Future Accelerators - Nima Arkani-Hamed

alright guys I hope you've all survive the last two weeks and that you've had a lot of fun before I get started with the Elector since this is the last lecture there's a large number of important people to thank for making this such a such a wonderful and smoothly running event and I just want to acknowledge all of them in case some subset of them are here whichever subsets are here or not we should clap for all of them so there was a mission sage who is one of the Masters of the Universe in our school of natural scientist you've all interacted a lot with Alison McIntyre who's been via the PHP program assistant and and Mia the events team Susan Abigail Julianne Sharon and Meredith ah the AV guys Sam and Dario who have amongst other things put up with these things going up and down at random intervals our staff at the school of Natural Sciences Lisa Michele dawn the dining staff chef Michele how many of you have been served by a French chef for you know 10 days of your life that imagine that's our life here all the time pretty good being at the Institute I have to tell you that chef Michelle Renee and the whole staff the housing and maintenance people that figure out how the hell to house all you guys while you were here including a sharin cozy goth and the Princeton conference and events team they're led by Mariana well Buki I don't know if I'm pronouncing that last name correctly um and last but most we should thank Chiara where's Cara there she is we should thank you are for for giving us these great schools and giving everyone a chance to come enjoy the loveliness of central New Jersey in the middle of the summer which has a lot of beauties to it despite the 120 percent humidity that we sometimes have so anyway so um so what I want to tell you about in this last lecture I think there was a relatively broad title the future accelerators that's really a huge topic so I'm mostly going to talk about a subclass of possibilities revolving around this idea of great big circular colliders and a sort of next generation of circular machines after the LHC Leon Tao talked a little bit about what we can do with the Higgs factories and he said a little about what we can do with the ILC and I'll have a small amount to say about that too but I just want to talk about this subset of ideas in a sense it's the newer kid on the block in particle physics over the last three four years people are talking about it then starting to plan for it more and more seriously of course we have to plan for these things 30 years in advance if anything is going to happen and so this is a good time to be thinking about them but roughly speaking we're imagining a machine around 100 kilometers around and if you take if you take this machine you could first run it in an e + c- mode it's a lot like leppe in the LHC so you could first run it in any classy - mode the center of mass energy around 250 GeV as Leon Tao explains that's where you get a peak of the for the Z Higgs production cross-section and so we can run it as a Higgs factor here produce millions of Higgs particles and study their properties and a tremendous detail something I'll try to motivate a little bit more as well see undoubted and then you can also in a later stage run exactly the same machine in a proton proton mode and potentially get up to 100 TeV and just so you have an idea of what's needed there let's say oh just like let's say you wanted to our Oh someone gives you 100 kilometer tunnel tomorrow they build it tomorrow could you tomorrow go and have 100 PV Collider in there the answer is no because what we need to get to 100 TV collisions in a 100 kilometer tunnel is magnets or about twice as powerful as the magnets the strong as magnets that we now have at the LHC the LHC has 8 Tesla magnet and the high field magnet people believe that on the 15-year time scale they should with sort of reasonable extrapolation of progress be able to get to 15 Tesla ok so 15 Tesla magnets in a hundred kilometer tunnel gets to 100 TeV Collider ok so even if you wanted it tomorrow you're not going to have the magnets for 15 years anyway and there's not much point putting in 8 Tesla magnets 100 kilometer tunnel it's a big fraction of the cost of the machine you want to wait till you have the best magnets you have and put them in so so this even if we have the tunnel this is not a wise this is not something you want to do immediately anyway and that's why the idea of actually running it in the mode of a Higgs Factory first doing very important great physics while you wait for the magnets to come online put them in and then go to proton-proton collisions is a good idea so so what I want to do send some of the stock up I'm using the computer even though I hate using the computer because there's a lot of plots in this talk but I will switch back to the blackboard every now and then to explain a few nice physics points but it's a little strange to try to motivate this ok so I don't like talking in terms of physics cases and things like that it's kind of silly why do we do this why are all of us in this room you know we could be doing many other things with our very mortal finite life and we do this thing because it's it's it's that's that's what attracts us to the subject big machines big physics big ideas going to the absolute extremes of what humanity can do to learn something that might be eternally true about the way the world works if we're interested in smaller potato things then there's many other things we could do with our lives but I think this is one of the things that really attracts people to this kind of fun of pursuit that's the most obvious reason if the frontier continues to be the frontier we've been doing this kind of experiment for a hundred years or 50 years depending on whether you start with the Rutherford or with the cyclotrons but in any case there's no reason to stop doing it now it's not likely all of a sudden became a factor of a hundred more expensive it's not that the world is ravaged with war and famine and all sorts of other things as any worse now than it was before absolutely no reason for this to be the moment in history where we stop continuing to go to the frontier and so that's the most fundamental reason for doing it but in the rest of the and the rest of this part of the taco give you the more professional reasons for wanting to do this and it's just a reminder of theoretically what the what some really big overarching questions are in the 21st century or in the 20th century we got these two huge pillars of of the picture of space-time and quantum mechanics and we have many reasons to suspect that that space-time is an approximate concept somehow is to be replaced by something else that's a big zeroth-order huge thing so that's an obvious that's an obvious theoretical challenge this is a challenge whose the resolution to it may well involve physics at energy scales that we can't probe with with any experiments we could imagine although maybe as we learn better and better what the nature of the answer to the question is we might be alert we might be awaken to the possibility of different kinds of experiments that might probe them so but certainly naively this is associated to physics at the Planck scale it's very far removed from experiment another question that is not obviously disconnected from the first one is how we can get a large macroscopic universe despite the fact that there are violent quantum mechanical fluctuations that would seem to destroy the possibility of a sort of coherence on very large scales and that's yet another way of talking about the fine-tuning problems at least in the context of the cosmological constant problem it may well be connected to the question of how space-time emerges because if you don't have a mechanism that makes the cosmological constant small well everything wants to be curled up on the PAC's scale anyway if it's curled up on the plum ski to the scale with the notion of space-time is breaking down anyway so somehow the emergence of something like space-time and a large space-time are not disconnected questions so they might be connected to each other it's less obvious how is connected with the Higgs but in any case this is a very basic zeroth order question that we don't have an understanding to but this one at least in this avatar involving the Higgs they eggs stars on that one and that's something that we can hope to get some experimental information about by the way our friends in astronomy are very excited about in cosmology are very excited as they should be for taking the big surprise that they discovered back in nineteen ninety eight in the universe is accelerating and measuring it to death and really convincing themselves that it looks something like a cosmological constant okay and and you could say well it's just one number W is just going to be minus point nine seven and minus point nine eight no who cares if you know experiments you want to go measure it you certainly don't want to take assurances from theorists very seriously because there are the people we're telling you you're we're going to see it to begin with right so it's you've discovered something surprising and if you're an experimentalist you pursue it and you try to characterize it more precisely the analog of that in particle physics is the discovery of the Higgs and so far nothing beyond the Higgs that's the extra that's the extra surprise and so we want to put the Higgs under a powerful microscope and look at it that's the most obvious motivation the LHC was powerful enough to make many Higgs is and in a messy environment to discover it in but it is not powerful enough to really characterize it with any with the sort of precision we need to figure out what it's really trying to tell us about about this physics so now there's a bit of linguistics here often when people talk about whether we should build another accelerator or not they say the obviously correct thing but unlike the case with the physics of electroweak symmetry baking and the weak scale we have no guarantee that new particles need to show up before we discovered the Higgs something hat the unit Erised WW scattering so we knew something has to happen beneath the scale 1.5 TV or something like that and that is just not true ah now we've seen the Higgs the theory is in principle theoretically complete up to exponentially higher energy scales than we have access to and so we don't know where the threshold is for the next particles and very often people say therefore we don't know where new physics is and so if we can't guarantee that how do we know we're supposed to build this machine not another machine what will come to that question in a moment but the sort of underlying thing as well is there any point if we don't know what's coming next or where to find it you know how can we motivate the continuing and the answer to that is first the very first slide because you just go and look to see what's there that's the nature of this business but also that in a quite profound sense the Higgs itself is new physics all by itself we've never seen anything like it before we've never seen in in particle physics we've never seen a a light elementary seeming spin zero particle and we've talked at ad nauseam for what's what's strange about having life elementary spin zero particles there's no discontinuous difference in the number of degrees of freedom between a massless and a massive spin zero particle unlike for all particles of higher spin where there is a discontinuous difference we don't have an understanding for why this can be light compared to heavy heavy heavy high energy scales on the problem we've seen particles like chiral fermions and gauge fields and condensed matter systems we've never seen without a lot of explicit fine-tuning in the system we've never seen something like an elementary scalar so this is something new we haven't seen it before and we're confused about it as last week in this week in many lectures made very very clear theoretically we're confused about it but experimentally it's completely obvious what to do when you've discovered something new you've never seen anything like it before and your theorist friends are confused about it you study it yeah you have to study it and look at it closely and more specifically ah the issue is just what we Luda - we've never seen a point like scalar fundamental elementary point like scalar now what does the word elementary or fundamental mean as as you all know there is no really invariant notion of element arity when we say something is elementary we just me but on the scale of its Compton wavelength it looks like its interactions are point like okay you don't see form factors it looks like its interactions are point lights and so when we say that the Higgs is looking elementary we mean on scales small comparators confident wavelengths you know it has some effective size that we've looked some resolution that we've seen experimentally so what would we literally mean by seeing something literally seeing something is bouncing a photon off of it right that's literally seeing it and of course with the eggs we can see it in other ways too we can see how it interacts with disease with other particles and so on and the picture of drum is really roughly on scale of the the picture of what it looks like now from the LHC in other words it's looking it's looking somewhat point-like but not dramatically so and in fact what we'll ever learn from the LHC after we're completely done learning everything about the Higgs would would give us a with that resolution of the size of the Higgs that we didn't fer is perfectly compatible with it being about as elementary as a PI on what okay so a PI on oh we say is a composite it's made out of up quarks and down quarks but in fact the sort of Compton wavelength of the pine is 1 over 130 MeV and it's size where we really see that it's not elementary and we see the form factors associated with it it's around step by the by the by the Roma's on that okay so so we have some ratio here maybe about a factor of five and that's more or less the picture we're going to get for the element arity of the higgs after we put after we make get to the Precision's that we think we'll get from the LHC let's say ten percentage Precision's on the coupling of the higgs of the z it'll be compatible with roughly the same kind of ratio in fact we just take the ratio of these scales squared is a good measure for the kind of deviation that we could look for so so we say that theoretically we're very confused if we see in an elementary spin zero particle and nothing else but we can ask do we know experimentally that it's so elementary and the answer is we don't even know that it's more elementary than a pile okay and a Payan was not associated with all of physics going haywire and and maybe there's a maybe there's entirely different things explaining fine-tuning problems all this theoretical drama I'll just ended up being composite and we will not be able to decide just about that super basic question from the LHC so that's motivation number one we would like to know if it's more point like than a PI on and you know by factor of ten that's the usual figure of Merit when you're making progress and experiment you want to see if you can just go a factor of ten better to really know and this really is a picture that we'll get from a geeks factory that makes millions of Higgs is and will improve fact this most critical couplings will will will improve by something like ten percent from the LHC down to fractions of a down to a few tenths of a percent from a Higgs Factory so will really go from this kind of fuzzy picture of the Higgs to picture the Higgs will look quite point-like so either that's what we learn in which case the experimentalist can confirm yes the Higgs looks point like 10 times more point like than any scales we've seen before okay and that's that's that's a solid fact about the world an important fact about the world or we see there are some evidence for a composite net in which case great that tells us something else but either way we're learning something fundamental that will guide our thinking about what it means theoretically there is a final thing which is extremely important not only do you want to see whether the Higgs looks point like to other external probes but the final test of how point like the Higgs is are the most incisive test of how point like the Higgs is if it looks point like to itself okay it looks point like to itself means that there needs to be an interaction between three kegs particles that you know the three Higgs is meet at a point in space-time right now that self interaction gee the heaters in many ways the simplest possible elementary particle it has no charge it has no spin it only has mass right ah and the simplest possible interaction you could imagine is having three identical elementary particles meeting but it's amusing that we've actually never seen that interaction in nature before ever nothing we no self interact no elementary particle self interacts you can say well what about gluons they change color what about the WS and Z's they change the su to flavor what about graviton what about gravitons well the self interaction of gravity what about photons you can check by both symmetry they cannot possibly have three identical Felicity photons self interact what about gravitons ah well the self interaction we get in gr is to positive publicity and one negative olicity Gravitron so still there's always a quantum number that changes okay the only particle that can enjoy a self interaction is the eggs okay and so so on the one hand looking for this interaction and seeing it would confirm in the most direct sense the point like nature of the Higgs and on the other hand it would allow us to see the simplest possible interaction that's allowed in nature that we've actually never seen before because this is the only particle that could enjoy it now the LHC will barely be able to tell us that this thing is there okay depending on how you talk to people talk about a 40% level measurement 50% level 30% level I think as it starts happening we'll have a better idea of what will really be like but it's not really incisively going to tell us whether it's there or not and to do this you need 100 TeV collider okay so 100 TV collider will make a roughly ten to the nine pizzas okay so a billion Higgs is at so many Higgs is that you will be able to determine that coupling constant to about five percent accuracy and people talk about whether three percent seven percent but it's about let's call it about the 5% level accuracy so we'll be able to see that it's there and we'll be able to measure it with some accuracy okay so that's it so ah there's the we should just go to the frontiers there's the zeroth order motivation and then the absolutely direct thing through a guaranteed to learn our about the Higgs and these important facts about the Higgs that a Higgs Factory 100 T V Collider will help us establish whether indeed the Higgs is as surprising as it would be in the standard model with no other particles around really looks elementary or if there is some some kind of sub structure associated with it those are those are just things that will for a fact learn okay now of course 100 T V Collider does blast further into the high energy frontier and here I just wanted to make the small point is that since the energies factor of seven higher let's call it ten the scale at which you make new particles the reach is also around ten times higher well it's actually more like a factor of five for some processes and for other processes it can be dramatically more could be factor of twenty okay and I'll give you examples of it and furthermore because the the sensitivity to heavy scales that we worry about associate of the Higgs scales quadratically with the cutoff of the theory a factor of ten and energy is really giving us a factor of a hundred extra probe into these violent vacuum quantum fluctuations that were so confused about theoretically all right so for the next for the next few minutes I want to just go over well I want to talk about the two obvious questions that you have to dress if you're really going into the unknown where we don't know we don't know where the threshold of new particles are and so there are two questions that you want to ask first you want to know about just the raw capability of these machines what can they do okay so what's the with the kind of technologies that that we can that we can imagine happening what's what's their actual capabilities and once you know what the capabilities are then the question is or any of these deep questions that we're worried about can we think of any of them that will really be robustly probed with this level of precision and energy so that's that's kind of a crucial question right again how do I know that I don't need a precision of a factor of 10,000 better than I had before in order to settle some question or how do I know that I don't need to go to energies a hundred times bigger than where we are why this factor of roughly is 10 to 100 on precision why the factor of town on energy are there questions that that amount of leap are going to help us settle okay or at least say something robust about if the answer is no then then apart from just the motivation of going there it's you can't make any extra justification but if the answer is yes then that's good and we have we have more things that we can discuss all right so obviously I wouldn't be giving the answer I wouldn't be giving this lecture if the answer to this question wasn't yes but but let's see let's first talk about the projected capability so first here is just a sense for how much better a Higgs and the factory can can do on precision couplings on measuring the couplings of the Higgs more precisely I should say that the circular pigs factory can also be run back down on the V pole in principle and depending on how aggressive you want to be you could get between 10 to the 10 and 10 to the 12 Z's which is a factor of you know ten thousand to a million more than we got from from luck and slc so that's a mind-boggling humongous number of Z's and so one can imagine doing a lot of interesting precision electroweak physics with them so I'll say a little bit about the G Factory also in a second but anyway uh these are the sort of fractional deviations in the in the in the Higgs couplings to different particles so that's the that's the that's the poster child we see this very big jump between the LHC which is the things in grey and the pigs Factory okay and if you do go back to the Z Pole then these are the projected and actually emphasize this is incredibly conservative okay but these are the projected increase in sensitivity on the SNT parameters okay so these are the old ovals for these are old ovals for SMT and these are the the small ones are what you could get projected going back to the depot at a Higgs Factory the reason these are incredibly conservative is you see I'm getting you a factor of 10,000 to 100,000 or million more Z's but my position on SN T is only improved by a factor of be ten okay so why is that what does that tell you what does that tell you when things don't scale like the square root you're dominated by systematics right you know so that's that's and so so people are being very very conservative when making these extrapolations one of the problems for example one of many problems is you need to know you need to know like alpha at MZ incredibly well okay just just alpha e m @ MZ incredibly well and if you just do it in the way people typically do you get errors just at the sort of part in 10,000 level okay and yet people about 18 months ago came up with a clever way of evading that problem which is to just measure alpha at MC by doing a scan of the line shape of the Z instead of doing what you normally do just take it from data at low energies and run it up okay so that can get you another factor of 10 so the Alpha is no longer the bottleneck and we have to think about other one okay but these projections are very conservative and once you think a lot one what one can do with like the factor of ten thousand two hundred thousand more Z's and I should also say of course our theoretical understanding of precision electroweak physics has got to improve to the three loop level sometimes to the for-loop level to be able to take full advantage of all these Z's so that's also theoretically interesting but anyway big leap in our precision age couplings as well as you know factors of 10 20 on the S&T parameters I apologize for somewhat busy plot but this is just telling you about what standard model cross-sections look like now at 100 TeV Collider and as always with these things annoyingly they're log-log plots but anyway that the all the even very rare standard model processes start start happening frequently enough to care about and as I mentioned those around the billion Higgs is 10 to the 11 tops that you can make at a hundred T V Collider if you're a flavor physicist 10 to the 11 tops is is enough tops so that reasonable rare flavor change mutual current decays at the top we become something that you can imagine looking for even at the LHC in order to be able to see top FC NCS which are not already in reasonable theories excluded by the things you have to stand on your head and build complicated models here are very reasonable theories of flavor could give you rates of FCN seeds that are visible what's the 10 3:11 talks and again ldiot drew these diagrams but for probing the triple hangs coupling we're looking at the interference between this diagram that actually dominates double Higgs production even though it's a loop but it's going through top quarks with the big topic a low coupling but you can see this is the kind of a 10% effect underneath that and with making a billion Higgs is it is enough to be able to extract the xxx coupling to the 5% lobe all right now before going to even new physics capabilities I want to mention some qualitatively cool things that happen at 100 T V Collider really for the first time at a hundred T V Collider we get to see the standard model start acting like it wants to look in the massless limit okay we don't even see this at the LHC as as you remember from sort of Hadron Collider physics 101 massive particles are produced at a Hadron Collider more or less on threshold even if you have energies that are vastly bigger than mass of the particle top courts of the LHC are produced more or less at rest okay the typical betas of order of third velocities of order two thirds something like that and so we don't see even W these tops we don't see if behave effectively as massless particles when you get to 100 T V collisions it starts being high enough energies that some somewhat qualitative things start happening and you start seeing it behave you start seeing it behaved more like massless particles one of these phenomenon it's at very high energies if you could imagine that su 2 cross u 1 were just massless particles you should see the phenomenon of electroweak radiation just like we see QCD radiation or electromagnetic radiation okay and the figure of Merit for radiation is the pseudo cop factor okay so if you have a particle and it's radiating something the probability that it radiates is given by a Casimir alpha times a log squared of the sort of typical t of the process divided by an infrared cutoff squared and what gives us the infrared cutoff here is the mass of the particle okay so B over m W squared or Z squared okay so that's the that's the pseudo-code factor that's the figure of Merit the the the Casimir for electroweak is like you get a factor of four there and so it's growing as a log squared so as you go from the LHC 200 TV collider that thing starts being significant and I don't need to look at these plots in detail but this shows you for example something like 20% of all dye jets that you produce with pts coming out at 10 TV or higher at 100 TV Collider 20% of these digests come along with WS and Z's just radiated okay so that's another effect is that there's a significant top quark content to the protons at 100 TV colliders just like there's a significant bottom quark content of the proton at at Fermilab okay at the attempt Ron so again if you're talking about high enough energy processes let's say you want to make some heavy Higgs at 10 TV or something like that so that you really need the 10 TV ish the attend thievish pts for some TT bar from the proton producing the sky then you would make a mistake of order 1 if you just thought of them as unusual as as not in the proton and the resounding those logs in the PDF really makes a difference so another phenomenon is that you can start seeing the tree node and no truth show neutrinos are normally just missing energy but well why do we see anything we see anything because they radiate electrons okay and again in high enough PT events you can start seeing neutrinos in this way and this is just the just to make it very clear it's an example from new physics but imagine you had a Z Prime up at 5 TV that's what it is in this plot and here what you just hear the branching ratios for the 3 body became Z prime 2 nu nu but where the neutrinos are radiated off a Z ok that branching ratio can get as big as you know 3% sometimes ok so that's a very significant fraction of the time that when something the case of neutrinos it actually radiates the and you can see it and this is actually something that can be used as a way of if you if you see a Z Prime like this is the way of doing much more learning a lot more about its couplings if you have any theory you can start distinguishing left and right-handed components all sorts of all sorts of interesting things from the fact that you can start seeing neutrinos these effects are barely there at the LHC but the log squared growth is enough that it starts being a more a phenomenon that you that you care about more as you go to a 100 T V Collider yes huh the rounding is not that big a deal okay it's really mostly this log squared okay all right so continuing with the theme of what we can learn going back to the Higgs here in a little bit more detail is the kinds of couplings that that that that we're going to try to probe so if you imagine writing down all the higher dimension operators all the leading dimension six operators beyond the standard model that involve the Higgs they come in three really - but I'm separating one of them uh two different kinds there's one kind which doesn't break any of the symmetries global symmetries of the standard model okay and if you like take anything in the standard model the operator H dagger H is neutral under all symmetries that's related to the hierarchy problem right so H dagger H is neutral under all symmetries so take everything in a standard model and shove an H dagger H in it okay so take H dagger H mu nu squared H dagger H in front of you Cal coupling a derivative on H dagger h squared these are totally symmetric operators if you have any kind of physics at the scale lambda there's no reason that these things are not generated and there's also H dagger H cubed then there are the operators that break the custodial up due to symmetry of the standard model okay and these they break of symmetry oh so this is a famous one for the T parameter even the S parameter operator is something that breaks custodia loss due to symmetry and you can have various couplings anything that involves derivatives on the Higgs in this in this way breaks the Kasota less due to symmetry okay so these couplings are probed in in different aspects of this of this program okay these things these totally generic things are probed at the Higgs Factory best the H dagger h cubed affects the triple Higgs self coupling and is best probed that's 100 T V Collider and these guys are best probed sitting on the D Pole okay so for example these things on the D pole that literally gives you T and F so the deviation of MW over mg cos theta from one the Z photon mixing and these are deviations in the coupling of the Z to various firm yawns okay so these are the things that are best probed and the combination of these things allows you in all these cases to probe the cutoff scale to the up to maltese malti TVs now just quick quick questions for you ah can you who can give me an example of something what could generate that operator what kind of high energy physics could generate that that operator anyone H dagger H F mu nu squared let's say for glue or for a hyper charge yeah you imagine there's some heavy Fermi on with you Cal coupling heavy even vector like Fermi on with you Cal coupling to the Higgs and if you integrate it out you can generate operators like that what can generate this what could generate H tag or H times a you cowl coupling this is something where where you imagine that some of the white standard model fermions are mixing with some heavy fermium okay um okay I don't know help to my chalk but if they mix with heavy fermions and the heavy Fermi on W Cal coupling to the Higgs then when you integrate out the heavy fermions you get operators you get operate just like that what I want to stress is that when you when you generate some of the operators you very often put them in different places okay so so very typically integrating out heavy fermions gives you that operator gives you this operator gives you many operators okay okay all right so that's for the basic capabilities and now I want to transition to the second set of questions which is are there are there important questions about physics that we don't know the answer to now that this level of leap and energy and precision are the right amounts to sort of robustly address and there are three questions like this that that we've those of us thinking about this thought of there there may be more but these are three very obvious ones and they have to do with the nature of the electric phase transition naturalness and dark matter and we're not talking about no lose theorems in this business you can probably find loopholes and counter examples to many of the things I'm going to say and there's really no point in trying to come up with a no-lose theorem because it's just not the same as it was with the LHC when we knew that there had to be something there because of utilizing WW scattering nonetheless I hope you'll see it's really very robust the answer we'll get to these questions and as far as dark matter goes it's also rather sharp will either see something or really solidly rule out the simplest possibilities the very simplest possibilities for what wimp dark matter could be all right so let's talk about these things in turn so first let's talk about the electric transition well the answer I'll set a little bit about this um what we've seen from the LHC so far for a long time we said something like the Higgs breaks electroweak symmetry now from the LHC we have just wiggled in the little quadratic nation to this potential around this minimum but we have no idea experimental II what the what the whole potential looks like okay we have no idea if it looks like this which is what it looks like in the standard model or if it has some other Wiggles in it okay we just don't know now why is this important to settle again I think if you're an experimentalist it's obvious you just want to go you want to know as much as you can about the potential you just want to try to measure it but you might say look your your theorists say come on why would you need lessly complicate things obviously it's going to be the simplest picture where you just have it's like landau-ginzburg theory you just write down something analytic you write down everything it's allowed by symmetries bla bla bla right so the simplest possibility is precisely what what you should expect and anything else is needlessly complicating your life what I want to point out is that the assumption the assumption that the potential is given by this landau-ginzburg form it's precisely associated with believing that there was a hierarchy problem to begin with it facts that's we're thinking about the hierarchy problem came from is from thinking about the analogies with condensed matter systems in other words the logic that tells you you should write down everything protected by symmetries just put them all in with dimensional analysis and so on that's exactly the logic that would tell you that you need a huge amount of fine-tuning or you have to have a lot of particles above your head and that's exactly what we're confused about so this is not an innocuous assumption in fact until we really know experimentally if you want to know when experimentally should we be absolutely convinced that there's something like this tuning problem to worry about we won't know that we have to be convinced by it until we experimental II confirm this is what the potential looks like okay and what else could it look like well maybe there's a quartic balancing against the sec stick okay or maybe it's not it's not even analytic maybe it looks something like this this is form that you might be familiar with from the from from the Coleman Weinberg paper alright now how are these things different from each other so let me just say right now the LHC will not tell us we have no idea whether this might have been the potential this might have been the potential the LHC will not tell us whether any of these things will not allow us to distinguish between these things what changes between these different forms of the potential let's Tripoli accomplish okay because what the what the potential looks like expanding around the minimum changes for example in this model the triple think shuffling is five thirds bigger than in the standard model okay just calculate this five throws bigger but we won't know from the LHC if it's five thirds bigger than the standard model or not okay so we want to know the answer to that question um just because we want to understand better what what the potential how electroweak symmetry is restored if you like is you go to higher energy then there's a cosmological question house lecture weak symmetry restored as we go to higher temperature okay and if you just take the standard model you imagine the universe is very hot and it cools there's just a smooth crossover there's a smooth phase transition as the M squared goes from being positive to being negative gradually okay so in the standard model and it actually depends on the Higgs being where it is if it's 70 GV we even have a first order phase transition but anyway the standard model is you've all seen the picture smoothly goes from there to there but it could be if we have physics we have physics beyond the standard model that it changes and we might have had a first order phase transition okay so if you have a first order phase transition the picture could look that it's some at some temperature you actually have at a slightly higher temperature this minimum was a little bit higher then at some temperature they become equal to each other then then at lower temperatures it slides down to look something like that what sorry with another drawing it badly okay so I'll just leave it like this okay so so here they become degenerate as you keep going this slides down a little bit more and the way you go from here to there is by bubble nucleation right you have to go over the barrier and produce a bubble okay so that's what that's a first order phase transition and you might want to know it could it could have an impact on your picture in the early universe okay for example many of you know about electric baryogenesis the idea of electric very Genesis need to strongly order leads a strongly first order phase transition for electroweak symmetry breaking even in attempts of anything about the CP violation you need a strong first order phase transition if you have strong first-order phase transitions at around the electroweak scale maybe a little closer to the TV skill but any in this neighborhood it could give rise to interesting gravitational wave signals that you can look for with the future space space experiments like Lisa ok it's in that it's in that range for both power and frequency that Lisa could be sensitive to it so these things actually have interesting impacts on how we think about cosmology even experiment so we'd like to know what's the electric transition first order or second order we'd like to try to address this question experimentally and this is something that we'll have no idea about from the LHC absolutely none of course we can't recreate high-temperature phenomenon in a Collider but there's the following simple argument which is that if there is something beyond the Higgs that makes the phase transition first-order this something needs to have two properties a the new particles involved cannot be too heavy they can't be much heavier than the electroweak scale because otherwise they wouldn't participate in the electric transition and be they can't be too weakly coupled to the Higgs otherwise again they wouldn't touch the nature of the phase transitions so that's why it's a perfect target for a Higgs Factory 100 T V Collider because these are particles that can't be too much heavier they can be hundreds of GeV you can I've had hundreds of GeV singlets I'll give you an example in a moment you have hundreds of tqv singlets mixing with the Higgs we have no idea it's there from the LHC it can't be too weakly coupled to the Higgs it has to be at hundreds of GeV maybe a TV at most but it must give you deviations in the position X couplings at the percent level or more as I'll show you and uh and it has to be accessible to 100 T V Collider for just direct production okay so that's why this is an example the sort of question that these colliders are the answer for all right so let me uh um can I raise thee can we raise the screen I need to use the board I know if there's anyone over there no okay can you guys see this or is it equally impossible when I was looking is there enough light that you can see this if I move it no that doesn't help well maybe if I just right up there okay okay I'll do that that's uh I'll do that it's gonna be a slight challenge but I'll do that all right so I want to just give you an example to see how this works and this is the sort of easiest example to talk about and it's also one where the effects are easiest to think about and are big I think in many ways it's also the sort of most natural way that something like this could work okay so let's imagine that we have so first first let me make a little comment that if we had an effective potential for the Higgs that look like M Squared H dagger H + lambda H dagger H squared and there's a sex ik term as well H dagger H cubed over cutoff squared then one way of getting a first order electric transition is actually if this quarter coupling is negative that's positive okay then it's sort of easy to see that that's what the picture is going to look like okay so and for it to be strongly first order you want electroweak symmetry breaking to sort of be dominated or at least comparable from this part as from that part okay so that's what we're going to do we're going to imagine some underlying theory that's going to give us this as ineffective as an effective theory and so how are we going to do it well obviously we're just going to add a singlet that mixes with the heat so now let me write down a series only dimensionless parameters so I'm going to add a singlet so I have this I have some let me call it lambda tilde H dagger H squared and then I have then I have a singlet so I have a singlet single has a mass and then I have a couple of couplings one of them is like the cubic term I'll take a dimensionless thing out of it so working units of the mass of the scalar singlet H dagger H and then I'll have some cortex dimensionless coupling Kappa s squared H decoration okay so now let me just integrate up this singlet of tree-level if I integrate this singlet out a three-level then what will I get well I have something like this with ku Higgs is H dagger H it's a great so I get a correction to the corner coupling of the Higgs which goes like a squared right it's like AMS squared over a mess squared so in fact this turns out to be negative so this is something of order a squared H dagger h squared but then I get sub leading pieces if I just sort of expand that propagator further out I have something else which is a squared over m s squared now times the derivative of H dagger H squared so that's one of those operators that we talked about okay okay that's one of the dimension six operators and I also get a sec stick term for example from this diagram okay so I have two A's here and I have that coupling cap of there so these are the singlets okay so from here I get plus plus Kappa a squared over m s squared I'm ignoring factors of 2 H dagger H cubed okay so this thing is negative it will be absorbed with lambda tilde to give me what I called my effective lambda before so I'm not going to I'm not going to write it down again so I'm getting but I'm getting the thing I told you before M squared H dagger H there are some lambda H dagger H squared and I have these two higher dimension operators so a squared over M s squared d H 0 H squared plus Kappa a squared over M s squared H dagger H cubed all right so let's keep that in mind and now let's ask for this thing to give me a first order phase transition what I'm trying to do with this what I'm trying to do here is show you in this example how precisely demanding that this gives you it's a big perturbation on electroweak symmetry breaking is going to force the the deviations in the couplings of the Higgs of the Z as well as the particle to both be accessible to the Higgs Factory in 100 T V Collider but just see why this is happening a parametrically so if I just go back to this picture I want to imagine the electroweak symmetry breaking is actually dominantly driven by these two terms okay so let me just ignore this one and so imagine the electric symmetry breaking is dominated by these two terms and so you get slightly different formulas for the weak scale which is now coming from balancing this against that so the weak scale would be MF squared times the magnitude of lambda since lambda is negative and putting magnitude there over Kappa a squared the mass of the Higgs squared is lambda V squared as usual and the mass of the singlet squared is which is just m/s squared but I'm now translating back in terms of V is the Kappa a squared over lambda times V squared okay so now from this operator derivative of H dagger H squared we get a shift in the coupling of the Z to the Higgs okay if you that's remember Lantau explain how that works when you put things to it intuitive EV this changes the wave function normalization for the Higgs okay and when you go to canonical normalization it shifts the couplings relative to what relative to what you expect so you get a shift in the Z Higgs coupling which is given by well roughly is given by V squared a squared over m s squared okay so that's so a squared V squared over M s squared and now here's the point is that now but I know what V is in terms of everything and so I if I put put all of these things in this formula I get that this is aMDA over kappa very pretty okay so the shift in the the shift in the z higgs coupling is given by lambda now we can't make lambda too small right lambdas setting the mass of the Higgs more or less like it did in the standard model the lamb does like a third or something like that okay and and of course this is a smallish quantity already fifteen percent at the LHC today ten percent of the LHC today something like that so cap has got to be somewhat bigger than lambda no problem right lamb is already a quite perturbative coupling okay so this just says to the extent that cap is a little stronger than than lambda we get a small seating shift but we cannot make Kappa arbitrarily big okay what's the biggest you could possibly imagine making lambda for pie you would think right that that's the absolute limit of perturb activity actually if I write it this way with this definition Kappas more like sixteen five squared but anyway however you can't go that far you can't go that far because Kappa radiatively induces lambda okay Kappas a quartic coupling so just that one loop of radiantly induces lambda so there's actually a limit on how big Kappa can be so we have to have the Kappa squared over 16 PI squared is you know smaller than lambda so that is the limit I can't make Kappa too big and so that tells you that Delta Z Hague's is just bigger than something okay Delta Z Hague's is bigger than roughly the square root of lambda over 4 pi that's the absolute smallest it could be and this is around 5% okay you put numbers and more carefully it can be closer to 1% oh but that just gives you the idea that this is the case where if this singlet drives dramatic first-order electric transition you must see a big deviation in the Z Higgs coupling and furthermore I'm from exactly the same argument you discover that we can't make MS too heavy right now this is even more obvious because well for the reasons we said before but anyway a mass is bounded by around 4 pi v and it's got to be smaller than around 2 te v let's let's call it so you have the scalar can't be heavier than 2 TV you have have a big deviation the coupling from the Z and now I need the board back down actually yeah sorry can we have it back down please I'm really making them earn their order is there anyone up there thank you yes we're yeah we're the place I enforce it is I said the parameters are such that our electroweak symmetry making minimum is dominated by the quartic versus the sex stick okay yeah so so that's right by saying I'm towards developing so that's what I'm saying if you did a more careful analysis you can slightly suppress this effect so it can go from five percent to a percent so I made it as big as it could be but in the case where the biggest could be it cannot be smaller than five percent okay so so that's why it's just making it reasonable that the answer is going to come out at the sort of percentage level and obviously the singlet can't get too much heavier than the them two weeks ago both of these things are pretty obvious I just wanted to show how it works concretely and now it's okay so these are this is sort of more generally what I said I was giving you in this example but but this is the operator that affects the electric phase transition these are the things that we can measure at a Higgs Factory for example and we can get these either at loop level or a three level I was focusing here on the three level case but first of all the five percent deviation in the Z Higgs coupling is something even one percent is trivial for a Higgs Factory which is getting down to the 0.2 percent level for those couplings so easily accessible and now this is the reach for 100 T V Collider for producing a singlet that mixes with the heat okay and so here we expect to have a significant mixing with the Higgs again obviously because it's associated with the what for the rate same reasons that we talked about this parameter C is a measure of the size of the mixing roughly is the ratio of the mass of a single eighth over the mass of the Higgs over the mass of the singlet but anyway if there's a you know it's even a mixing of order attempt this is the kind of reach we have at a hundred T V Collider I forgot to say luminosity 100 kini Collider is projected to be around a 3000 inverse four empty barn okay so that's that's not super aggressive but people will talk about even higher luminosities potentially these days but with 3000 inverse hemp the barns compared to a 300 mm to barn for example at the LHC you can get a read sort of into the multi TV scale in a four and a half TV for reach Woodley singlets so if they're lying around at the TV or lighter you will produce them okay so in this example this thing drives the first order phase transition and it is totally visible at the Higgs Factory indirectly and then the thing that's producing it is completely accessible to the hundred T V Collider okay but again it could trivially be sitting around here and totally inaccessible to the LHC alright so that was a that's an easy case to talk about the electric phase transition there are harder cases where it's induced at luke level and those are actually harder theoretically as well it's harder to make them affect the phase transition because it's happening radiatively but even in the most difficult cases that people could come up with there's always between the ships in the triple Higgs coupling a shift in behaves and direct production of the particles between those three things all the all the even most difficult parts of the parameter space in the hardest series to look for in this way can be covered alright so now let me switch to the second topic which is about naturalness and here we've talked so much about the naturalness of the school I have deliberately zero slides about the philosophy other than to say that whatever we learn about it we're learning something I mean either either the physics the scale where the Higgs mass becomes calcula and understood is comparable to the weak scale or it's much higher than week scalar has nothing to do with the week scale doesn't occur anywhere in our universe at all okay and if this happened to get a complete understanding electroweak symmetry breaking and even more a phenomenon probably so that would be spectacular of course it's very overdue with the LHC ah and okay here if it's true we might get less direct clues from around the scale about what's going on but it means either kind of unprecedented correlation between the UV and the IR or a breakdown of the reductionist paradigm that as we discuss the ultimate explanation for the origin of the weak scale might not be found in the micro physics of our of our of our universe so we don't know oh we don't know which way things are going to go but it's a big deal either way and we really need to be very sure about whatever conclusions were drawing about it now the first thing to say is what if we're just missing Susy say and this is a stand-in for any natural physics but what if you know we say percenters accidents happen the moon eclipses the Sun and blah blah blah maybe it's not a big deal these sort of factors of 10 20 tuning hundred that we knew before soon into the LHC you really want to make sure that there's stuff there and it's just around the corner you miss that you're really going to see it right so what is the reach for 100 TV Collider 4 and this is what it is enough supersymmetry and these are the usual kind of plots you see for for example gluey no as a function of the mass of the lightest neutralino so you're always underneath this line because you imagine we make the gluey no and it decays to the bottom of the spectrum and one of the fun things about making these plots is that finally the axes are in units of a TeV okay so and the reach is as you see here you know is in 10th 20 TeV for glue enos quarks the colored particle reaches can are typically in the 10 20 25 TeV range okay so for gluey nose and squirts for example here's where we're sitting from the LHC and here's the projection from a hundred T V Collider so in the sort of twenty TV range okay um now so that means that if it's around the corner we're just going to obviously see it but we're going to take that roughly factor of five a little more extension in the in the in the exclusions so that whatever are however disturbed we are by our notion of naturalness before it gets multiplied by a factor of 25 okay okay what about directly for stops I won't go through this in detail but but you can see just for a sort of direct stop production the limits go up again to the sort of four or five TV range about that factor of five higher than the direct limits that we get from the LHC and similarly for top partners okay so all these things are going to the five six TEB range okay so this is something which if you said well we've seen percenters accidents before maybe it's not a big deal okay now if we still don't see anything you have to say well these are now Parton almost part in 10,000 accidents okay and you can't say that we've seen that many times before elsewhere in particle physics you know maybe it doesn't matter you could say already if it looked at part in 100 bad it was already bad and as we said last week you've already decided what kind of person you want a person you are now we're haggling over the price okay but still it is true that it's forcing us into into into regimes of tuning if you imagine these were the theories that are going on that we've not been forced to before in particle physics nevermind the cosmological constant of course oh now now let's take the opposite end let's say we do see new physics at the LHC there's two TV Glee nodes right hiding in the data and we're going to see it soon okay here it's very obvious here we also want to go to 100 TV collider but for much more obvious reasons but I just want to pause the comments on this because it's sort of amusing that if we had you know 300 GB bluie knows the way my advisors generation of people thought would happen then the motivation for going 200 TV would be a lot lower actually ok so you've already seen this whole huge spectrum you might immediately want to go do much more precision measurements the picture of the world people have that you'd build a linear collider then and go measure the couplings of the slept on to present this level accuracy and verify suzi relations and so on that was a reasonable picture of the world if you thought they were already seeing the zeroth-order picture from the LHC now that we don't have that picture even if we see something we're not going to know that we have a right to call it a gluey no we're maybe going to make a hundred or a thousand of these guys we're damn lucky okay and and that's not enough to be able to actually say that they're a gluey no you might know that it's a colored adjoint you might not even be able to really say that it's a color that joint with with the amount of data that we get we can see enough to make a discovery but not enough to say what it is then what you want is 100 TV collider to get you the rate okay and if you remember from how drawn Collider 101 the rates at Hadron colliders scale roughly like the fourth to fifth power for heavy state scaling force a fifth power of the center of mass energy so the factor of seven gain is a huge gain in the rate at which you produce these things so you would have a factory for these guys at a hundred TV and there are other interesting cases again if we imagine let's say with let's say just at the 11th and 1/2 hour we saw something like natural Susy so stops our light but the first two generations are heavy ok and maybe we even missed the stop but anyway so we make the stop 100 T V Collider but what about the first two generations this is an example or the reach for a hundred TV collider is much larger than the LHC because you can look at something like Associated production where you make a gluey no that would be lightish let's say two or three TV in association with the light two generations okay and here the reach goes all the way up to around 35 TeV for the first two generations you're not pair producing them you're making one white guy and one very heavy guy okay so it's the T Channel process where you make where you make a light blue ino and ah and the very heavy scalars and this this goes all the way up to around 35 TV so that really wants the reach that we get from the LHC all right now something else that you know if especially if you're a if you're a model builder trying to hide supersymmetry or other natural solutions entire key problem is that opting especially since you're dealing with colored colored partners you can try to find theories where they're there they're there around their light but they somehow decay in complicated ways our parity violation more complicated scenario so they're just hidden in the hydronic muck all right now and you see that that just emphasizes the sort of fundamental sense in which making these particles are they have your own Collider is an indirect test of whether or not these particles have something to do with the hierarchy problem you might even make these colored particles but until you've verified for sure that they talked to the Higgs and they have something and they're couplings are related to the top and so on you don't really know that this that they have anything to do with the hierarchy problem at all well you really like is something that's absolutely directly checking the coupling of new states to the Higgs and that's exactly what he eggs Factory does okay so let's say we have I'll take is the concrete example of stops stops just have nowhere to hide you can you can make them decay in 30 jets okay so so totally make it totally invisible and it doesn't matter they will still if they talk to the Higgs they have to have a big coupling to the Higgs they'll still give you a shift for example in the Higgs of glue-glue coupling or they give you a shift in the SN T parameters and those are things that you can measure if the Higgs Factory and on the Z pole and they give you reaches already into the you know a TeV one-and-a-half to TV range but I emphasize that this is something completely model independent of how it the case you cannot hide this in hydronic muck okay so that's another complementary piece of very important complementary piece of information we can get from X Factor and finally let me make the following comment about naturalness before we switch finally to a at the end to the dark matter you can say look at 2020 we haven't seen any new particles at the LHC isn't this all sort of crying over spilled milk right uh when we already know that this idea of naturalness is just wrong right it's meant already percent this wrong now you're arguing whether it's good or bad but do we really need colliders to further beat an already dead horse right that it's already a wrong idea even though it's only a percent but that's already a pretty good clue and of course the answer is it's certainly both theoretically and experimentally no because we already have examples of theories that people wrote down long before the LHC turned on that that worked perfectly compatible what we see so far now it's true that they're not particularly popular well they weren't particularly popular ten years ago they're more popular now okay it's true that they look a little broke it's true that it's not the first thing that you would write down but it's also true that it's possible for the top partners to just not be colored as we heard at some length last week but here's another kind of inevitable here's a little bit of inevitability that you have to have if you have some kind of partner that's giving you a diagram like this that removes the ultraviolet sensor to be associated with the top with some coupling here that has to do with the topical coupling maybe this stuff is not colored maybe the three comes from some some some partner mechanism as we talked about as you heard about last week this diagram means this diagram must exist okay you just take the same vertex and attach it to the top so there's a completely inevitable shift in the Z Higgs coupling because this gives you the D mu H dagger H squared operator and you have to be able to produce these guys in at least in vector boson fusion tech processes like this at 100 T V Collider okay so in other words if this theory is sitting around with like 400 GeV top primes totally natural miss that the LHC then it'll give you a big shift in the DX coupling at least that loop level and this direct reach and in fact in concrete theories of this sort that you write down you can get much larger effect so many theories like this are paired with the general idea that the Higgs is a pseudo Goldstone boson as we talked about right at the beginning it's perfectly possible for what we're going to know directly from the from the couplings of the Higgs to electroweak States that it could be about as elementary as a PI on without a problem okay and so the only way when we say that all naturalness theories are in trouble at the LHC it's it's all indirectly from the from the assumption of color partners right so you can imagine a theory the Higgs is the pseudo Goldstone boson with uncolored top partners and this theory is totally fine from the LHC but it still predicts these it's still prediction these 10% ish and roughly that scale deviations in the DA couplings so if you go measure the Zeke's coupling and you don't see it you're forcing for example the decay constant associated these Goldstone bosons to go to like a three pev scale right and that means that even this theory which is suitable zone uncolored top rotors all of that stuff even this theory directly from how the Higgs talks to talk to electrics talk to electric states would be forced into these tenths of a percent level of attuning okay or you flip it around that it could be completely natural and but then we have to see a big shift in the Xia coupling easily accessible but even in these cases where the effect is radiative that unavoidable diagram that I talked about before then the effects are big enough that that you that you force these particles to be to to cover the range in which they would really be natural okay so even in the most indirect possible way they have to be accessible in there in how they ship the ZX coupling and this is I apologize another busy another busy plot but the particles have to be light enough that you can directly produce them at a hundred T V Collider now what I will say is this is maybe the most important the the important feature of this sort of analysis that even in these kind of theories the the important claim is that if the even in the hardest cases if the shift in the Z Higgs coupling is sort of barely visible enough to be seen at the two sigma level the particles have to be light enough that you can discover them at five sigma at 100 TeV collider so again they give you a shift in the Z Higgs coupling and then by going to hundred TV you can verify but that's actually what's going on if these top partners are electric charge not colored but electric charge then you actually get a very strong probe of them from how they affect other things like how they affect kicks the gamma gamma it not they want effect takes the glue glue because they're not colored but they can affect takes the gamma gamma and again that pushes you these are sort of contours of of tuning if you like just just what we get from from the shift in Hixton gamma-gamma it forces you into the sort of 10% range for a poor tuning there you really want that thing to be of order 1 and oh they also give you shifts in the SMT parameters that again force the particles already into the sort of bug into the TEB scale even when we're going to all this distance to make it on coloured not not visible at the LHC all of this structure if and this shows that that we can even push these things well into the unnatural territory all right so that's all I want to say about the naturalness the summary there for me is that is that these you know what's the problem what's the issue with the LHC the issue is the LHC the models that were popular on the 90s are in a lot of trouble ok and the models that were not popular in the early 2000s are now slightly popular because they're not dead alright now of course Suzy is also not dead it's just it's just much more tuned than anyone expected it to be so whatever is going on maybe something small is wrong and they're really just lying around and we're missing them and you just take this big factor of 7 leap in energy and you for sure make them and you'll see lots of evidence for their existence by more position measurements of the Higgs maybe there's some more exotic standard natural possibility going on like neutral naturalness and then the sort of bulk you know where those theories are actually natural you do not see them at the LHC and you just cover them with the the Higgs factor in 100 T V Collider and even push them into a natural territory all right so let's finally talk about dark matter and this is something that we stressed last weekend this week a couple of times so wimps are still the only calculable models of dark matter that we have the only the only models where we get to remove the we get to remove the uncertainty with initial conditions by assuming that that the dark matter was once in thermal equilibrium with everything else and as we said already a few times if the W in wimp stands for weak though weak interactions then it could clearly be that the wimps are at a few TeV and completely inaccessible to the LHC so we gave examples this is not something where the theorists are trying to hide the Dark Matter this is something you could have a calculation you could have done probably somebody did do in 1979 uh what math what an electric double it has to have to be thermal dark matter one to Evie what mass would a neutral triplet have to be dark matter three T V okay and those things are inaccessible completely inaccessible to the LHC and as we stressed before they're even invisible to direct detection because the leading interactions with the Higgs are just not there everything a tree level everything is mediated radiatively and i think i the number i put on the board there when i was talking last week that the cross-section was around 10 to the minus forty six centimeters squared is wrong it's actually more like even ten to the minus forty seven centimeters squared or even smaller so they're really even at or below the famous neutrino floor so we won't even see them with direct detection okay so what do you need in order to be able to produce these particles that colliders you need to be able to have a Collider that produces one to two to three T V weakly interacting particles the LHC is great at producing four or five 600 GV weakly interacting particles in to three T V strongly interacting particles so you need to go up from that by your factor of five to ten to have an electro weak Factory alright now just a little bit more some a little bit more basic physics let's talk about those very simple cases the very simple cases were the very simplest cases of dark matter I'll just go back to the board here but don't don't raise it I'll just write where something like a Higgs II know or we know okay does anyone know why it's so tall so I said that like a TV Higgs II know is inaccessible to the LA to um does anyone know like how many Higgs inos are we making at the LHC when I say it's inaccessible are we making no big xenos if you have a TV exam any of them were making every year today okay if you're a particle business you need to know these numbers okay so we're making huh definitely not less than one we're making a lot of them actually that's a little exercise for you okay from what Leon touts told you you should be able to easily figure out how many Higgs Eno's are making it the LHC it's many many more than one okay we're making a lot of exams at the LHC not tens of thousands we're making what big dinos at the LHC so what's the problem the problem is that they decay in an absolutely horrible way right so they're very difficult to see now why is that so what does it look like let's say I give you a an electric doublet right what does the spectrum of the theory look like what's in an electric doublet there's a neutral particle and a charged particle right I've charged one what are their masses if I say the mass is a doublet is one TeV what are the masses of those two particles what do you think there should be degenerate right you know they don't know about electroweak symmetry breaking the mass is much bigger than a TV so you would think thank you but I'm going to need it back down the SEC you would think that the masses are are are equal and they are two very good approximation but they are split they are split by electroweak symmetry breaking after all so there's no symmetry that rotates them into each other they are split and so whatever your representation is you can draw a diagram that looks like this which maybe has WS and DS in it and and photons or hyper-charged right but in terms of math excite wzz and photons in it and these diagrams will be different for the neutral in the charge state right so there's some squidding now what do you think the swimming is how would you estimate the splitting you have some rough idea what the splitting is well first of all there's an alpha in front of it right so Delta M is going to be around alpha so what do you think it multiplies so I'm going to try to I'm going to try to confuse you a little bit okay so what do you think should happen if the mass of the particle goes to infinity way heavier than the week scale right oh you might think the splitting should vanish so so so this is this is what I would have guessed without thinking about it much okay is it alpha well there it better be a 1 over m right and what should go upstairs m z squared right the trevan --is-- wz squared it should vanish in the limit as you don't break a lecture weak symmetry okay and wrong right now this is the reason I'm bringing this up is this is a general important fact that expressions like this you see MC squared that's something that occurs as a parameter in the Lagrangian so this is the formula that you would say in a fancy way this is a formula that's analytic in the couplings that appear in the Lagrangian ok things that are analytic are always things that come from short distances everything which is generated by physics that long distances is not analytic in anything it's not analytic in the couplings it's not analytic in the momenta it's not analytic in anything that's the sort of hallmark of something which actually comes from long distance physics this is a long distance effect ok the wnz mass is that much longer distances compared to the mass are actually are generating this effect if I have some higher dimension operators the higher dimension operators could split the states for example if it was a double it double its I could have the operator H dagger sy up H tags H side down say okay sy up and side down divided by some high mass scale doesn't have to be the mass of the particle and you see this would be someone goes like V squared over lambda right so that's like your rough intuition but this is this is not like that in fact the effect goes like alpha times mg okay there's no there's no master pression at all and the non analyticity is that it's that MZ doesn't occur in the Lagrange's it's really the square root of MD squared okay so that's something that is an analytic that's a very formal way of saying what it is but what's what is its effect physically it's a very pretty and beautiful effect which I'll say roughly and then I'll leave you as an exercise I'll give you the right answer so you can know if you're doing it right it'll leave you as a nice exercise to think about on your plane ride your train ride their bike ride tome to figure it out but this is the physics imagine you have a the charge component of the doublet okay the charge component of the doublet the charge component radiates a photon field so there's a photon electromagnetic field around it okay so that's the usual photon electromagnetic field photons so this is the charge guy the neutral guy let's say su 2 is not broken so the neutral guy what is the neutral guy shining it's shining the Z all right I'm saying it a little loosely there's really the different components but loosely shining the Z so it's got the Z a field in front of it right now there's some electrostatic energy that's stored in this electric field right do you remember how that electrostatic energy goes it's divergent at short distances right but it goes like alpha divided by the short distance cutoff right so if I put some some short distance scale here then the electrostatic energy if you integrate the electrode the electric field squared this goes like alpha over a where a is this length scale that I cut it off by all right now that was a famous fact about the self energy of the electron that was ultimately fixed up by particles and antiparticles and all of that stuff in a field theory right so these linear divergences disappeared and they were replaced with the logs that were used to in field theory but here there's a different effect you see at very short distances you don't see that the that electroweak symmetry is broken so this the short distance contribution here is identical to the short distance contribution here but there's a difference from long distances because at long distances the Z contribution shuts off but the photon contribution keeps going okay so in this mass difference there is something which is the extra electrostatic energy stored on the photon electric field which is not there for the Z okay so in the mass difference the Delta M you get something that goes like alpha times MZ okay that's exactly what this one over a is if you now cut it off at around the scale associate of disease okay now this is something that you can definitely convince yourself is true by looking at this diagram without actually calculating the loop okay and that's what I want you to play with on your train plane bike ride home is to understand how the very standard and famous thing about how when particles are heavy you can interpret pieces of loop diagram is coming from these classical from these classical self energy effects and just just so you know whether you're doing it right or wrong let me give you the answers so for for for a Higgs ìno so an electric doublet with hyper-charged 1/2 Delta M always in units so I'm going to say Delta M is alpha mg over 2 times something and the some things are the following and I'm just giving you the dependence on the Weinberg angle and this is all you need to know to know if you're doing it right or not it's sine squared theta Weinberg for a Higgs ìno and it's cos theta Weinberg times 1 minus cos theta Weinberg for a we know and if you have energy to do a charged triplet so a triplet of charged one of hyper-charged one so that there's a so that there's a charge one and charge to state the mass difference between the plus and the zero is 2 times 2 plus cos theta Weinberg times sine squared theta Weinberg over 2 and for the doubly charged - the singly charged it is 2 times 2+3 co-state of Weinberg times sine squared theta Weinberg over 2 so these are various sort of simple theories for what the what these electroweak states could be they all contain something neutral and we have all these Corrections that are parametric set by alpha N Z over 2 I've given you these dependence on sine theta Weinberg so that you can make sure you understand if you try to do the calculation where all the different pieces are coming from the coming from w's these have to stare at the pictures and figure out how to extract these classical pieces from them without doing any work all right but anyway that's the basic physics all right and so these are very small splittings there are roughly in the hundreds of MeV range but in detail in detail for the Higgs II know this ends up being 330 MeV this is for the we know 260 MeV and in these other cases just for fun it's 500 MB be 800 MeV okay so this is not a situation then where you're like like you're used to where you produce a charged state and it decays to a neutral state you see a lot of missing energy this is not like that right the states are very nearly degenerate with each other and so how do you look for them so let's say first of all let's say I produce the we know what happened what happens I produce the neutral we know nothing right it's the neutral we know is the dark matter here right so it's just stable just escapes the attacker I see nothing what if I produce the charge we know then then then because this mass splitting is so small it travels a macroscopic distance before it decays do you know parametrically what it is what's the lifetime in terms of Delta M I mean not numerically what is it parametrically what's the formula it's around Delta M to the fifth over M W to the fourth okay very much like neutron decay right so so and if you put in the numbers the travels at sea towels around 10 centimeters okay so that's nice sea towels around 10 centimeters for this guy that's long enough that the charged part can actually you see it in the tracker right so you see a charged track and then what happens it decays what do you see what is it decay to first of all just a Payan right actually has barely enough room to spit out a PI on but it does 160 s bigger than 135 okay so but it gives you a very soft PI on which you don't see okay just spirals and you don't see so what you see is what they call disappearing tracks right so it just goes and then it just stops a very spectacular cig right so that helps a lot to look for it what about the Higgs II know here it's much harder just this lousy factor of two means that what's its C tau at C tau is like half a centimeter all right it scales like the sort of worse sorry it's like almost a millimeter scales like v power of Delta M so just that factor of 2 means that it travels 32 times less far and so it's much harder to to to look for it in a in the tracker okay and these other cases are you don't get any leverage out of that all right so what's the broad thing you're looking for whenever you're making something invisible at a Hadron Collider you have to tag it with something so it's a mono jet or a mono photon signal okay so you have to radiate off the hard jet from the initial state in this case because the particle is in neutral but if it's in the particular case of a we know you get a little bit more leverage from the fact that the adult atom is small enough that we get via displacement so can I guess well I'll screen back down and I'll just say this and I think we will we'll stop there oops all right so this is the kind of reach that we get from the LHC versus 100 T V Collider and remember the figure of Merit what you're after for we know is roughly two and a half three T V if it's a thermal relic okay so two and half three T V totally hopeless at the LHC ah but with the but it's and the sort of differences so this is a five Sigma band five Sigma discovery sort of to Sigma exclusion there are some assumptions being made here on on how well you can control the systematics and take advantage of the disappearing tracks but it's fairly conservative and and three T V is is coverable okay it's quite robustly coverable in this case so you can get to you can get to the three tv.we knows the Higgs inos are just you know getting to a TV is is hard so that's what you need for a thermal relic and again these are the very first rounds of analyses so you might be able to do better but you can get the sort of 800 GeV okay so not quite all the way there for if it's completely a thermal relic okay if it's some if it's even 50 percent of the dark matter no problem okay but so here a little bit more thinking needs needs to be done but but it's close and again of course it's a big leap relative to the LHC that's the thing to keep in mind is that the hundred T V Collider is an electric factory and we're starting from the worst hardest possible case where we have the huge rate for producing them but only but because of these tiny splittings we have to pay the extra factor to radiate off the extra jets okay but even these very vanilla cases the we know is covered pig Zeno is almost covered and maybe with more thinking we could really even more robustly cover that kit now now to something a little more a little easier to think about let's say it's not just one state there but you have a whole electroweak sector so this is what would happen in split Susie for example okay ah in split Susie if the glue II know if the bottom of the spectrum is in this TeV range as dark matter the glue I know somewhere around 10:20 TV number 10 20 TV is no problem at heaviest 1020 TV you can make directly but even the electroweak part now you are making so many 340 evey electroweak states that if there are you know reasonable splittings between their masses that you're looking for the usual kind of signals leptin plus missing energy same sign opposite sign try leptons and so on but now the sort of mass reach is really robustly going into the multi TV scale now we really take advantage of the fact that we get an electro weak Factory and so we can really probe this very robustly so I would say that every reasonable version of split suzy that i could think of would be easily covered by the 100 GV collider so this is a summary for dark matter i think there's a quite robust coverage for for whips and a whole bunch of different a whole bunch of different scenarios that go into the TV multi TV range except for the gino which has a which has some challenges and if we have these cascades we have more we have more stuff in the electroweak sector then we really go into multi TV Everywhere very very robustly so again it's not a know loose theorem a wimp could be some crappy particle annihilating to towels and then we're not going to see that 100 TV Collider but it is interesting if we take the simplest series most obvious things which are by no malice invisible to the LHC and to direct detection experiments that we can quite robustly cover them with under TV Collider all right so that's really what I what I want to say about these these things where there are important physics questions where we get some very solid answer to these questions from the degree of leap in precision and energy that we get from these guys so the final comments are will it happen might it happen as I'm sure almost all of you know our friends at CERN have been talking about it for a long time for the past several years what particle businesses like to see more than anything else as maps of the maps of the world with giant circles on them and so so there's a there's a picture of the area around Lake Geneva and so there's the LHC and this is what this is what I think in this case in 80 kilometers tunnel would look like and you you do have to go under the lake and our friends in China are talking about it and this is actually by now an old picture this is one of the sites one of the sites that they're thinking about now there are others but this is an area around 300 kilometers northeast of Beijing it's where the Great Wall starts I'm told there's no pollution because the Communist Party officials go there for their summer holidays so it's very beautiful and so on I've never been but there's a 50 kilometer tunnel and 100 kilometer tunnel and this in in at CERN the whole program is called a future circular Collider program so FCC in China it's the circular electron positron Collider or the super proton proton Collider and one of the reasons this is out of date is that our friends they're really almost exclusively talking about hundred kilometer tunnels now so we would always have to draw these pictures and you know I would always say hundred kilometers and they would always say 50 kilometers but now almost everyone's talking about hundred kilometers all the time so what's the what's the only problem the only problem is that it costs 10 billion in your favorite units okay and is this a problem well uh it's it's an incredibly naive thing to say that these things now cost oh my god that in cost the LA sea costs to billions of dollars these things going to cost tens of billions of dollars yes it's true but there are decades between when these projects these projects separated by decades if you went back and told someone in 1950 that you know my former crappy Mitsubishi cost five thousand dollars to buy they would be very shocked right the world is getting wealthier it's the ratio that matters not the absolute cost and this is something that this is a little table that's the upon long who's leading up the separate and China made which like very much which just shows that the cost of accelerators compared to GDP has been basically constant for the last 3040 years and it's always roughly ten to the minus four okay so you know the LHC is around three ten to the minus four European GDP the ILC is to ten on the - for everything here the SSC was around ten to the minus four when it was canceled right so and if we do these things it will still be around ten to the minus four okay the amusing thing in China of course is that when they've made their little electron positron Collider in Beijing in 1984 was also a ton of the - for of Chinese GDP back then so for the same ratio they can go from having a little 250 meter each plus C - Collider that puts them on the map to having the machine that leads the world for the next 30 or 40 years right um okay now is kind of the - for too much maybe it's too much that's something that we should decide and talk about but it's not something new that we're asking we're not talking about something that's qualitatively different than what we're talking about before and you know in previous epochs in the history people have thought that fundamental advances in science were made much more were worth much more I always used to talk and talk like this about the how much the how much Tycho Brahe he's King um gave of his GDP to Tycho Brahe he to give him this island where he could sit there and make measurements of the motions of the planets for 30 years that led to the modern will led to Kepler figuring everything out about orbits not being circles and ellipses and all the rest of it so obviously a wise investment and you know just as a joke in talk that would say oh I don't know that was probably like 10 percent of his GDP well some historian emailed me and actually it was around 2% of the G so it is anyway so I was joking I didn't think it was remote I didn't sighs the % but was around it was around 2% or two of a Danish GDP back then and while it was probably worth it okay so it's about a hundred times more than we're talking about now so um so banana kiss that's that's that's not really relevant to this discussion but we're not talking about something qualitatively different compared to what we have done before all right so now I think I've gone over time so I won't go through this too much we can maybe talk about it over lunch if there are people who are interested there are a lot of common there are a lot of common objections there's no point to planning ahead for these things before we get all the results from the LHC the answer to this is while it's definitely true that we're entering the most we're in the most exciting phase of the LHC ah no matter what the LHC sees we already know there are questions that we're not going to get the answer to them from the LHC important questions we're not going to get to the answer to from the LHC whatever happens if we see nothing but the Higgs totally obvious we have to study the Higgs and put it under a more powerful microscope because as I stress we only get a fuzzy picture of it from the LHC okay so in this case it's obvious we need to know more experimentally what if we see new particles when we talked about that too in the case of gluey knows let's say we see stops well we'd only put that in quotation marks at the LHC we have no idea they're actually stopped because we don't make them with an up rate so we need the hundred T V Collider to up the rate by a factor of a thousand so that you make a factory of them and you can study them and figure out what they're telling you so we don't need to wait to see which one of these possibilities is realized whatever happens there are they're important questions that we're not going to get the answer to and so we can start planning and thinking about it now another common thing if we only see this is all a crazy pipe dream if you only see the Higgs at the LA sea and nothing else we can never convince politicians to build machines so this is just so stupid to be thinking about these things well um I find this argument hilarious because especially in this country now it assumes any enormous amount of intelligence on the part of politicians you know imagine they're sitting there in Washington they're like looks like naturalness was I'm right no not very surprising and I really thought the stops would be around the corner and I don't know right oh they have no idea what the hell's going on you know it's a job of scientists to tell politicians what's scientifically important and if the scientists think it's important and you convinced the world and the country I think it's important then we'll do it if we can't we can't but but they're not sitting there with some sort of prejudgment about what's scientifically exciting or not what I find about people who make this argument is that it's actually not the politicians and they might be a little embarrassed to say it it's themselves they don't think there's a point to continuing they think oh my god we're not going to see new particles I wanted to see a plot with giant spikes in it just like they did in the 60s and that's not going to happen so I'm a little worried I'm a little depressed and instead of saying it's me I'll blame the politicians okay well we're in a different place intellectually now on the subject than we were in the 60s in many ways the stakes are much higher now than they were back then there are big structural issues on the table now compared to the issues then but the nature of the kind of experiments we have to do in the kind of questions we have to ask and how long we have to wait to get the answer to the question is just longer that's the win that's been the typical way it's been in fundamental physics for a long time okay and people have to expect that it can take decades to figure things out you have to do difficult measurements for a long time that's why it's a tough business and no one promised you a rose garden but that's why also it's an important business okay and it's a deep business and so if we believe that these questions the ones that I talked about are important then we just have to tell the world we have to tell people we have to tell politicians we have to tell them why we think it's important I think it's important I think it's worth spending a decades of my life on many of my experimental friends think they're important they're other people who even matter more than me because I can go fool around on the side every now and then right they have to devote their lives to doing this there's enough of them we think it's important great we have to go tell the politicians and hopefully they'll agree with us but I think the intellectual case is like super strong okay we are extremely theoretically confused about deep things and we can do something about it experimentally so doc you should just go ahead and do it okay um analysis if we don't see new physics the whole thing is a big failure right I'll be such a waste tens of billions of dollars and what's the problem with this the problem is the assumption that this word means new particles okay and as I've stressed many times just learning anything about the strange quite like particle we learn nothing else will tell us a lot about the way world works there's no sense in which these things could be a failure because we're learning something very fundamental about something we're very confused about and there are concrete results that experimentalist will get concrete facts about the world that we will get that are important and will be important 10,000 years from now as they are today finally what about the ILC okay this is actually a very important question for for the geopolitical reasons but scientifically it would be both scientifically and geopolitically it would be awesome to have an IOC okay first of all now for purely measurements of the Higgs couplings these circular Higgs factories do similar measurements and they broadly give you the same kind of sensitivities as the ILC there are people are now talking about perhaps staging the ILC even starting with lower energies down at the 250 those things would be very similar very very similar measurements you get in circular colliders but something worth remembering is that eventually to get to super high energies we're not going to do with proton proton machines will eventually have to do them with electrons there are these ideas like plasma wakefield accelerators and things like that that that could in principle get you you know factors of a million larger electric field that could accelerate particles that's the sort of limit around alpha cubed inverse around a million times bigger than the electric fields we can get in materials that are limited by by just dielectric destruction of the of the material that's hosting the electric field so that effective is a limit to how when normal materials we can accelerate things but in principle in plasmas you can separate charges by a lot and get huge electric fields the electric field are ultimately limited by shrinker pair productions but if you look at this sort of ratio of the biggest electric fields you can get that don't destroy materials to the biggest you could possibly get it's roughly a factor of alpha cubed or a million so you can impress it will get much much higher energies but those things there's still a long way off it's very difficult to accelerate particles many many times and get high luminosities like that but if they do start working even partially you'll use them as afterburners on linear collider okay so there's a sort of there's an ultimate path forward for very very high energies eventually where you definitely do not want to lose linear collider technology we're going to need a linear colliders and if we don't have linear colliders on the planet then then this whole generation people who knows how to build them will be gone it'll be very hard to uh to keep it going so it's so it's great for scientific reasons and naturally for geopolitical reasons especially in China in my view nothing would more quickly guarantee that China built a circular Collider than Japan building a linear one okay so I'm a very big fan of the ILC for a scientific and geopolitical reasons alright and finally I alluded to it instead of bidding big big bigger accelerators shouldn't we wait to develop some revolutionary new methods and do it cheap and I just quickly alluded to what those methods were and it will be fantastic if we could make them work uh it's not I mean it's not something which is even as far as I can tell even on the horizon to have an idea but how you could get the luminosity sign up again the problem is you can get huge electric fields I can give a particle a big kick once but then you know you have a bunch of them you give a big kick and you spray them out in some horrible way and it's hard to keep them collimated and kick over and over and over again ok so while you can get very large gains in small distances it's hard to do it in a coherent way and so this has been something that's been said about particle experiments for decades or our friends in condensed matter physics told us told us when the SSC was being built that we should wait for a high key magnet to come along that would revolutionize everything in the world of course but in particular make accelerator is much cheaper well it's 40 years later they haven't happened ok and it would have been a very bad idea back then to listen to them and stop everything and wait for it ok so we do what we can at any given time we make if there are reasonable things that seems like we can we can wait great but I don't see any reasonable thing out there that's a feasible alternative to doing this and so that's the case I think we should make so that's all I wanted to say let me just end by thanking you all for coming to the school I really hope you had fun with with each other I hope it was in intense couple of weeks so I hope you got exposure to all kinds of physics that you haven't thought about before and that's you keep in mind what I told you on the very first day that it's an ideal time to be your age because there's all kinds of wrong things you don't have to learn and there's all sorts of opportunities for very interesting totally new directions some of which have been lectured on at the school that might carry the field forward on the next 20 or 30 years and it's really your job to do it so thanks a lot [Applause]

Channel: Institute for Advanced Study

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Length: 106min 43sec (6403 seconds)

Published: Fri Jul 28 2017