these two things talk so you have to make a hypothesis on what are the most relevant interactions you can write among this sector and this other sector and these interactions l int so these interactions are gauge interactions for what concerns the electrowig bosons and the gluons they are coupled by gauging so you already know that the interaction here for the gauge fields will be G global current so we will be doing symmetry on the composite sector times W mu so this will be for sure the structure of the interaction of gauge fields for the fermions you have to make an hypothesis and this hypothesis is what we call partial composiness and this I will explain next time please can you repeat what the TR question mark is yes it means that the right-handed top quark opponent of the top quark could actually perhaps is not here but is there there is a violator same series so the question was whether some other symmetry could be violated by air dimensional operators symmetry is like biome number or leptome number in general of course it could be violated by new physics that is biome dimensional operators leptome family number as well the Weinberg operator for instance it violates leptome number and clearly if you do new physics at the TV scale like here you have to forbid this to happen so you have to impose that biome and leptome number are symmetries perhaps for a good reason but they have to be symmetries of all this stuff so basically I saw yeah basically done basically this course will be about characterizing these two elements and the way they talk to each other and drawing the implication of these of these hypothesis just before concluding I wanted to to mention to continue also one second with analogy with QCD because I find this instructive so the analogy with QCD is very close here so in QCD there is an exact global G is not really exact within the composite sector because in QCD there are the quark masses but suppose there are no quark masses in QCD it's a limit you can consider taking then QCD would be exactly invariant under some flavor group the chiral group take two flavor QCD the chiral group will be broken and this as correctly said will generate the mass of the addrons the mass of the resonances independently of the quark masses and nothing to do with that and there will be gorshton bosons which will be exactly massless from the viewpoint of QCD alone which are the gorshton bosons of QCD the pions also the elementary sector as is so analogous which is QED so the photon is clearly not part of QCD but part of the elementary sector it is a gauge field like one of those guys and then it interacts by gauge coupling so J electromagnetic of QCD let's say photon mu and also well also the electron and the mu ones they are elementary guys and they couple in a specific way through the photon to QCD in a way that by the way it assembles very much what we are going to discuss for the really for the couplings of the fermions and of the gauge fields to the composite sector in composite ticks in composite ticks theory ok that's it thank you first question can I afford a few seconds of awkward silence so tell me why should it be that the top is special in being the composite one rather and a little bit of bottom you said and other quarks or is this just an approximation there are two different things when I say that the top right could be completely composite is because phenomenology suggests that it's not excluded ok this thing here the fact that there could be not an elementary microscopic top right field the top right could be a chiral resonance of the other side that's just pure phenomenology the other thing I said is to discuss how to make these fermions interact with the composite sector you will we will see that we are going to do this partial compositeness hypothesis and we will motivate this hypothesis in a way that you will see has to do with the top quark mass so basically we will see that to reproduce the top quark mass right since it's so heavy we cannot do with say the bilinear ways of the technical and the option that only people consider viable is the one of partial compositeness so are two distinct things if the Higgs forms a multiplet a cost of multiplet how is the Higgs potential formed how does it generate yes the Higgs of course it's a gore stone boson it's an exact only from the viewpoint of this side here but there is interactions and yeah thank you for the question because I wanted to finish I forgot to mention the interaction not only are important to make this sector communicate with this other but they are so important because they transmit the breaking of the g symmetry to the composite sector which was completely invariant and I immediately understand because I'm saying that there's going to be a large global group on the composite sector under which the Higgs is involved and clearly there is not such a larger group in the standard model so the standard model feels they feel incomplete multiplets of the g symmetry and so necessarily their coupling with the composite sector will cause g breaking by the way QED, the QED photon only gauges one generator of the carol group over three and so it breaks it ok, so QED breaks carol symmetry the same way coupling of these guys break the global symmetry and then the Higgs overall will become pseudo number of stone boson it will be untitled to have a tiny mass some mass and also of course the potential which you will be able to compute within this framework let's say what puzzles me that TR is composite and TL is not, could you develop on this idea a little bit please what do you mean? puzzles me puzzles you same question can I say what can I say of course if you are looking for flavor symmetry this will not help you this is a breaking of the somehow the idea that flavor comes in a sort of universal way and then it's differentiated it gets differentiated by some structural mechanism it's also true that flavor symmetric scenarios we know many of them this is a new, say if you want it's a new flavor symmetric scenario it's an alternative it's a possibility it's a possibility so I was wondering you wrote down in the elementary sector just as the standard model fields minus the Higgs is there going to be another elementary sector which would be related to the composite sector as well or is the composite Higgs in the end made up by the standard model fields I was a bit confused about this so here there is the Higgs minus the Higgs plus the Higgs ok so the Higgs will be delivered by as a resonance of this sector as a resonance, sorry, as a govstone of this sector ok and so we don't need to put it here we don't have to put it here otherwise we reintroduz the hierarchy problem but you also don't have to extend the elementary sector to allow for this now that's a good question you may want so you don't need you don't need for model building reasons you don't need there are alternative ways to do this in which you should extend also the elementary sector so either because you want to practice model building or because you want to enforce some other special property like some additional cancellation in the Higgs potential like in the Twin Higgs stuff so there are some models in which you do extend also the elementary sector for instance realization of little Higgs little Higgs is a composite Higgs of a special kind ok in little Higgs the so called top part of little Higgs are actually elementary things couple so additional elementary stuff here ok so in some cases you may also want to do that maybe a related question do people learn also because now you only are focused on the hierarchy problem but for instance something like dark matter can it also be solved in these models? I don't find a particularly there is not the equivalent of a parity of course you can construct plenty of smart models or even not so smart in which naturally you do have a possibility to have a stable particle like other goldstones of the composite sector and not all of them are really a dock no they are ok I decided not to enter too much into model building and also I don't find the equivalent of a parity of supersymmetry supersymmetry is really this big thing which is a parity, seems needed in all places it also gives dark matter here dark matter can fit very well but not at the same level ok thank you ok so thank you again Andrea