 Oh, thank you very much. Really a pleasure to speak here at PASCOS. And a particular pleasure to be back at the ICTP. My very first conference when I was a graduate student was down at the Adriatico Guest House. And there I was talking about physics way beyond the standard model. And so I'm as surprised as anyone that I'm here talking to a lot of my friends that I know from the Beyond the Standard Model world, but talking about QCD and pure standard model physics. And so hopefully you'll get a little bit of a sense about how a Beyond the Standard Model Physics approaches jets and perturbative QCD. And I'll try to explain through this talk what I mean by this unsafe but calculable. So the topic of my talk is jets and perturbative QCD. And we've known about jets and perturbative QCD for almost four decades. This is, to my knowledge, the first LEGO plot ever made at a hadron collider. This was back in UA2 time. So we have protons and antiprotons colliding together. And we have this now characteristic picture of what jets are. In this collision, we have sprays of particles coming out of the collision point. And those sprays of particles are clustered into jet regions. So if I slice the detector open, lay things out flat. We have this LEGO plot type display where the height of the bar corresponds to how much energy was deposited. And just by eye, you can see the presence of jets, in this case a diejet event, two clusters of hadrons. And we interpret those clusters of hadrons as coming from the shouring and fragmentation of, let's say, final state gluons. So in this hadronic process, proton, antiproton going to many hadrons, we interpret this as being at short distances, let's say, gluons colliding, and then giving me gluons in the final state. And it's the subsequent shouring and fragmentation that gives me these jet patterns. So we've known about jets and perturbative QCD for, again, four decades. So what's new? Why am I so excited about jets and what it can teach us about physics of the standard model? And there's been a bit of a renaissance in QCD starting around 2008. And I'll explain why 2008 in a second. It's just coincidental that that happens to be when I wrote my first paper on jets and QCD. But that's actually not why 2008 is special. So there's been two different types of advances. One has been in advance on the pure experimental side, of course, with the LHC, which compared to previous machines, of course, we all know it has higher energy and luminosity. But crucial for the story I'm going to tell today, it has way finer segmentation compared to previous machines. So this cartoon picture that we have of protons colliding, making quarks and gluons at short distances, those showering and fragmenting, giving me hadrons, pions and caons in the final state, and then those pions and caons being detected by calorimetry or by tracking. This last stage from hadrons to detection is more or less one to one, especially with techniques like CMS's particle flow algorithm. You can basically think about really consisting of hadronic constituents and not having to worry too much about detectors getting in the way of your understanding. So that's on the experimental side, this fine segmentation. On the theoretical side, there's been a number of progress, the most important of which has been the development of new jet algorithms. And 2008 is a special year, because that's when the anti-KT jet algorithm came out. And anyone who's looked at LHC data knows that almost every jet at the LHC is an anti-KT jet. And the first time in four decades that you've got theorists and experimentalists to agree on what an appropriate definition is, and that came through this anti-KT algorithm. Around the same time scale, there's been this explosion in multi-loop, multi-leg calculations, as well as enhanced understanding of logarithmic resumption. I'm not going to have time to talk about that today. Here I'm going to be focusing on jet substructure, which is a field that had some origins to work that Mike Seymour did in the 1990s, but really came to the fore with this paper by Butterworth, Davison, Ruben, and Salam, saying how by looking inside of the substructure of jets, you can actually enhance the search for physics in and beyond the standard model. So for those of you who haven't heard about jet substructure, you're going to hear a lot more about it coming up. Why? Because this jet substructure field, which may have been a little bit in the background for this time period, is coming really into the fore with this recent Atlas diboson excess, which has shown how jet substructure really can help us search for new physics. So this search starts as just a regular old die jet resonance search, where you're colliding, making some x prime that decays to two jets. And if you look at the die jet spectrum, you see absolutely nothing. Just a nice, smooth following the expectation from QCD, no die jet resonance at all. But if you look at those jets and look into the substructure of those jets and preferentially select jets that don't look like ordinary quark and gluon jets, but rather look like a highly boosted W or Z boson decaying to nearly collimated quarks that then shower and fragment to make subjets. If I look with fat jets with two prong substructure, then you start to see something. In particular, there's a variety of discriminant variables you can use. Here, this is a y splitter variable, which if you cut on it and isolate WZ-like jets above QCD-like jets, then this smooth distribution turns into something that has a very tantalizing 2 to 3 sigma-ish peak around 2 TeV. Now, we don't know whether this is actually physics beyond the standard model. CMS has a comparable search that we're looking forward to an update from. But this shows you that by using the substructure of jets, you can basically learn something about the parentage of those jets and help enhance new physics signals over overwhelming standard model backgrounds. Now, I could spend the rest of this talk talking about all the awesome applications for beyond the standard model physics of jet substructure. But here, I'm really going to talk about the standard model. And so today, I'm going to talk about jet substructure as a way to probe something that's basically bedrock quantum field theory, probe the universal singularity structure of gauge theories in particular of QCD. And I find myself, again, as surprised as anyone, that someone with a beyond the standard model mind finds this kind of structure of gauge theories to be so fascinating. The ingredients that I'm going to be using are ones that we've developed over the past three or so years. I work with Andrew Larkowski, Simone Marzani, Gregory Swaya. And these terminology, I expect no one, unless you happen to be in the jet physics world, have ever heard these terms before. Sudikoff safety, I'll explain what this is. This is a way of talking about how observables can be calculable using Sudikoff form factors. Softrop, which was a technique actually intended to mitigate pileup, multiple proton-proton collisions per bunch crossing. And then standard candles, which we're very familiar in other contexts, but in a jet physics context, we don't usually think of jets as anything standard and candidly about them. And in this talk, I'm going to try to walk you through these different ingredients and tell you how we can actually learn something about the structure of gauge theories. OK, so in the remainder of my talk, I'm going to first try to explain the unsafe part of the title and review for you what is safe observables so I can contrast safe versus unsafe observables and then show that by going beyond the standard paradigm of safe observables to unsafe ones, you haven't just thrown the baby out with a bathwater that actually you still have a degree of calculableness or calculable control. And we're going to use that degree of calculable control to try to make a measurement that if you had told me 10 years ago, could you make this measurement? I'd say no possible way could you make that measurement. But it seems possible, and that measurement gives you a standard candle for jets. And then depending on whether my session chair lets me go over, I'll try to summarize by telling you what new tools we now have for perturbative QCD, tools that are more generic than the specific case study that I'm going to be showing today. OK, so let me now move to a review of what safe observables are. This is, again, textbook. But for those of you who don't think about jets day in and day out, this is hopefully going to help you get your mind in the right place. OK, so what do we know about the structure of gauge theories? Well, we know that gauge theories have infrared and collinear singularities. In particular, let's just start off with some jet, some quark or gluon that has a shower of gluons accompanying it. What do we know about the singularity structure of those gauge theories? Well, we know that there is a singularity to have infinitesimally soft emissions. This is actually exactly the same as the soft theorems that Freddie Kachaza was talking about yesterday, that soft theorem says that there is a singularity to have infinitesimally small emissions accompanying whatever parton configuration you have. So those are the infrared singularities of QCD. There's also a collinear singularity where a parton can split into two partons that are exactly overlapping in angle. And there's a collinear singularity as well. Now, these singularities are there in the gauge theory. But of course, we don't want to measure singularities. And infrared and collinear safe observables are ones which are insensitive to arbitrarily infrared or collinear emissions, such that these singularities disappear in the final calculation. In particular, there are infrared singularities in virtual diagrams, which are canceled against these real emission type singularities. And if you've done an appropriate infrared and collinear safe measurement, then, at least at the partonic level, you're gonna get a cancellation of these divergences order by order in an alphas expansion, such that your calculation makes sense at leading order, next to leading or next, the next to leading order, and so on and so forth, if you're measuring a safe observable. So the easiest way to explain what safety is is just to give you some examples of what safe observables are. So here are some examples coming from jet substructure. So let's imagine you have an algorithm like anti-KT, which is able to find clusters of energy deposits in your event in an infrared and collinear safe way. So that was one of the achievements of anti-KT, was to define jet regions in an infrared and collinear safe way. But let's say we've done that already. Then there's various questions you can ask about the jet. You could ask about the jet's total transverse momenta, summing over the individual PTs of the constituents. And that's a safe thing to do. Why? I add an infinitesimally soft particle that doesn't change the sum. Or if I take a particle and split it into two, that doesn't change that sum. By contrast, there's an observable that CMS uses, actually as part of their Higgs analysis, that's called PTD, which sums over the squares of the transverse momenta. That's still infrared safe because if I add an infinitesimally soft particle, I don't change that sum. But because of the sum of the squares is not the same as the square of the sums. That means that if I have a collinear emission, I get a change in my answer. So that's a collinear unsafe observable. Multiplicity, that's something that's definitely infrared and collinear unsafe, because if I add a particle that one increments, or if I split a particle in two, that increments. So that's something that we don't think that we can calculate in perturbation theory. The mass of a jet, that's infrared and collinear safe, so we can talk about the mass of a jet. And insubjettingness, which is a variable that I introduced with Ken van Tilburg, who's somewhere in the audience here. Back when he was thinking about jets, this is an infrared and collinear safe observable. And part of our excitement about this observable was that this is a way of testing for n-prong substructure within a jet in a way that we think is calculable in perturbation theory. And in fact, for the CMS version of that diboson excess, they actually use n-subjettingness as a discriminant variable to try to find these boosted W and Z bosons. Okay, so the world is divided into safe observables and unsafe observables. And the lore, at least, is that if you are safe, then you are calculable in perturbative QCD. And nothing that I'm gonna say in this talk challenges that lore, that's really true. If you're safe, you're calculable in perturbative QCD, you can just march order by order in an alpha-s expansion. And the lore, at least, is that you have controllable hadronization effects that the mapping from partons, quarks and gluons, to hadrons, high-ons and caons, that this mapping is under control and effectively those hadronization effects are suppressed by lambda QCD, such that if you're at high enough energies, those corrections are small. On the other side, if you're unsafe, then you're totally incalculable and nothing you can do. Unsafe, no calculability in perturbative QCD, no control over hadronization effects, go home, don't measure things that are unsafe. That's at least the standard lore. And today, I'm gonna tell you about challenging that standard lore, that basically the new lore is that, well, it's complicated. I have examples of safe observables where you can calculate order by order in QCD and then once you put hadronization effects in, you fall flat on your face and you get no control. I'm gonna be focusing on this column, observables which are formally unsafe, they do not have a valid expansion order by order in alpha-s, yet, the fact that they don't have a perturbative expansion order by order in alpha-s, still you can get calculability control, which sounds contradictory, and I'll try to explain that coming up. And moreover, something that I'm not gonna emphasize too much, there's still a degree of hadronization control in these type of calculations. So one should think, instead of being the world divided in two, one should think, maybe the way that Orwell would say it, that really all observables are calculable, that some observables are more calculable than others. That is there's degrees of calculability, the gold standard is still maintained by infrared and collinear safe observables. Those are the ones that have the largest degree of calculable control. And I'm gonna now march you towards the boundary where you start to lose a little bit of calculable control, but remarkably by losing a little bit of control, you're actually able to expose some interesting singularity structures in gauge theories. Okay, so let me now tell you about a standard candle for jets by going to this unsafe regime, what can we now learn about QCD that we couldn't learn before? So let's go to even more textbook QCD. And this is something that you learn on chapter one of a QCD textbook, and so I'll just remind you of here about it now. So let's say I have a scattering amplitude for two to N process, this is at the part on level quarks and gluons. And let's say two of those partons get really close in angle. There's a factorization in this collinear limit that says that if I wanna understand the process two to N, I can factorize that into a two to the N minus one scattering process and taking that one part on and splitting it in two. This is known as an ultra-eliparisi splitting function and this ultra-eliparisi splitting function is governed by two variables, one that tells you what the opening angle is between those two partons and one that tells you about the energy sharing Z between one part on and another. And this splitting function is all over QCD. Parton shower Monte Carlo generators are based on iteratively doing this one to two splitting over and over and over again. That's how you generate arbitrary numbers of emissions in programs like Pithya or Herwig. Parton distribution function evolution is based on this. This is the standard D-glap evolution comes from taking these ultra-eliparisi splitting functions really, really seriously. Almost every single next-to-leading order calculation uses this in some form as a technical collage to do subtraction so that you can actually put that on a computer. So we know that this is true. This is textbook QCD. But can you actually measure this splitting function experimentally? Is there a measurement that you could do that would not just be correlated with that splitting function but actually give you the value of the splitting function as an answer? And the standard answer is no way you can't measure that why? Because this splitting function encodes the singularity structures and you can't measure singularities. In particular, this splitting function has a one over theta singularity saying that there's a singularity for things to be collinearly emitted. That's this collinear singularity of QCD. And the actual splitting function itself, this P of Z that encodes a soft singularity that you can have now a probability of having a soft emission goes like one over Z. And so again, arbitrarily soft emissions you get a singularity, nothing you can do. So normally we say that this is truth but you can't actually measure the truth. But let's go on undeterred and use now techniques from JET substructure to try to gain access to the splitting function to this P of Z. So can we measure the universal singularity structure of QCD? Can we measure this one to two splitting in data? So let's say I have a JET clustered with some algorithm, has various constituents whose energy here is just indicated by the size of these circles and you say I wanna measure one to two, I can't do that because I have many N particles in my JET so how do I get one to two out of that? But actually there's this history of developing tree-like structures clustering algorithms that can take those N particles and bundle them up and you can use an angular ordered tree for the experts. This is a Cambridge-Ockin clustering algorithm where you can take these particles in the final state cluster them sequentially to form a tree-like structure and at the top of the tree you have a one to two splitting. Not only do you have a one to two splitting but that one to two splitting has exactly the kinematics that you would need for the splitting function. They're separated by an angle theta with an energy sharing Z versus one minus Z. Fantastic, this thing looks like the splitting function. At least it has the kinematics of the splitting function and you can now say can I measure this Z for example if I measure this Z distribution shouldn't I be able to pull out this famous alter-reli-pullery Z splitting function? And the answer is no you can't, why because it's unsafe. If I add an infinitesimally soft particle at the edge of my jet that would add an extra branch to my tree that would change my distribution and therefore it's not infrared safe and you can go through and show that it's not cooling your safe either and so you say you try to apply perturbation theory and you just fall on your face, you're done. Okay, but we have this toolkit of jet substructure and one of the tool kits, part of the toolkit is saying if you have soft crap well soft crap looks kind of like pile up contaminating your jet let's just throw away soft crap and one version of this throwing away soft crap algorithm is known as the soft drop procedure where if you take these soft particles at the periphery of the jet just toss them away, effectively you take this tree and you lop off branches of this tree if the energy fraction carried by one of these branches is below some energy threshold just throw away soft crap and by throwing at that soft crap you've now regulated the infrared singularity of QCD and now these groomed ZG so this procedure of taking a jet and throwing away radiation is known as grooming this groomed Z is now something that's infrared safe just by construction you threw away soft radiation and so you might say oh great I can use this groomed Z to try to extract the splitting function ah but shoot it's collinear unsafe and the easiest way to see that is collinear unsafe is you take one particle and you ask well what do I do with one particle if I do or do not split it so if I take one particle and I don't split it well I don't even know what Z means what does it mean to have the energy sharing between two partons if I just have one parton versus if I have a collinear splitting which is singular to do that and I end up getting two jets then I can define the Z so I have undefined versus defined well that means my calculation doesn't make any sense under a collinear splitting so this is really unsafe and again you feel like you're stuck and this issue of having unsplit versus split basically give you an ambiguous measurement this is what also impedes us from extracting this ZG so what are we going to do if we really want the splitting function we want to extract this from data what are we going to do can we calculate this distribution from first principles after all this procedure that I just told you is something that you can absolutely just do on data or do on Monte Carlo and we've done it and you get interesting distributions but how would you actually be able to calculate the perturbative QCD and actually this exact same issue arose in the very very early days of QCD and if you ask me in a backup slide I can tell you what happened in 1978 where they actually faced the same issue and they were lucky they had symmetries back then that they could use because they were using E plus E minus collisions here in a hadron context you don't have those same symmetries so you don't know what to do I can tell you about that offline if you're interested but now I'm going to tell you these new techniques that we've developed in order to do this type of calculation essentially saying despite being unsafe you are still calculable and calculable and perturbative QCD okay so there's two techniques and one of them is easier to understand than the other so let me start with the easier one to understand this is using Sudikoff form factors in order to basically regulate singularities so we have this observable this energy sharing observable which is infrared safe but collinear unsafe but it's only collinear unsafe because I have two particles exactly lining up on top of each other I don't know how to define this versus just one particle by itself I don't know how to define this energy sharing okay well then let's make a supplemental measurement that's gonna force these partons to be far apart in particular if I measure the mass of a jet that forces the partons to be well separated and once the mass is forced to be positive then this is something that is now infrared and collinear safe so if I were to measure the mass and measure ZG in that case I'd have something that's perfectly fine but the problem is that QCD has a singularity at mass equals zero so that's the jets kind of in perturbative QCD which is all lie singularly at M equals zero but if you actually look at data you never encounter a jet that actually has mass zero a jet is initiated by a quark or a gluon but even if you have a massless gluon initiator the jet itself has typically quite large invariant mass and in fact that's driven by something that's known as pseudoconform factors which I'll explain in a moment but basically the mass is never zero and because the jet mass is never zero this ZG never gets to visit the singular region of phase space and so the ZG is something that we'll call pseudoconf safe so let me show you this in a plot so again if I were to measure the mass then I would be able to measure the Z but oh shoot the jet mass distribution at any fixed order in alpha S has a singularity at M equals zero so I visit that M equals zero all the time this is shown here this is a generic distribution but for jet mass in particular it shoots up near zero but you have never encountered an actual plot in a particle physics experiment that actually has this type of singular structure why is that? That's because if I'm measuring let's say the mass I had this growth at a fixed order in alpha S but I end up getting large logarithms of this observable in this case logarithms of the jet mass that need to be resummed and of course nature performs this resummation and if I go not at fixed order in alpha S marching order by order in alpha S but just account for the fact that I can have multiple emissions and work at all alpha S orders and resum logs then actually this singular structure turns over and you get something that's known as a Sudikoff peak or this structure here is known as a Sudikoff form factor it's a form factor that regulates the divergence at M equals zero and this demonstrates that there's a huge difference between having order by order in alpha S where there's singularities at a given phase space point order by order versus working to all orders all perturbative orders where those phase space singularities are suppressed and because these phase space singularities are suppressed you end up getting a Sudikoff suppression of the singularity and you can actually use this as a mechanism to actually do this ZG calculation. So that's one way of doing the calculation I'm not gonna walk you through that calculation in detail I'll show you the answer in a second just for the experts let me just tell you another way of doing this calculation another way of doing this calculation is using fragmentation functions this ZG distribution is something that's infrared safe but collinear unsafe but collinear unsafety is something that Hadron Collider Physicist encounter all the time anytime you interact with a part on distribution function strictly speaking you're interacting with a collinear unsafe observable and what these part on distribution functions do is not only give you non-beturbative information about how a quark or a gluon is extracted out of a proton but also absorbs collinear singularities into these universal part on distribution function functions. Part on distribution functions in the initial state are called fragmentation functions in the final state and they serve exactly the same purpose and so here I have a situation where I'm trying to calculate this cross section for this ZG observable I can't do it on a single part on not well-defined, fine, not well-defined slap of fragmentation function on it which is represented by this blue blob then do a higher order calculation involving loops and real emissions this loop calculation has a one over epsilon divergence in dim reg we have a singularity d sigma over sigma divergence that would also give you one over epsilon and in general these things don't cancel I have a singularity oh crap I have a singularity but we know how to deal with that in the context of fragmentation functions you have to renormalize when you renormalize and absorb those singularities you get sensitivity to the scale mu the renormalization scale and then the really cool thing happens so this is a non-perturbative object like PDFs are something that you have to extract from data similarly this fragmentation function is something that you'd have to extract from data but despite the fact that you have to extract from data this observable, this function has a renormalization group evolution that you can run and let's run to really high scales and what happens this particular fragmentation function hits an ultraviolet fixed point we usually think of Lagrangians as hitting ultraviolet fixed points but we don't usually think of these type of non-perturbative functions hitting an ultraviolet fixed point but in this case you really get that behavior and this is saying that if you go to high enough, high enough collision energy that you end up asymptoting to a universal form this fixed point behavior and the fixed point behavior of this observable happens to be precisely equal to the ultra-reli-prezy splitting function so using either one of these techniques we end up with a standard candle for jets what did I do, I took a jet I threw away soft radiation motivated by pilot mitigation and remarkably this jet substructure technique gave me a function which is remarkable for what's not in it this ZG gives me the splitting function okay there's a bar over it because it's symmetrized and there's some normalization factor so a normalized, symmetrized version of the splitting function but the splitting function nevertheless this black curve here has this one over Z singularity structure that is baked into QCD you go to high enough energies and simulations and you see you asymptote to that behavior you basically RG flow so that you asymptote to this universal behavior and what's not in this function is totally fascinating what's not in this function is there's no alpha S we're doing a calculation in QCD and yet the coupling constant has disappeared it's independent of the jet PT and the jet radius at lowest order it's even the same for quarks and gluons which is remarkable of course that's just this leading order term there's plus dot dot dots which give you calculable deviations which you can even see the deviations here between the black curves and these other curves but those deviations flow away when I RG evolve deep into the UV and so starting off with something that's unsafe pushing hard and trying to figure out how to calculate we actually get something that's really surprising not only is it calculable but apparently it's universal and that universality is mapped on to the universal singularity structure of QCD namely the ultraliprezy splitting function so just to tell you just a little bit about how deep this rabbit hole goes you can take this procedure and deform it a little bit by actually not just making a cut on energy but making a cut on energy and angle so I can introduce this angular exponent beta that lets me adjust whether I throw away radiation preferentially at the periphery or the center of my jet and I'm not don't expect you to understand in detail what this is but let me just show you this kind of phase diagram of observables that we've been playing with and having a lot of fun so I've been showing you stuff specifically at this beta equals zero point where you get this remarkable UV fixed point of renormalization group evolution this universal form if I make this beta parameter negative then I get something that puts me back in the safe regime and I get exactly what I expect which is alphas, great color factors, great splitting functions, great logarithms, great all the things I expect for a standard calculation and then if I make this beta positive I get into a totally bizarre regime where I'm doing a perturbative QCD calculation but when I do resummation I end up getting square roots of alphas square root of the coupling constant appearing this is something that you don't usually expect coming from a perturbative calculation but nevertheless comes from this type of observable so my chair is telling me to stop so let me skip this summary I can tell you exactly how we do these calculations or people are interested but let me just summarize here that infrared and collinear safety means that you're defined order by order in an alphas expansion and this has been the basis of 40 years of jet physics relevant to take for jet sub structure but what I've told you about is that if you think even just perturbatively not even non-perturbatively but perturbatively all orders in alphas yields new insights into the structure of quantum field theory and remarkably has given us a new way to measure the universal singularity structure of QCD so with that I look forward to taking your questions so maybe very very naively couldn't I approach the whole thing from somehow a different perspective and start by having jets which are so fine that what you call substructure would be independent jets to start with ah good so why is that not a good approach which would kind but could have taken many years ago maybe right so you're asking the question that always comes up in the context of jet substructure which is that one way of building jets is you build big fat objects that sum over all sorts of radiation and if I think that my jets have substructure why am I not just going to a really small radius and looking at jets that are just at a smaller radius and indeed there's an interesting debate within the jet substructure community about which way is a better way of thinking about jets do I think about jets that are big objects with substructure or do I just talk about little jets so from a practical point of view or a QCD point of view the reason why it's challenging to go to small jet radii is that as you go to smaller and smaller jet radii you end up getting jet radii whose size is now starting to become comparable to lambda QCD or lambda QCD over the energy and so now you're starting to become more and more sensitive to non-perturbative physics and even if you stay away from the non-perturbative regime there's large logarithms of that jet radius that you start to get and so when you're talking about degrees of calculability in QCD you're actually better off thinking about a fat jet with substructure rather than trying to build micro jets and this shows up in experimental analyses which is that if you actually just compare apples to apples a jet substructure, fat jet with substructure versus tiny jets you actually find better performance in looking for physics beyond the standard model if you go to the fat jet approach but you can actually think about exactly what you're doing, what you're saying and there's people who are pursuing actively that strategy. How does extracting these universal structures depend on the clustering algorithms that you use to start off with to cluster all these? Ah, good, good, good. So, you know, one way of answering your question is to ask why did it take us till now to figure this out? This universal singularity structure we only talked about this past February. Why given the whole four decades of people thinking about perturbed QCD why did people never encounter this? And the answer is interesting. So one it really does depend on the way you cluster and if you cluster in different ways then you get different analytic forms and this is shown a little bit in this phase space which is that this is one dimension of the phase space but there's another one saying as I change my clustering algorithm how does my analytic structure change? And this particular form really requires you to do this angular ordered clustering structure. But the other answer to your question which is more historical is why did people never see this before and the total irony of this is that people should have seen this before. This structure is buried inside of that 2008 paper by Butterworth Davison Rubin and Salam. In there they talk about an observable which is extremely close to the Z with an angular order structure which is almost exactly the same and they just didn't think about it in this context. They were thinking about it in the context to boosted Higgs physics and they just never bothered or never saw that if they happen to take their method to an absolute extreme limit that they would have seen this structure. So in some sense this structure was just waiting to be discovered. The methods had already been there for quite a while and then it just effectively required some to think not just about the method but thinking about how you would do that calculation perturbatively and really banging your head against the wall and saying, how do I calculate? How do I calculate? How do I calculate? And then the breakthrough realizing that oh, once I know how to calculate I know how to arrange my clustering algorithm in order to expose this cool feature. But without the calculation you wouldn't know which type of clustering would give you this nice behavior. Would you like to comment on how to distinguish gluonjit and quarkjit? Oh yeah, yeah, yeah. No, this is an awesome area. So I wrote a really fun paper with Valtor-Volivine and Andrew Larkowski about trying to use the concepts of information theory motivated by people writing about holographic entanglement entropy and using concepts from information theory to try to better understand what we even mean by a quarkjit versus a gluonjit. The easiest way of thinking about quarks and gluons is that in an extreme limit, the Iconal limit where you have a hard quark or gluon that just radiates off, then it actually is well-defined what you mean by a quark or a gluon. It's labeled by essentially the color structure of the associated Wilson line. But of course in real life we don't get to work in that extreme Iconal Wilson line picture. We're always having to deal with the practicalities of jets in a real experimental environment. And there there's an active debate about what exactly you mean by a quark or a gluon. I think we believe that a quark is something that has barrier number a third and color factor a chasm or four thirds and a gluon is no barrier number and a chasm or three. So we agree on that. But then as you start marching order by order in perturbation theory things get murky. And that's what we're trying to figure out. But whether or not we theorists figure out what our quark and gluons really mean experimentally those techniques on separating quarks and gluons are being actively developed. And as part of for example CMS's Higgs analysis they introduced that PTD variable that I mentioned precisely to try to separate quarks from gluons. And they said who cares about the theory issues about how you really define it. Let's try to enhance signal over backgrounds despite that ambiguity. And indeed they were successful in doing that. And so we theorists need to catch up and now put rigorous definitions to what you mean by a quark jet versus a gluon jet. Okay so let's thank the speaker again. Thank you.