 I'm going to be talking, for better or for worse, something much more conservative, maybe less interesting, but I'm going to be talking about some work that I've been doing over the last few years with a bunch of collaborators listed here. First of all, I'm going to talk about what I call induced electroweak symmetry breaking, and I'll of course explain what that is. As an interesting example, I think, of non-de-coupling physics, then I'll talk about it as an example of improving naturalness in the context of supersymmetric theories, and I'll talk about the phenomenology at the end. So just to set the stage, let's just remember where we are. This is something I think we all know, but it's worth remembering the long journey we've been on. It was actually since the 1930s when Fermi wrote down his theory of weak interactions that we knew that there was an interesting scale of a TEV, and Fermi, literally, if you look historically, he really, literally understood this. Of course, we made huge progress, especially in the 80s with the discovery of the W and Z bosons, but still if we take the theory, including only the degrees of freedom that we know, we still had the same cutoff, this time for WW scattering, and it was only in 2012 with the discovery of the Higgs boson that if we take the theory containing the particles we observed, now suddenly we have a theory that has a cutoff near the plank scale. So this has obviously caused a lot of angst. We've been living with a fixed target for new physics for a long time, and now we don't have one anymore. But in this situation, people have naturally wondered about whether perhaps the standard model is all there is, or perhaps whether we can only see small deviations from it, and in fact this is sometimes enshrined in what's called the Higgs decoupling theorem. And this is not my formulation of it. This is stolen from somebody's slides who you probably know, but I'm not going to tell you who it is. The Higgs decoupling theorem says that suppose the Higgs sector contains additional Higgs bosons, but one of them is the light 125GB particle that's been observed, then necessarily the rest of the Higgs sector just gives you some additional corrections to the standard model which are higher dimension six operators suppressed by mh squared over m squared. And the proof is, well, just go to the Higgs basis where the VEV is all in the one of the Higgs eigenstates. And if you take the other guys out, you get dimension six operators. That's the proof. So this theorem, as it's usually stated and understood, is just not correct because it can be spoiled by non-decoupling effects. In other words, the theorem is true only in as far as it is true, as you assume that there's no decoupling. So let me just remind you a little bit about non-decoupling physics. The canonical example is the top quark. If the top quark mass gets heavy, it leads to effects that are not suppressed by the inverse top mass. And we understand that because the top mass gets its mass from electroweak symmetry breaking. And so, for example, this top loop has a power of m top downstairs from dimensional analysis, a power of y top, so the coefficient ends up being independent of m top. And exactly the same thing can happen with the additional Higgs bosons. Can also get their mass from electroweak symmetry breaking. And just as with the top quark, that will require some of the couplings in the Higgs sector to be somewhat large. But again, like the top coupling, not non-perturbatively large, not 4 pi or not 10 to the 10, just order one, order one large. So rather than try to give a general analysis of this for the Higgs sector, I want to talk about one particular example, which I think is very interesting, very concrete, very simple, and as we'll see later, not just phenomenologically, but also theoretically motivated. Wow, I'm going fast. You guys go to slow me down. Okay, so this is a two-higgs-doublet model. It's a very specific two-higgs-doublet model with a specific structure. I have one-higgs-doublet that has an ordinary quadratic plus quartic term and has a negative quadratic term. Then I have another Higgs sector, which has just a quadratic term plus this linear term. So I'm just writing down the most important couplings. And this mass squared is positive. So you can see what happens very, very simply in the limit where kappa goes to zero, this linear term goes to zero, I just have two decoupled Higgs-doublets, one of which gets a Vab, sigma, and the other one doesn't. Now I'm going to turn on kappa and treat it as a perturbation. In the low energy theory, if m sigma squared is much bigger than mh squared, in the low energy theory the leading effect of this is going to be just the fact that sigma gets a Vab gives a tadpole for the little h. So the potential for this little h here is rather than being quadratic plus quartic, it's linear plus quadratic. And so it looks just like this. It looks like a shifted harmonic oscillator. And the Higgs Vab is just given by some expression like this. Now I want to identify the H field with the excitations of the H field with the 125 gv Higgs that's been observed at the LHC. So that means that I need not only to get the mass right, I also need to get the couplings of the Higgs right. They've been measured to about 10% to agree with the standard model. And the way to guarantee that is that the light field or the H field has to have the dominant share of the Vab. So what I need is I need the Vab f of the sigma field to be small compared to the total Vab v. I need this mass squared of this heavy field to be larger than mh squared. And that requires the quartic coupling of this sigma to be large. When I say much larger than one here in practice, I'm going to be taking numbers of order one. I'm just talking about the parametrics right now, okay? And you can ask whether that's really consistent with treating Kappa as a perturbation. After all, when Kappa goes to zero, then the Vab of the H field is zero. On the other hand, I'm requiring it to be the dominant source of electro-week symmetry breaking. So actually you can check that these conditions are compatible with each other. So if I'm doing the expansion in Kappa, you can work out that the expansion parameter is actually an expansion in this combination of parameters right here, okay? So in order for this tadpole approximation to be valid, I need this combination of parameters epsilon to be small. On the other hand, I need V to be bigger than f, say a few times bigger than f, in order to get the constraints right. And you can actually see that this is perfectly okay. But it does require, at least parametrically, it requires a large quartic for this sigma, okay? So you may be a bit suspicious about having some low energy theory with a linear term. Of course, the reason I don't just write that down in the standard model is it's not gauge invariant. But remember, here I'm integrating out electro-week breaking fields. So that's the first order answer. In a little more detail, you could say the more correct answer, correct way of looking at this is to say that we have a non-linear realization of electro-week symmetry from this sigma. And so there are some goldstone fields here that are the angular modes in sigma that survive below the sigma mass, right? If sigma was all there was, those would be the longitudinal Ws and Zs. Those things, these pseudo scalars pi coming from sigma will mix with the pseudo scalars coming from H. So actually this tadpole is dressed up by these goldstones. And the pseudo scalars mix, okay? And so that's actually an important part of the phenomenology. So let's take a look at those. So I have, I include the excitations of H, the pseudo scalar excitations of H. Those mix with the pseudo scalar excitations from sigma, okay? Which I call pi here. And what you can see is that the physical pseudo scalar is an admixture of these guys, which is mostly the sigma, okay? Mostly because I'm assuming F is smaller than V. VH is the VEV of H, right? So these are mostly sigma and the even goldstones are mostly H, which they have to be because H has most of the VEV, okay? And so what does the spectrum of this kind of theory look like? So there's the usual standard model spectrum down here. And then I have these pseudo scalars here, which are mostly made out of these sigma guys, okay? And they have a mass given parametrically like this. And then I have the sigma fields, and you can see there's a hierarchy of order epsilon between these guys right here, okay? And above, it's only above the sigma scale that I see the full electroweak symmetry being restored. So again, just the parametrics here. The coupling of the Higgs to vectors is given by something like this. Coupling of Higgs to fermions like this. So notice that when F is small, these approach the standard model values, okay? And if I want something like a 10% accuracy, I need something like F to be about a third of V or something like that, right? One of the things that is very interesting phenomenologically and also shows you that this is nothing like the standard model with additional operators is that notice in all of this, I never put in a quartic term for the Higgs. Of course, it wouldn't hurt to put such a thing in, but if I don't have one, if I don't put one in, then the quartic, and also the cubic coupling, is suppressed by this parameter epsilon. Actually, epsilon squared compared to the standard model value, okay? And just remind you that phenomenologically, suppressing the cubic H coupling actually enhances the HH production, because it's usually, it eliminates a destructive interference that's usually there. So in this kind of a model, these additional Higgs bosons definitely do not decouple. They're a very important part of electro-week symmetry breaking. In fact, electro-week symmetry breaking wouldn't break without them. That's why we call it induced electro-week symmetry breaking. And this also means that if you work out the coupling of these heavy states to things like the light Higgs, WZs, tops and so on, they are unsuppressed as opposed to the normal decoupling limit where they are suppressed typically, especially at least the couplings to the Ws and Zs, okay? So far, I've just talked about this as a possible way of having non-decoupling physics in the Higgs sector. But there's also a theoretical motivation for this kind of model in the context of supersymmetry. So in supersymmetry, the problem that I have is that, at least in the MSSM, that the quartic couplings for the Higgs are given by the gauge couplings squared. And therefore, the mass of the Higgs is of order, the quartic times the VEB squared, which is of order MZ squared. And it's not just a parametric thing like this. There's a tree level bound that says that the lightest Higgs has to be lighter than MZ, as we know. So there are various ways of getting around this. One, in the MSSM itself, we can just look at loop corrections. The problem with that is that we need M stop to be large to make this logarithm large. This is the correction to the quartic. But if we make that large, then this should be M stop squared, I apologize. There's a quadratically sensitive contribution to the Higgs mass squared. So this leads to a tuning of at least the 1% level, even in the low-energy MSSM. So if we don't like that, the typical thing that's been tried is to look at new contributions to the quartic. So we can have new tree-level contributions from D terms, from F terms. We can have some partial Higgs compositeness, fat Higgs models, and so on. These all have in common that they're trying to increase the quartic from this G squared. But based on what I've just said, there's another possibility which is induced electroweak symmetry breaking. Who needs a quartic? So in the MSSM, a quartic is naturally small. That's exactly a natural situation where we could try to do what I've just done here. Okay? Now, do I say this here? I don't know where I... Just a second. Let me just look a look here. I think I should say it here. Yeah. Okay. So let me just say it here. I didn't think I put it on a slide, but you might think that here I'm just postponing the problem one step. Because if you were paying attention before, I said that we needed a large quartic, but now the quartic was for this other field. So we do need a large quartic somewhere else. But the point here is that this other Higgs field doesn't have to have any Yukawa couplings. So the field with the large quartic doesn't have to have any Yukawa couplings. And so it turns out it's easier to give it a large quartic. And I'll give some examples of that. Okay? So the general framework here is that we have the MSSM with its field H up and H down. And H up and H down have the normal Yukawa couplings. Okay? Then in addition, I have some what we call the auxiliary Higgs sector. It includes some Higgs doublets sigma and also some new fields phi, okay, whose role we'll talk about in a second. And there can be couplings like this, phi, sigma, H. Okay? And this auxiliary Higgs sector has to be more strongly coupled than the MSSM Higgs sector. It needs to have bigger quartics in particular, right? And there are two ways that it can do that, at least two ways or two limiting ways it can do that. One is for it to truly be a strongly coupled theory, truly like technicolor, okay? And the other possibility is to write down perturbative models. And I'll talk about both of those. So the first class of models were actually written down by us first, okay, super conformal technicolor, okay? And here the idea is that this auxiliary Higgs sector is really some strongly coupled super conformal sector. And what happens to it, what that means is that it is at a strong fixed point, it is basically strong at all scales, okay? So above the TV scale, far above the TV scale, it is super symmetric and conformal and strongly coupled at all scales. And we definitely have concrete examples of theories like this and we actually analyze concrete examples in this theory. Then we assume that supersymmetry is broken at the TV scale. So back here, supersymmetry breaking feeds into both of these sectors here at the TV scale. And at the TV scale, Susie breaking triggers confinement in electro-week symmetry breaking. This is very plausible. For example, the scalars will get a mass from electro-week symmetry breaking, but the fermions will typically be protected. So you'll end up with some gauge theory with no scalars and fermions that very typically confines and breaks electro-week symmetry breaking and breaks electro-week symmetry. So we can imagine there being some F scale associated with this technicolor of order 80G EV, that turns out to be a good number for all the phenomenological constraints. And then the resonance masses of this sector are then around one TV, right? Because the coupling is so large, it's now non-perturbatively large, the mass of the resonance is very high. And the kinds of couplings that we imagine adding are linear in the elementary Higgs fields, and they are then proportional to some operators in the strongly coupled sector, sort of like side barbed side, right? Where the sort of technicolor is contracted through here. And this VEV induces the tadpole, just as we talked about, okay? Now you may be thinking that I've gone off the wagon because we all know that technicolor died, not once, but at least four times, right? First of all, soon after it was invented, it was realized it had terrible flavor problems. Then in the 1990s precision electro-week, predictions, corrections were too large. The top cork was discovered in 1995, something that was much too large to accommodate in technicolor. And finally, in 2012, the light Higgs was directly discovered. And there was this famous slide by Nima, that many of people have reproduced. But a lot of people haven't really looked carefully at this slide. If you look carefully, you actually see that there may be a chance, okay? That's something. All right, but let me explain to you that actually it's not just that I have four different excuses for all these things. Really, these things are just, they're just completely, this is a completely different sort of beast here, okay? Because first of all, what's really crucial is that flavor, the Yukawa couplings are just done by the ordinary light Higgs, okay? I have the elementary Higgs's, I have the ordinary Yukawa couplings, there are no problems with flavor whatsoever. So forget about those. Precision electro-week, there there's still a worry, there's still some problem. But the fact is that, so first of all, you might think for a millisecond that having F much smaller than V will suppress the electro-week corrections by some power of F over V. Alas, that is not the case. And it's basically because the S and the T parameters are really dimensionless things, okay? So they're not suppressed by that. But the crucial thing is really the S parameter, and it is suppressed because of the fact that in an ordinary technicolor, about half of the contribution from S comes from the heavy vector resonances, and the other half comes from the light technipions. And that comes from the fact that the light technipions are dominantly the longitudinal W and Z. Here they are dominantly not the longitudinal W and Z. So the S parameter is about half of what it is in technicolor. And if you look at a minimal theory of technicolor, not these crazy things with whole technique generations that were needed for flavor, again flavor, they were already sort of marginal with precision electro-week, so this is actually fine. Plus, you can get a positive contribution from the T parameter from the fact that you had different couplings H up and H down. So this can very easily bring you back into the precision electro-week ellipse. Z to BB bar is actually somewhat constraining but actually works. The light Higgs couplings work fine, okay? So I claim that there's really no problem with these theories, and we'll look at some of the details of the phenomenology in just a little bit. However, no matter what I say, most of you won't like non-perturbative physics, okay? So another possibility is to have perturbative models, okay? So here the idea is that these auxiliary Higgs fields are charged under a new gauge group, okay? And the very simplest minimal thing is just some SU2, okay? And because they're charged under a new SU2, they have additional D terms in their quartic. So if this SU2 is somewhat strongly coupled at the weak scale, I mean, you know, stronger than you want hypercharge, basically, or SU2 weak, then they will have additional quartics and that can make this whole mechanism work, okay? So this is conceptually similar to the non-decoupling D terms that have been discussed earlier. And so the basic idea is that we have an SU2S, this extra gauge symmetry. It's broken by the VEV of some five particles at the scale U. Below that scale, we have the electro-week gauge group and then we have these psi particles getting a VEV and these are the induced electro-week symmetry breaking fields. Okay? I'm gonna sort of skip over this slide unless somebody wants to ask a lot of model building questions. There's some nice features of the model building. Actually, unification and precision electro-week work out quite well. And here you can't, you know, we can really just of course calculate precision electro-week and we did and everything is fine. Bottom line, you can ask how well do you do? This is sort of motivated by eliminating the tuning in the MSSM and so how well do you do? And here is the most important parameters in the theory are the gauge coupling of this GS and the VEVF, okay? And in this plane, what you see is that there's a line here and in this line right here, I didn't talk about this limit, but in this limit you actually go back to the standard model. So actually one of the reasons that you sort of know the phenomenology of this model is going to work is it has a limit where it does have a decoupling limit, okay? So in that limit you're guaranteed to get back the standard model. Of course in that limit the Higgs's are also very heavy and you have not solved this tuning problem, okay? But then on the other hand, if you go away from this limit, you eventually get into problems with Higgs couplings. That's the gray region and so what you're left with is this white region which first of all is a pretty big size region and second of all, you can see the tuning contours, you see you're never really tuned in any of the allowed parameter space, right? So I don't know about you, but I never liked these things where people said we scanned 10 million points and we found one that wasn't fine tuned. That looks a little suspicious. Here it's just not tuned, period, end of story. Okay? So let's look at the phenomenology of this, okay? So in general in the phenomenology of this, you have many, you can have any number of additional Higgs bosons. So we wanted to, since we were motivated by supersymmetry, we wanted to look at the minimal thing we could in the context of supersymmetry. That would be a three Higgs doublet model. So in addition to the H up and H down, we have this new field sigma, okay? And then, but then what we assume is that one linear combination of H, U, and H, D does approximately decouple. So we really are left in the end with a two Higgs doublet model, but it's now a type one two Higgs doublet model because only this linear, the light linear combination of H up and H down has Yukawa couplings, okay? You can certainly look at more complicated things, but we think this is a good representation of the phenomenology. So what does the effective theory look like? It has pretty much the potential that we talked about. We actually do include a quartic potential for the Higgs, but the point is that since we don't assume any heavy stops or any other mechanism to beef it up, it's not very important phenomenologically. It's actually only important for the cubic coupling which directly gets a contribution from this, okay? So with this simplified model, we have five parameters here. We can fix the VEVs and the mass, sorry, we can fix the total VV in the mass of the light Higgs. And so we're left with three parameters and we usually look in this plane of F and lambda sigma for some particular value of tan beta. So we looked at all of the current constraints on this model. And here they are plotted in the plane of sigma and mA. We actually don't use F because this shows the different constraints in a better way. And what you can see here is that, for example, the Higgs coupling constraints are here or this vertical line here, I'm sorry, that's a little bit hard to see. But, sorry, yeah, I believe that's right. Yeah, this line right here. But they're actually, the direct searches are actually more constraining. A to ZH in particular is extremely constraining here in this model. But we considered many other things. And one way of saying how non, thank you, how nonstandard this is, is that we can ask, given the experimental constraints, what is the smallest value of the Higgs-Cubic coupling that's still allowed, okay? And what you can see here is that here's, those contours are shown here. Here's 0.4, here's 0.7. So we can have around half of the standard model value in this simplified model. And if you look at what the, I guess it should be the 13 TV LHC, but it doesn't make too much difference. If you look at the 14 TV projections, what we see is that A to ZH and is this purple hatched region and A to TT bar are expected to be the strongest constraints, okay? And here you can see you're now pushing things out so that you need about, you can only have about point, if you don't see anything in the 14 TV LHC with 400 inverse femto barns, you can only have about 0.8 times the standard model value for the cubic coupling, okay? So we'd like to know whether the cubic coupling could perhaps be a discovery mode for new physics, but that will only be done with the high luminosity LHC, right? Now one comment I wanted to make here is if you look at this plot, one thing that if you're following this in detail, which probably nobody is, is that, in fact, you can't really see it very well. I apologize. But if you look at the Higgs couplings, the Higgs coupling constraints have not really improved much compared to the previous plot, okay? So I just want to explain what's going on there. And this just, again, emphasizes the, I think the important complementarity between direct and indirect searches. See the thing is, is that if you look at the present, the present preferred value of the Atlas and CMS bits is already in somewhat intention with the standard model. And in a direction which is bad for our model, right? Our model wants to move things in this way, whereas the standard model lives here, okay? So they're too strong already, too strong if you're a believer in the standard model. So that was incorporated in the initial slide. And we did the only thing we could think of that was sensible for the other slide. We assumed that at the next run, you'll converge on the standard model value. If that's true, you'll get significantly reduced error bars, but because you've removed the tension then, okay? So that explains why the Higgs constraints didn't get stronger. But it doesn't mean these are not important. Tell me to the contrary, obviously, if they were to converge on this value, or something compatible with the present value, it would be extremely constraining, and of course, extremely interesting for everybody, okay? So, but the direct detection bounds are, the direct searches are also incredibly important. In the strongly coupled models, we considered both the, there is the sort of model independent part, which is the A, these extra pseudo scalars, which are parametrically light compared to the strong interaction scale. And there, here I'm showing the present bounds here on those from LHC8, okay? And then this is basically the boundary where your effective field theory breaks down. So you see that as far as the, and here's A to tau tau. So you can see that as far as the present bounds go, it's already very constrained. On the other hand, you can have values over here, which have very, very small values of lambda H over lambda standard model. There's essentially no limit to how small it can be. But if you look at LHC14 with only 20 inverse femto barns, it's gonna completely clobber everything here, okay? So this, basically, if you don't like technicolor, you won't have to wait long, or you'll have to, you'll know, we'll know soon, okay? Whether this kind of model has any chance of being right. And I'm not gonna show it, but we have constraints. There are interesting constraints on the vector resonances, but there's more model dependence and the story is much less clear than here. Lots of, lots of constraints. Okay, so that's it. I hope I've convinced you or made you think that perhaps induced electroweak symmetry baking is an interesting possibility. It's motivated, theoretically, by generating 125 GeV Higgs in supersymmetry without fine tuning. Also, I think just phenomenologically, it's interesting as an example of non-decoupling physics. It's consistent with all bounds. It'll be stringently tested, and in fact, direct searches for new Higgs states really dominate the phenomenology here, okay? Thank you. Okay, so time for a few questions. So as someone who does like strong dynamics, you're talking about some heavy sector that's giving you a small value of F? Well, it's not that small and it's not that heavy. So it's just technicolor scaled down by say a factor of three. And do I have states at the scale four pi F? Yeah. So I do have those states. So it's the standards. It's just normal technicolor scaled down by a factor of three. So that does two things. It makes the states lighter. So you might think that I should be dead because I have strongly coupled states, but it also makes them couple less to electroweak because there's a smaller share of the VEV. So for example, the dominant way to produce, you know, Techni rows or vector resonances in the strong sector is just by mixing with the W and Z. But that mixing is now suppressed actually. So, yeah, so anyway, we really did the phenomenology. And so it is not, you know, there's a lot of, we don't know all the parameters of the technicolor row, but you can see that there are, you know, strong constraints, but not ruled out. Yeah. It's just technicolor scaled down by a factor of three. That's all it is. Four, maybe. Other questions? Your strongly coupled version reminds me something. Warped space, I may know with the, what's the, is it the 4D version or something you? The actual model we wrote down was a version of Suzy QCD. The strong sector is some Suzy QCD model in the middle of the conformal window. Okay. So, but yes, you could definitely make a 5D version of this. You would just have a supersymmetric bulk and I don't see any problem with doing that. Yeah, something I was thinking, I was doing with the Chaco and so on and so forth. Yeah, that's right. I'm sure you could make a model like that. We didn't actually do it, but I think you could definitely do it. And because in the basis of mass science states, then it's like Quoric is coming from your big Quoric coupling times mixing on the 2D force or something, right? There is no big Quoric coupling. No, that's a misconception. So, the potential really is in this limit where this parameter I called epsilon being small, the potential is really dominated by a quadratic plus a linear term. The linear term is of order epsilon. The Quoric is of order epsilon to the fourth. So, the Quoric is completely negligible. It really is a different kind of limit. The other limit is also viable. You might think it sounds like cheating, but it's actually not. You can have an induced Quoric, okay? So, you can be in the different parameters based on the values of the parameters of the original theory. I think you're right, yes. Yeah, but the induced limit, it really is different. We have a shifted quadratic potential for our Higgs. Any other question? All right, so let's thank the speaker and complete the session.