 Thank you very much. As it has just been said, we are going to go a bit of topic compared to the title of the school and get our hands dirty. So as you might or might not know and you talk to experimentally, many of them think that we are full of crap to be interested in such a problem. But the only reason is that no one explains it properly. V konce je potom izvržil, da bi h FRP nekaj nepravil, in imal niske v bonesh teori, da ne zelo se vnešljenje med zelo v tom, da ne lahke je vizivne. specično roastedite. Ne zelo, čekaj, da ima to napraviti. No, zelo sem to, čeh ti je zelo. N Themenje zlovali v dišli, In, potem, sem prišličeti, da se pravamo nekaj solutov, ki veli nekaj solutov, ki tu svoj nekaj vši včin ni včalj, in kjer se nečo všim vseče je izgleda. A prišlič je izgleda, da sem vseči sem in nekaj tega, v kjer nešto je všeč napravil v teoretizaciju fyssiku. OK, priča in nekaj vseči, Zato bo me zelo, da je to nekaj stvari izgledaj, da je to najpravno način, da je tudi način, da se kaj več avšojeva izgleda, kako so prišli, da je zelo, in nekaj nekaj nekaj težne začin. V vseh uklavna časke izgleda v vzivnih vklavnjih je to vsez nekaj, odlega elektronovih sredne energij. So, you might ask what's the electron rest energy and it's is mass, you can measure it quite precisely. Let me write it bigger. And you know that this number is roughly alpha and imd. And of course, throughout the lectures, I'm gonna use natural units. And then at this point, you might wonder how to compute it in potrebujte to v pridikšnih. Evoč there'a svega člistnika z večem Belagranjšem parametrem. I tega v državnih elektrodynamikv, there'a svega energija, kaj je zelo v elektroni kaj je zelo, da je to vsega. Zavrčazim všem svega, na razlog od nekaj povedaj, that we know the electron size roughly up to 100gv. Assuming that we still have classical knowledge of electrodynamics, but we have lab-type knowledge of the electron size, so this just comes from having collided electrons at these energies and not having seen any constituents come out. The actual best limit right now might be better, but that doesn't matter. To je nekaj, če je zelo počke, da prijeljemo, če je to problem. PLAYING B for this number, you immediately see that in the experimental value you need a huge cancellation. So this quantity here is going to be of the order of 10 to the 5 MeV. And somehow it has to cancel against something else to an accuracy of alpha and MeV. Prvno je nečo vzelo viztelijno problem, boš ne možete začiči vzelo vzelo vzelo, ti je zelo blizi, da se dobro vso drugi zelo vzelo v zelo vzelo. In taj počet način iznačen, kako jaz nekaj začeljamo način, in je to način izbavno, tako pa se zelo tudi način vzelo vzelo, laughed that if you go too close to this kind of scales, quantum mechanics is going to start to play a role. In these problems, precisely around our radius of roughly 1 over the electrodimus. We're going to have quantum effects become important. Then if you do the computation properly and interacting in classical electronics, tudi ga se je zelo našem energijih, zelo početnega, pa je tudi se je inoč, in tečnji pa se vse. Vsih vse tem, načo je zelo način, je početna inčenja. Zelo početno, vse pa je začin. Tako, zelo, zelo začinj zelo, in ki je zelo, je zelo začin, več nekaj, that at some point your classical description breaks down and a completely para d Flag kicks grew. So these already should be enough to give you a hint of why these kind of tuning problems are interesting. But let me tell you about another historical example that has a completely different resolution and which is something that I've stolen from a public lecture by Prof. Sойдberg that will lecture you later in the day. So, at the time of Kepler, in planetarii orbit nič del situ Personal saturni začeli pri takrenu slajna izevimi. V 1569 vse začeli Vistaj, če mu je pokazila, da je tih svi orbiti Sorbetem semetrično zelo skor dejКu. Vse je obiteljba, kako je zs крanji rašad tudi tudi platonici zelo za pomečne in način tudi. Čekaj, on je začet v rečjo zredno in pri vseh 14. stvari, imaš vidno, da v tom, da je zelo po komentaciju, vseh 6 planeti, po vseh Saturni, se na pomečnosti. Se ga da vseh, inželimo to, kaj je ničične počarje, inšli je to našli izgod, od komentacija Kepler. Zato počri se bo, kaj je ničično počarje, izgleda, da se držemo, that we discovered that we are not alone, that there are many, many other systems that are just like a solid system. And these kind of accidents, even though they are likely, get one other one probability when we integrate over ces huge amount of starts and planets up there. So you might say that the resolution of these inter public problem was kind of completely opposite to the electron. There is no dynamics going on. The dynamical explanation was the one by Kepler. Svekštno,다는či,akštino z vsej zelo potrebovali izvršenja in če je stvarne do vsey. Svekštino izvršenja pozicija in našeljamo, da je zelo zelo več neče nekaj, da sem videla. Svekštino neče neče neče nekaj, da sem videla. Zato videlem tudi bolje zelo težko in je zelo pohvoj, všeč, da se je vsega pravda, da je več nekaj nekaj vzelo. Najske v pravda je, da se je zelo izgleda, da ne da srešem, kako ne bilam že, kaj je ještje, in kako je do vse kategori, nekaj da se srešem, da se je zelo izgleda. Vzelo se, da je zača. Zato vsega prišla izgleda, ki se pristim. in tudi počkaj smo počkali v arhiji problemu. Prezivno, da smo počkali, da počkali, da smo počkali počkali počkaj rejučnji teori, da je tudi vse dobro. Vse teori je tudi vse, da imaš teori, da je počkala počkala počkala počkala. ,, but your experiments can prove nature only at a much slower scale. Early reasonable question is whether the degrees of freedom appear, influence the nanomix down here and in which way. So you might start in purely formal way by biting your thought integral of your full theory and then split outra центр in 2 parts. There are modes that are light in the sense that theirordan ki da energije bolj zelo, in možume, ki je zelo, ki energije bolj zelo. Tudi je to tvoje komponente, in taj rač, kjer je vse vse vse. Vse je vse, vse vse vse vse, ko drugi pojelite. Vzelo vse na to, na naša vse, zelo pojelite, izgledaj, ki je pojelite, in vsebezgav, ki je izpravil. Od njih ne zestavim vseb, če je nisi, da je neko neštrža, kot na delovaj splušč? Zato izgledam, da nekaj je nekaj delovaj energi, ko je nekaj, in je kaj, nekaj neva infinitsa vsezne rukov z delovaj splušč, nekaj je večo vsezne, iz noženja. Zelo sem zelo v lokal, zato je, da je vse in tegrati moči vzelo v Londonu, tudi je operatori, ko je nezelo v lokal, če je to in spančenje v derivativnih. Tudi nekaj, ne zelo vzelo v nekaj, zelo v nekaj vzelo v nekaj, zelo v nekaj, zelo v nekaj, And you're gonna see that the symmetries that are broken are almost just as powerful as symmetries that are not broken. So in this case, the symmetry that we care about are dilatations and its selection rules. Clearly, dilatations might be broken in this theory, but we can still categorize these operators in terms of what representation of the dilatation operator they transform into. And this is just a fancy way of saying that we can do dimensional analysis. So we set h slash to 1 and c to 1, so our only dimension for quantity left is energy. And I can classify the operators based on what's their scaling dimension. In order for the action to be dimensionless, given that I set h slash to 1, then I know that the coefficients of these operators are gonna have dimension where d is the number of spacetime dimensions. And since I have a large scale in the theory, I can always make an answer, well not an answer, but I can always rewrite these coefficients in the following way. Where now the lambda i are order 1 numbers that multiply the right dimension for quantity. And notice that, again, here I've not lost generality in any way, so these g i's might get contributions from many different scales. But I know that my theory is only valid up until lambda. I know that lambda is gonna be the largest contribution, so at most I'm gonna get this. And maybe for symmetry reasons the lambdas are not gonna be order 1, but a bit smaller. So this is just a parameterization. But with this parameterization and knowing the dimension of the operator, so now I know how each of these g i's contributes to unobservable low energy. So the contribution to the action of one of the terms in this sum will be roughly scaling like this. Oh, sure, sorry. So what's the contribution to unobservable low energy? This is just given by the contribution to the action roughly of this operator. And it's gonna go like this. So from here you can see that based on their scaling dimension I can classify the operators in operators that have dimensions larger than the number of spacetime dimensions. And these at low energy are going to be suppressed by a power of this small number, the ratio of the low energy over the high scale. And so they're called irrelevant. Operator with scaling dimension equal to the number of spacetime dimensions are called marginal. And you can guess that these guys are called relevant. So now we have prescription to do something useful with this theory. Because given an experimental accuracy we can target this sum at some scaling dimension. And the contributions after that are gonna be smaller than our experimental precision. So we have a Lagrangian with a finite set of terms that allows us to make predictions after we fix the coefficients with some measurements. And so this is a very nice general way of taking a UV theory and getting its infrared counterpart. Or vice versa, it's also a tool if you don't know the UV theory to make predictions just purely based on low energy observable. So you might identify a set of fields at low energy, identify the symmetries of the problem, and then just write down this expansion up to whichever order you care about. So this might have been already familiar to some of you, but now we're in a position to define the hierarchy problem properly. But before doing that, I would like to show you really the power of this framework by writing down some low energy Lagrangians and asking whether they are surprising or not. Because this is another thing that this kind of formalism can do for you. So if you know the symmetries and you see some set of terms, you might ask whether they make sense or not. Even if you don't know the UV theory. But actually before that, I'll spend one more word to make this idea more precise. And the reason is that you might say, yes, this is all very nice, but you haven't taken care of divergences. So you might worry that when I integrate out the stuff at the high scale going down and I close some loops, there might be divergences that mix operators of higher dimensions with operators of lower dimensions. And it might be that all this construct is completely useless because in the end all the operators contribute at the same order. In practice, however, there is a very simple way of making this more precise. I'm not going to go very much into the details, but it's the usual Wilson way of the renormalization workflow because you can just integrate in small momentum shells and do this step by step. And at each step, you don't have any divergences. The limit of integrations are all fine. And you'll see that in the end you're going to get precisely this result. So what this step by step integration generates is a flaw in the space of actions that is moved and is precisely the renormalization workflow. So given a UV theory, you can ask where the action is flowing to. OK, so after this parenthesis, let's get to the power of symmetry and let's make this construction a bit less abstract and more concrete. So let's say I gave you this Lagrangian at low energy. Would you be surprised? For this, the answer is obviously no because you know why there aren't any other terms. So there is just a simple shift symmetry that this scalar possess that sets to zero the other terms. And when you see something like this, you might ask, is there a symmetry that allows me not to write down all the other terms? And in this case, there is a very simple symmetry. So then there might be higher derivative powers in this expansion but they're going to be suppressed by powers of the cathode. So this one was easy, but let's say we had this. So by definition, since at low energy you are seeing this scalar, the mass must be much smaller than the typical scale. And again, the answer is that this action is not surprising at all because this mass is breaking the shift symmetry. So if you make it very small and get to zero, you are restoring a symmetry in the Lagrangian. So there is a sense in which contributions to this m square are always going to be proportional to small parameters that break this symmetry. Typical in this theory but to m itself. However, there is another way of seeing why this Lagrangian is not surprising that I think it's more novel and more instructive and I heard it first from Ricardo Rattazzi. So this is not the only symmetry that justifies the form of this Lagrangian. There is actually an infinite power of higher spin symmetries for the free scalar that you can see immediately if you write it in momentum space. If you write the action in momentum space, you are going to get something like this. And any rotation of the scalar of this type, the alpha satisfying the form and property, is a symmetry of the action. And you can check that this sets to zero or higher point functions. It's very easy to check by just doing this rotation. And what is nice about this symmetry is that it also gives you selection rules that will sit in a second. And it's going to tell you what powers of the coupling can enter the generation of the mass if you have any. OK, so now one more example and then we're going to be done and get to the hierarchy problem per c. And the last one, again our friend, the scalar, in this time I'm just going to add an interaction. And as you might have guessed, even not from physics, but just from the fact that at some point I have to give you an example that is surprising, this is surprising. And the reason is very simple. The reason is just that this coupling is breaking the shift symmetry, is breaking this symmetry. So you can expect a mass term and other couplings to be generated. And you can even from the selection rules of this symmetry predict that it's going to be generated with one power of the coupling lambda. So the typical contribution to the mass you expect is going to be generated, for example, by this diagram. It's going to scale us lambda without loop factor times the large scale. So the mass, at least of this order, you should be surprised. There is no symmetry, I mean, you might make lambda small and again go into an approximate shift symmetry limit, but nothing is protecting you from generating a mass of this order. And it turns out that this is precisely the case with the standard model. So the problem is not just free scalars in general with a mass smaller than the cutoff, but interacting scalars with a mass much smaller than the cutoff. So if you write the standard model Lagrangian, or at least the partial element to the problem, they're going to have something like this. Actually this is enough. So from the argument we just made, we expect contributions to the mass at this order, whatever the scale up to which the standard model is valid is, but also contributions at this order. So if you want to extrapolate the standard model up to in Planck or the Gutt scale, you're going to immediately eat a wall because these couplings are both order 1. Well, at least the top two couplings has been measured. And so you might wonder what is going on. So clearly the symmetry is broken enough to generate a mass that is much larger than the weak scale if you want to extrapolate the standard model to very high energies. And this is the hierarchy problem. So there are no quadratic divergences, no nothing, there is only symmetry and some physical scale. So you might think that this physical scale is very close to us, is approximately the weak scale, so that you're going to get the right contribution to the X-mass. More precisely, you might expect that lambda is sort of the order of 4 pi on X, so a few TV. So here comes the problem. It was very easy to state once we introduced the framework of effective theory. But I want to show it to you yet in another way by showing you where the cancellation really comes from. So this was all very nice, based on symmetry, and simple, but let's take a concrete example of something leaving at this scale and see how it affects the X-mass. So let's say that I have a theory valid up to some large mass plus a small increment, and this theory looks roughly like the standard model. So again, we have our more scalar, and then we have a Yukavo with some evi fermion. Can you still see, or is it too small? OK, so at this high-scale m plus some small incremental dm, we have the equivalent of the standard model. So this is our toy representation with an evi fermion and the scalar. OK? So now, let's say I want to do what Wilson did and integrate out small momentum shells, one after the other, until I get to the weak scale, or the scale I'm making a measurement out. And I'm going to start by integrating out the shell between m plus delta m and m minus delta m. I'm integrating out the whole of the fermion since it's massive. At three-level, you can check immediately by looking at its equation of motion that is not going to contribute to the Lagrangian of the scalar. But at one-loop level, it's generating everything. So we're going to have some contribution to the two-point function of the scalar, some contribution to the four-point function, even six-points interaction, and so on. And we care mostly about this two-point function. We care about the contribution to the mass. You can do the usual one-loop calculation that you always see when they present to the hierarchy problem, and you're going to get something of this form. So let's say that now we are in four dimensions. OK, so this is the usual one-loop integral where the quadratic divergences come from. However, now I'm integrating over a tiny momentum shell. So those that traditionally are quadratic divergences are actually a tiny contribution of order delta m squared. And what matters here is some finite threshold contribution from the mass of the heavy fermions. From the mass of the heavy fermions. OK, so in the full theory, the mass of the scalar is going to come... Actually, let me write down the couple. It's basically... The mass of the scalar is going to come from this contribution and the parameter in the Lagrangian. In the full theory, my physical scalar mass that I can measure as the pole of the two-point function has two contributions, the Lagrangian parameter and this leading one-loop term, plus sub-leading terms. And now I can match it to the effective theory. So the effective theory below the scale at which we integrate out the fermion is just what we said before. So all the operators you can write are actually the scaler that are consistent with the symmetries. So in this case, everything. And let me call this m prime. OK, so at the scale at which I integrate out the fermion, this m prime squared in the effective theory should match the result of the full theory. And I can keep doing this step by step and generate more and more corrections. If this coupling is somewhat small, all these corrections that I generate until getting to low energy are going to be sub-leading to this first term. Because they're gonna come from this lambda here and the loop diagrams we wrote before. But this lambda was only generated at one loop by the fermion with four powers of this small yukawa. So in the limiting which this yukawa is sufficiently small, this is all I get also at very low energy generating out all momentum shells. And now, here is the fine-tuning problem in all its concreteness. I mean, you can see it. So if this scalar still survives up until very low energies, you can measure its mass and find it to be something, say 100 GV roughly. And then you might wonder how comes this contribution that was much larger and generated at a much higher scale cancels against this parameter that has nothing to do with it So now, we've seen the hierarchy problem in many different ways, just from a symmetric perspective and from this more concrete perspective of directly integrating out stuff. So I hope I've convinced you that it's just a problem of symmetries and physical scales and that now you're ready to confront your experimentalist friends. Now, you repeat all that I just said. I'm just kidding. Okay, so this concludes also part two I think I've been way too slow. I should have checked the clock long ago. All right, so now... But anyway, so this was the nice part of the talk where you see the power of theoretical physics at work. And now we're gonna go into the painful part of the talk where you see theoretical physics meeting experiment and failing horribly. And how much time do I still have? 25? Oh, okay. That's much better than I thought. All right, so... Roughly speaking, well, I mean, there are many solutions of the hierarchy problem on the market and you can categorize them in different ways. I'm gonna show you one possible categorization, but you shouldn't take it too seriously. It's just a way of organizing our ideas. So there's a set of solutions based on symmetry, a set of solutions based on the cosmological history of the universe and these are similar to what we've seen for the electron self-energy. These are something completely new that pertain only to the hierarchy problem. And finally, there is something that I'm gonna call a not well-posed question, meaning that the hierarchy problem is not a well-posed question and these kind of solutions are more similar to the Kepler resolution, so we are not the only standard model out there. Roughly, the symmetry category contains, of course, supersymmetry or, well, let's call it composite eggs and extra dimensions, which are the same thing and some conformal solution to the problem, which is almost the same thing as the next dimensions, but we're gonna see why it's not exactly the same thing. And then here we have the relaxation and naturalness and finally here we have the multiverse plus some tropics and in some sense we also have a naturalness. So you see that these categories are a bit fluid and not very precisely defined, as I said, it's just a way to keep track as I speak of what we're talking about. So to be completely honest, the idea of composite eggs is not really a symmetric solution but is yet another solution that falls outside of these categories because it's just based on an accident in some sense. So if you imagine that at some very high scale you have only marginal operators, okay, a gauge coupling, then your theory is going to flow very slowly towards the infrared, meaning that these couplings are just gonna scale logarithmically and again this is purely based on dimensional analysis all the story I told you before about effective theories. At some point, if this theory is asymptotically free, the coupling is going to become strong and you're gonna generate a new dynamical scale and this is roughly going to be of this order. So you might say wonderful, I have a huge hierarchy of scales, I generated it dynamically, I'm good to go, it's down here, I'm done, no symmetry, no nothing, very easy, QCD inspired, it already happened in nature, maybe it's gonna happen again, who knows. But then, okay, so let's put the eggs here, but just as in QCD, around this scale you expect all zoology of stuff, you expect from mesons to show a variance and maybe pions even below and so on. And all these particles are strongly coupled to the eggs, so you definitely expect to have seen them already. If nothing else in indirect experiments, like those that measure flavor violation or those that measure precisely parameters of the electro-wikla grange, like the WMAS, for example. So this idea that was called Technicolor is now considered almost unanimously dead. However, there is a small deformation and that's why I put composite eggs down here in the symmetric solutions. That kind of saves it, because you can say, okay, sure, but what if the eggs is really a pion of this strong interacting sector. What if there is a spontaneous symmetry, like in QCD, Karol symmetry, sorry, there is a symmetry that is spontaneously broken, like in QCD. And then there is some separation of scales where the strongly interacting sectors become strongly interacting and where you find the eggs. Sure, that's definitely a possibility and you also know roughly what this separation is, because this symmetry is going to be explicitly broken by the couplings of the eggs in the standard model. So based on what we said until now, you expect to generate an X-mass of the order of the largest coupling it has in the standard model, so the top yukawa over a loop factor times your strongly interacting sector scale. So since the top yukawa is order one, you generated an hierarchy of at least four pi, so you can put all these guys at a few TV and keep the eggs down here at 100 gV. So this all seems nice, but again let's confront experiment one more time. So what you have here, at this scale f, is a complicated nonlinear Lagrangian as you usually have for pions, which is definitely not going to look like what I wrote down before. It's not going to look like a phi to the fourth theory. So by just writing down higher dimensional operators that you know are going to be generated by the strong dynamics, say something like this, again purely based on our previous effective field theory arguments or any other stuff, you know that x-covins to standard model particles are going to be affected by these operators at order d squared over f squared, where now v is the measure digs vacuum expectation value. Compare this prediction with experiment, now that let's see those discoverings say at the 20, 30 word cent level and you find that you cannot possibly have the lightest digs live up here, but you need another separation of scales that is mild, but it's there, and there are two ways to generate the separation of scales. Either you just call it attuning or you add more structure, you add another symmetry, and this other class of models is called litholiks, but it has a lot of structure, so you are getting a small hierarchy out of a lot of new fields and new symmetry, so you see that you start confronting experiment and you build up more and more crap on top of it, to the point that when you get here, you just don't want to look at your theory anymore. And this is more or less the story with any of these solutions, at least any of these solutions that is on solid enough theoretical ground as to be compared with experiment, because some of them are not at all. Okay, so this more or less concludes what I wanted to tell you as far as this composite was. Now let's take a look somewhere else into this landscape of solutions. So what about the not well posed question story? So here I'm not going to tell you a lot, but just to get a feeling the point is the following. So it's exactly like in Kepler's case. We have a mechanism that can generate many causally disconnected universes with different values and different parameters. And by many, I mean an exponentially large number which is what we need if we want to explain an hierarchy between the plan scale and the X mass, which is a big exponential number. But now you have to wonder why do we exist in one of the very unlikely universe where the X mass is small. And here come the anthropics, which until recently was the part I like the least about the solution, but now I like even less the first part. The reason why I didn't like the anthropic part is that there are some unwavy arguments for why you cannot take the X-veb too large or too small without destroying life. Essentially, if you take it too large the nuclei become unstable and you don't have chemistry anymore, you just have hydrogen. If it becomes too small then the proton decays and you don't have hydrogen anymore so it's hard to form starts. If you take the X mass to be positive so zero-veb, some huge disaster happens I mean like the C and B fries chemistry and then spalarons cancels the varnas humidity but all these statements I'm making are very dependent on not changing any other parameter in the theory. So if you change also the Yukawa couplings for example together with the X-veb almost nothing happens in most of these cases. So somehow you need a model in which you are generating a universe in which essentially only the X-veb is barring. And if you look at the explicit models that generate this exponential number of universes they really don't work in such an accurate way. They are just generating all possible metastable vacuum of your UB theory so it's kind of hard to imagine a concrete model that realizes this paradigm. In the other end this is really the only paradigm that at the same time is addressing also the other tuning we have which is much larger which is the cosmological constant tuning that I'm sure you heard about. So right now the energy density of our universe is dominated by this tiny number so if you compare it to the Planck scale or whatever scale you think your theory is valid up to even the electron mass whatever there is a huge tuning not to completely destroy the cosmological history of the universe as we know it. And so far this idea of generating an exponential large number of universes with different values of the parameters and then invoking the fact that we are alive to justify why we live in an atypical universe it's really the only way to address both these problems at the same time. So if you look at it from a very low energy perspective and incredibly simple theory one of the best known examples is split supersymmetry you just have supersymmetric partners of a few hundred TV that gives you gauge coupling unification a dark matter candidate you have no problem at all comparing with experimentals in these cases and then how to take inflation generating all these universes plus some form of the anthropoclims it tells you why these parameters are small. Ok, so in my very very personal opinion this is this looks appealing because it's still very far away from us because we haven't even started writing down concrete models of how this game is gonna look like like when a very ugly person is walking towards you so long as they are one kilometer away you don't know they're ugly but sooner or later they're gonna approach enough that you realize they are probably worse than your friends that you didn't like before. Ok, but I want to stress that it is a very personal opinion and other people definitely otherwise among which, distinguished among which is NEMA that lectured you a few days ago. Ok, so this concludes my list of insults to the multiverse which brings me to cosmology and then if we have time I'm gonna go through the rest. So, both of these solutions that I've called cosmological have been proposed in recent years in the last couple of years and the reason is very simple and it's that you have to relax a lot your aesthetic criteria so they're also very ugly but they are ugly in a precise way unlike the multiverse so I can tell you that they are ugly and I personally think that the ugliness is not a good criterion in theoretical physics I mean so far it has not beauty has not really guided us very well I mean the standard model is kind of a random addition of components that have nothing to do with each other there are some random gauge groups some fermion masses that spy five orders of magnitude there are a lot of parameters that we don't understand maybe one day they will all merge into something beautiful and complete but we don't know yet so since experiments keep killing our beautiful ideas maybe the solution is not so beautiful and comes from something completely different there isn't why these solutions are worth of attention is also because in spite of looking a bit artificial they are very deep in the sense that they link the hierarchy problem to something that a priori has nothing to do with it which is the cosmological history of the universe so there are very spectacular consequences for experiments and they truly represent a change of paradigm they don't even fit into the previous examples of solutions to turning problem that we had so no matter how ugly you find them I think they are worthy of your time at least to realize what kind of thing they are and I think I'm gonna tell you about naturalness in one of the let's say proud but maybe not so proud authors so in the naturalness you imagine that you have many copies of the standard model and each one has a different value of the X-mass if I imagine that zero is not special at all so we have both sectors that have a positive X-ma squared in the Lagrangian and sectors that have a negative X-ma squared in the Lagrangian so this means that in this sector zero and this is different from zero here fermions are almost massless but not exactly massless because electro-wiximetry breaking is sorry, electro-wiximetry breaking is triggered by QCD so you're gonna expect some masses of the order of lambda QCD cube over Mx squared for the fermions and for the gauge bosons you expect masses of order lambda QCD so it's a very different universe compared to us many weird things happen as I said but I want to stress that this is not a multiverse so all these sectors exist are part of our Lagrangian you can write only one Lagrangian they're all gravitation like apple, to us etc etc these sectors are very similar to us and then as you take the X-veb larger and larger things start happening but that is not that important for now I've imagined the existence of this sector so now I have to tell you what's the distribution of the X-ma square and I'm gonna take the distribution of the X-ma square parameter to be uniform and the reason is that if I take it peak close to zero I'm cheating I'm not really solving the problem with this mechanism but I'm imagining that there is some extra dynamics that is helping me if I do the opposite of course I have to explain why the X would be peak somewhere else so I'm just gonna imagine that we have a uniform distribution for the X-ma square parameter which means that for a theory that is valid up to some scale lambda you naturally expect the lightest of these X bosons roughly of lambda over the square root of the number of sectors and here you already see the problem because even if you want lambda to be say miserable 10 TV you need 10 to the 4 standard models so if you want now you can leave the room but if you don't leave the room I'm gonna go on and tell you that if you really wanna solve the problem all the way to where gravity becomes strong then you need 10 to the 16th sectors because in this case what happens is the following g newton is renormalized by this huge amount of stuff and gravity is becoming strong at the intermediate scale roughly 10 to the 11 g and at the same time this 10 to the 16 is bringing the naturalness cutoff of the theory at the same scale so this is in a sense a full solution of the problem however if you know something about the C and B then you can really solve the problem and this model is awfully excluded because we know for example for the measurement of at the time of plus scattering that we dominate the energy density of the universe so there is not much stuff out there that is gravitationally coupled to us which can be phrased more precisely in terms of the effective number of neutrinos at the time of the C and B which is roughly one half which means that you can make alpha standard model neutrinos and I've just told you that I'm adding 10 to the 16 full standard models so now there is an obvious answer to this which is let's say that at some point in the history of the universe there is an inflaton that couples only to us so it decays only to us after inflation and it populates only our sector but again this is not a solution to the hierarchy problem because now you have to explain why the life sector is also the only one that couples to the inflaton so you have to save yourself without making our sector special in any possible way but it turns out and this is the only part I truly like about this old business that there is a way of doing it and the best part is that this way is possible at all only because there exist operators that generate the problem in the first place so the only reason why I can write down a viable model of treating the universe is that in the standard model you can write down relevant operators with a combination of x bosons that is a singlet or even also marginal operators of this type the way I'm going to solve the problem is by imagining that at some point so there is inflation say then the inflaton decays to some gauge singlet of all the gauge groups then the density of the universe and then in turn decays to all our sectors we are one of these two relevant or marginal couplings let's make another assumption which is where the true audience comes in which is the fact that you want the mass let's focus on this model for example so now let's take the mass of this guy to be smaller than the mass of the lightest sticks and of course I mean you can you can imagine constructions that give you these, right? you can imagine that these are all brains in an extra dimension and the guy lives so in the fermion case it's easier so you can imagine that this is the Lyak fermion and one of the two vile components lives in the bulk but the other one lives on a brain and then you're going to get a volume suppression for its mass that is precisely of the order of the square root of n so there are ways of doing this or in the case of the scalar you can imagine that again you have a tower of scalars just like this and then they all decay to the lightest one before the lightest one decays to us so there are ways, they're not pretty but there are ways but what happens if you postulate this then in the effective theory that describes the reading of all the sectors from this gauge singlets it's noics anymore, you have to integrate out and you might ask what operators can I write down with lighter standard model fields and this guy that treats the universe and this is very simple of course you can write some Yukawa coupling say to be d bar but then what do we expect the coefficients to be here so this coupling here is breaking a ship symmetry on phi so again by selection rules you have to have it here in front but you can immediately notice by looking at this operator that this coupling is dimensionful so in four dimensions scalars have dimension one so this guy also has to have dimension one which means that you need a scale down here to restore dimensions and in the effective theory the only scale you have is the X mass itself so you're going to generate this operator plus there is yet another symmetry of the fermions that you know is broken by the Yukawa and the Xbeb so you need the Yukawa up here so this is the leading operator that you can generate in sectors in which you do have electro-wix symmetry breaking and you're generating it just by mixing of phi with the X to its bed however in sectors where you don't have electro-wix symmetry breaking contribution is obviously zero because here what you really have to think about is something like this because the spurion that is along for this operator is really the Xbeb so in these other sectors it turns out that the leading operator is something like this where f is the field strength of one of the gauge bosons actually all of them which is generating at one loop through this diagram and again where these are the X and this is phi so again you can do the trick of dimension as before and you know that this has to scale like this and this is very nice so I've added a very simple operator to all the standard models and now I have a natural way of populating the most the sectors that are the lightest because from these effective operators here immediately that the decays of phi into sectors with electro-wix symmetry breaking are going to scale like mhi squared and the sectors without electro-wix symmetry breaking they're going like mhi to the fourth so I've coupled all the sectors in the same way I haven't cheated but I'm getting much more energy density into our sector what's even better is that these yukahuas give you some natural protection from the UV because as the x-veb grows also the masses of the leptons grow so at the beginning you might be able to decay to bb bar but after a few sectors you have to decay to cc bar so you're going to have a ci yukahuas oppression and so on so there is a way of truly solving the hierarchy problem without making a special and I'm not going to go more into the details but I mean there are the formations of the simple models that can get all the way to 10 to the 16 but what's nice here is that no matter how hard you work you're always predicting something for the next generation of cmb experiments so even if you have the scaling you're still going to populate nearby sectors a little bit which means that you're going to predict some amount of radiation that should be detected in the future and I think that really the rock bottom value that you cannot do without is roughly comparable to the sensitivity of the next generation experiments that should be start taking daytime 5 to 10 years so if you don't see any of this and naturalness is dead of course this is not the only explanation but you can keep hoping and the way you can concretely do something to follow up on your op is to look at neutrinos because not only you're going to generate extra radiation but you're also going to put some energy density into the neutrinos which in practice means some consequence for the cmb that I'm not going to go into the details but if you have infinite resolution it would be very spectacular we would really see little stairs in the matter power spectrum that nothing else can generate anyway let's not dwell on this too much finally one more thing to be aware of is that of course this coupling is tiny so it has to scale like some power of n so you're never going to see directly this reeton fields at colliders so this is an example in the third category you see that these models started simple and beautiful and then got ugly while confronting experiments while these models start ugly by construction with this huge number of copies but a priori this is not necessarily a good reason to discard them but what am I doing? that's it so I'm glad I managed to make at least one example per category well I think you're not gonna miss the usual Susie lecture you must have heard it a million times might would have been nice to talk about the relaxation but well next time so in conclusion there is really no conclusion we have a very deep problem what the right solution is so many people are depressed because they are not finding anything they are crying and they are sad but I am incredibly happy because I would have died if I had to do ten years of supersymmetry spectroscopy in the rest of my career instead I have a truly deep problem that is facing me and I have no idea what the solution is so maybe I'm not gonna find that job but at least I'm gonna be happy with that new position thank you