 and phase-space saturates. And then you have this slow decline in the cross-section going roughly like 1 over s, or logarithmic corrections, depending on some combination of 1 over the Higgs mass or 1 over s. At high energy, it goes down like 1 over s, but there's logarithmic corrections as well. Anyway, so designing these machines to be near the maximum, but you want to take it as low as possible because it gets very expensive to run it at higher energy. So optimum, choose to be around 240. We're not actually building any of these things yet, so they could build it anywhere here, depending on other reasons. Yeah. Yeah, I was wondering in this plot, what about 2-Higgs production? Yeah, so it depends on what you want to do. So if you want 2-Higgs, you would go to higher energy, but you would need at least 250. But then you guess you want some phase-space for it, so you go higher than that. So 2-Higgs production is useful for probing triple Higgs couplings. But then again, if you want to probe triple Higgs couplings, you can't just do it plus or minus 2-Higgs, so 2-Higgs. So you have to do Z-Higgs or something like that. So you actually want it to be higher above 300. So it's hard to directly probe triple Higgs couplings at these energies. But you could say indirectly. I'll just leave that there. No, it's from the phase-space, so think about it. If we insist that they be on shell, the Z and the Higgs, that means the cross-section has to go to 0 at 2.15. And it should be a smooth function. So if it goes to 0 at 2.15 as a smooth function, it's going to look something like that. Just draw some curve that goes to 0 at 2.15 and draw a line. That's what's going on here. And it grows rather steeply. But really what's going on is the phase-space available for the decay. So if it's exactly on shell, the Higgs and Z are at rest. And then everything goes back to back. But once you get above that, then they start having some energy. And there's a lot more possibilities when it has some energy than if it's just at rest. And so that extra phase-space from where you can produce the Higgs and Z, instead of just one point where they're at rest, you start to get a bigger area of momentum that you can do. And that's what's going on. That's what we call the phase-space effect. And this is typical. I mean, any on-shell production will look like this. But you have a turn on. And then it basically saturates. And you have a slow decay with energy. But this is an important one. OK, so what I want to do today is talk about the different particles that we have in the standard model, which I've drawn here in this nice circle that I like. So Yuval is going to tell you all about the standard model itself in Lagrangian and gauge invariance and spontaneous symmetry breaking and fun things like that. I'm not going to write down Lagrangians. I'm just going to tell you about what these particles look like in the real world. So how do you see them? What are they? How do they interact? That there's the sort of mathematics if I write it down, and then the physics of what's actually relevant and how they decay and how they show up in colliders. So this is going to be sort of complementary to what Yuval is doing. I would just go to go around sort of from the inside out, although I'll save Higgs to the end. And so the particle is the standard model. I like this picture because the Higgs is sort of the centerpiece. We know it's related to the mass generation mechanism for fundamental particles, but also it sort of connects to everything in an important way. So we have the Higgs here. The other fundamental particles are the gluon, the photon, the W and Z bosons. And then around the edge, we have the various fermions. The up charm and top are the up type quarks, which all have charged plus 2 thirds. And then the down type quarks are down strange and bottom, which have electric charge or minus 1 third. We have the neutrinos and the leptons. So we kind of separated the charge on the outside. I guess W has charge plus 1, this has charge 0, which is why we put WZ, photonic glue, and also have no electric charge. So we'll start with the W boson. So the W boson couples to all of the fermions. So what can the W decay to? The first thing we're going to talk about. Well, OK, let's do the mass first. What's the mass of the W boson? 80GV. Maybe we'll put, maybe we should do the masses first. So 80, what's the mass of the Z? 92, we'll just say 90. Mass of the gluon, mass of the photon, where should we start? Mass of the neutrinos, 0 from the collider point of view at 0. Andrea and Yuval might have different opinions. But from collider physics, we treat them as 0, not that you're sensitive to their mass anyway. Mass of the bottom, 4, roughly 4, strange. They're all in GV. Do you want to know the mass of the strange quark? 100 MeV, good. Down quark, 4.7, what? We'll say 4 MeV, close enough. So this is sort of scheme-dependent. Up, 2.2, again, that's very precise for something that's not that precisely defined. But let's just say, we're going to say 2 MeV. The collider point of view, we'll treat that as 0. Charm, 95, 95 what? 1GV, really like 1.2GV. Top, 170, what? 3, OK, we'll come back to that. Tau, roughly 1.7, Muon, 100 MeV. I don't expect you all to know this. Electron, you should all know, because you see it on a license plate, apparently. 511KV. OK, so we're going to start talking about these particles and understanding them. A lot of these masses aren't so well-defined that you have to be a little bit more careful about what we mean by the mass, and we'll get to that. W is not ambiguous. 80GV, again, I'm sorry about my voice, I'm struggling with it. OK, so what can the W decay to? So give me an example. Leptone, neutrino, which lepton? Electron, neutrino, it can decay to what else? Muon, neutrino, it can decay to Tau, neutrino. What else can they decay to? What? Up and down, good. Charm and strange. Bottom and top. Anything else? What? Up and strange. All right, let's try to draw this more systematically. So you have up, down bar, up, strange bar, up, bottom bar, charm, down bar, arm, strange bar, arm, bottom bar, up, S bar, and top, bottom bar. So the couplings of W to these various things are determined by the various CK elements. So this would be VUD, which is approximately one. This is proportional to VUS, which is 0.2. This is VUB, which is 0.04. Am I, can people read this? Am I running too small? All right, I'll try to take care that they can read it. VCD, 0.2, VCS is approximately one, VCB is approximately 0.004, VTB approximately one, VTS, 0.04, and VTD is 0.008. So what you see from this structure is the diagonal elements, which go to the quarks of the same generation are approximately one. So through a leading approximation, the W decay is diagonally. But there's some non-negligent opponent where the W can decay in a mixed generation, where it tends to be a second generation or a first generation. And it's very hard for it to decay to a third generation or a first generation. So we say these are sort of Khabibow suppressed, and these are Khabibow squared. But the off-diagonal elements, farther from the diagonal. So there's this weird structure to this AKM matrix that we don't really understand. Why should it be close to the diagonal? It's just an accident of nature. And maybe someone will figure that out one day. But for now, these are the couplings of the W bosons that we observed experimentally. OK, so now let's ask, what is the... So first of all, which one of these can the W not decay to? So these are all its couplings, so tops, right? The top is 175 and W is 80. So none of these can decay to. OK, so that being said, what is the branching ratio of the W? So we're going to treat everything else as massless. What is the branching ratio of W, say, to electron and neutrino? So you can look it up, but let's calculate it. So the nice thing about the W interactions, they're determined by SU2. And they're the same for all these couplings. And here, we tell you the strength of the interactions. And we're taking these to be approximately 1. And we can take these to be approximately 0. It doesn't really matter, because the sum over all of them is determined by unitarity to be the same as the sum to the diagonal components. So could anyone give me an estimate for what this is? How much of the time? How many W's do you need to get one electron? What? Say it again. 20%. 20%. So where'd you get 20%? What did you do? 5 equals channels. 1, 2, 3, 4, 5. But we're setting this as approximately 0. This is approximately 0. That's not quite right, but that's close. What is he forgetting? Color. Great. So color means, so you've all told you that the quarks have color as a representation of SU3. From the collider physics point of view, I think it's easier to think of color as red, green, and blue. So that color is really a charge, like electric charge. So instead of electric charge being a number, we have discrete indices. But there's three colors of quarks. And so the easiest way to do the counting is you say, this can happen, and this is red. Since color is conserved, this has to be anti-red. And the same way, if this charm is blue, this has to be anti-blue. Nevertheless, I could have a red, anti-red, green, anti-green, or blue, anti-grew. So there's three possible decays to three different colors of quarks. Now, the way we do the calculation, we do some traces and sums and so on, and it's fancier mathematics. But you get the same answer as if you just count the number of colors, especially when you do inclusive decays. This is a much more easy way to do it. Yeah. What argument is too quick? The argument is? No. So for quarks, it's fine. Because it's red, it's a three-in-a-three bar, right? So we have the triplet and the anti-triplet. So there's no approximation here. This is exact, right? You're producing, there's three possible final states. So we don't normally measure the color of it. And we know color is conserved. But you could, in principle, measure the color of a quark if they were asymptotically free particles, which they're not, right? I mean, if you could see a quark, it would have a color, much like isospin. So think of it like SU2. SU2, we can have a neutron and a proton, right? So at the point of SU2, one is isospin a half, one is isospin minus a half. So think of the case of neutrons and protons. It can make to a neutron, neutron bar, proton, proton bar. I can just figure out what it was. Was it a neutron or a proton? And then I have one of those and one of those. And I just count. And that summing of two types of isospin is the same as the summing of three colors here. Well, I'm saying it doesn't have to be, right? It only has to be when you're at large distances and things hadronize and you end up being color singlishes. Yeah, well, eventually. So these aren't stable particles, right? But I'm using the sort of approximation where I produce the quarks and then something happens to them. So in the approximation, I'm just doing perturbation theory. And I don't care if they turn into color singlet hadrons, right? So from perturbation theory point of view, I can just produce red and anti-red quarks. And I can pretend I can measure that. And I don't have to sum over. I don't have to treat them as color singlet objects. And this is a useful tool to really think of them as having separate colors, like we think of particles as having a separate isospin. In the same way, I can say, well, I could have SU3 at variance. I don't have to worry about up and down. But it's helpful to separate out the up and down times. Yeah. Now, again, color these here. No, no, no, but because this isn't quite one, right? And so when you sum everything, when you sum the squares of the elements, does he get a matrix when you sum the squares of everything that WK do, it sums to one anyway, right? And so, but anyway, there's three here. So you get the same suppression. This is down by a factor. This is 4% of this, right? And whether or not you sum over colors. Because the color, you have three of these and three of these. So it's still down by 4%. So I don't care, but yeah. But so either way works out. Anyway, so we have three colors of this and three colors of this. So we have six over here, plus three altogether here, right? So we have nine total instead of five. So the answer here is one over nine, right? Which is around 10%, right? So basically, you get 10% here, 10% here, 10% here. And then you have, well, so we have 30. So we have 70 left over. So we get, I guess I did an approximation here, 35 and 35. So what we say, if we draw a pie chart for the W-Bredge ratio, so we say, what do these look like? So if the W decays the upper-down quarks, they become these jets that I talked about last time. So we have basically 70% of the time it decays the jets and 30% of the time it decays the leptons. So we can draw it as a sort of pie chart. 70% jets. And then of the leptons, we say 10% electrons, 10% muons, and then there's Tau's, which are another 10%. So these are useful numbers to know, right? Because leptons are much easier to see than jets. So if you see an electron or muon, mostly those are the decays you want of the W. So if you're interested in leptonic W decays, we'll talk about Tau's in a minute. But they don't decay leptonically, and they're much harder to identify. So these things are easier to identify. Remember I showed you those like Zebo's on plots or the transverse mass distribution for the W. And they always involve the leptonic channels, not the jet. So basically, when you have a W, you get a clean measurement of the W. I mean, you get neutrinos in this process, but you get a clean trigger, at least, that there was a W, 20% of the time. So that's a useful number. The 20% of the Ws are sort of useful and clean, in a sense. And that'll come into other processes, too. And the question's about this, how we did the estimate. OK, so now let's do the Zebo's on. Do the same thing. The Z is neutral. We know its mass is 90 GV. We wrote that over there. So the Z can decay, since it's neutral, it decays to things like BB bar, can't decay to TT bar, CC bar, SS bar, UU bar, and DD bar. It can decay to leptons, mu, mu, tau, tau, and finals. There's three neutrinos. Let me write them out as their separate particle. OK, so what's the branching ratio of Z to electrons? You guys think about it for a second. I heard a 1 over 21. You have 30%. 33% of the time goes to electrons. So those are very different answers. You want everything else? OK, so how do we do it? Well, we did the same argument we did before. So these are the hydronic channels. So we multiply them by 3. So we get 5 times 3 is 15 of these, and there's 6 of these. So we have 21 total. So then we get this 1 out of 21% of the time, which is maybe 4%. There's one catch with the Z that it decays differently to the uptight part of the SC2 doublet or the downtight part of the SC2 doublet. So the Z couplings are proportional to T3 minus Q times sine theta. So I've got the electric charge of the isospid. But anyway, this is a sub-number of order 1. So this is plus or minus 1 half, and then it depends on the charge. So you get slightly different couplings to different things, but the numbers are about right. So it turns out this is closer to 3%. 3% here, 3% here, 3% here. It ends up becoming the trinos a little bit more. So 6% for these guys. And in the same way, you get a slightly larger percentage for the Bs, and 11% for the uptight quarks and 15% for the downtight quarks. So if we draw the pie chart, we get, so if you add up all the jet decay modes, you get around 77% jets. But you only get a little bit, so you get 3% electron, 3% muon, and 18% neutrinos. So what this means is that the Z, these kind of golden decay modes for the Z, you only get 6% of the time. Well, for the W, you have 20% of the time. So this is a problem. You pay a huge penalty for asking for Z. These are very clean because you see everything. So W is you get neutrinos, and they're missing energy, and you can't completely reconstruct the W. Zs are fantastic because you always know if you have a Z when it decays leptonically, but you only get leptonic Z decays 6% of the time. So that's a trade-off you pay. And so there's been a lot of work to understand these hadronic modes because they play such an important role. I mean, I take a lot of developments in collider physics over the 10 years. I've helped increase the amount of Ws and Zs that we consider useful from including the hadronic decay mode. Questions? So another question from the problems yesterday was what happens if there's another neutrino? How would it affect the Z width? To answer that, you just add another one here. So if you have another neutrino, then instead of 21, you would have 22 modes. So a rough approximation, you would get maybe 1% difference in the branch species mode, and 1% difference in the width. So you have to know, do we measure the Z width to within 1% and the answer is yes. And then you can put a bound based on knowing how many neutrinos we have. If we had covered this yesterday, you would have been able to solve that problem. Let's keep moving. We have a lot more particles to do. Next, we'll talk about the top. The top is a very interesting particle because it's so heavy. Because it's so heavy, a couple is very strongly to the Higgs boson, and that actually makes it very useful for Higgs physics, among other things. It's also related to the stability of our universe. So the third particle we're talking about is the top. OK. We talked about, someone said its mass was 173. Let me say 175 GV. Does anyone know what mass that is? When we talk about this mass, what do we mean by mass? Can you go put a top on a scale and weigh it? That's not what we mean. So this is a particular type of mass called the pole mass. Here's another mass, 5GV. That's also the top quark mass. Here's a mass. I'm defining it to be 5GV. This is the Schwartz mass scheme in which I've defined the top 55GV. You can pick a mass scheme and make it a TEV. You can do whatever you want. There's no physics in associated with the scheme. So when we tell you what the mass is, we have to be more careful about what we mean. And this is particularly important in the top quark. So the top quark, nobody uses the Schwartz mass scheme. Instead, let me call this M pole. The most common are the pole mass and the MS bar mass, which is 163 GV. MS bar mass. So the pole mass is more closely related to what you would measure in a collider. If you try to produce tops and look at the invariant mass of the decay products, the thing you'll be extracting is close to the pole mass. Not exactly, but if you understand how to do the calculations, you can relate the two. But the thing that's used in precision calculations, like in the calculation of the stability of the universe, you would use the MS bar mass. You can convert between these two perturbatively, so the difference between them is proportional to any one of them times something like 1 plus alpha over pi times some number. I don't know, 6, whatever it is. So there's some perturbative correction that you could do to relate the two, but you see they differ by 10 GV, right? So 10 GV a lot, I don't know, it's 5% of the difference, right, but this is a typical difference. And the reason it's large is because, first of all, the top is colored, so you get a factor of CA, which is 3 in this correction, and that's fairly large. Well, for the W boson and the Z boson, they don't interact strongly, and so there is a difference between the pole mass and the MS bar mass, but it's very, very small, it's less than 1%. So the top cork, because it's so big, you notice the difference, and it's just important to keep in mind when people talk about the top cork mass, you always have to know what mass they're talking about. And as we're getting towards precision measurements from the top mass, this has become an interesting issue, theoretically, because it's not clear when the experiments measure the mass exactly what scheme they're doing the measurement, partly because they're just doing fits to Pythia, and Pythia doesn't have a well-defined short-distance mass scheme. So it's not clear that the ambiguities in the simulations they use are accurate enough to distinguish different mass schemes. So there's some controversy. I wouldn't say controversy, there's some development that's required to get beyond the, you know, if you want to get 1% on the top mass, you have to know the difference between the different schemes. Let's see. So how does the top decay? So the top almost always, I erased the CKM elements, but it almost always decays through a W boson. So the top goes to B and a W boson, and that's because the VTB, all the other couplings were very, very small for the top. So from a collider physics point of view, 100% of the time it decays to a B and a W, and the W is on shell, because it's lighter than the top, and then the W decays to whatever it decayed to before, which we had here, W decays. Right? So typically tops are produced in pairs. So the dominant production mechanism of the LHC is gluons come in and interact with tops. So this is gluon top pair production. The cross section is pretty large, the picobar range for TT bar production, especially the high energy where the top mass becomes negligible. So you produce tops in pairs, and then you want to identify them. So most of the time they decay to jets. And if the tops are decaying to jets, it's very hard to see them because there's a lot of jets that don't come from tops. Right? So if it's just the top, so one thing you could have is a top, so it decays to a B and then a W, and say that decay to UD bar, then you would get three jets over there and three jets on the other side, and you can B tag it to help, but you also have just glue glue to six gluons, and that's an enormous cross section that's a million times bigger. So it's very hard to see, or more than a million times bigger, these fully hydronic modes. So usually what you do is you say, let me have one of the Ws decay to jets, and one of them decay to leptons, so you might have something like electron neutrino. And then what you do is you use the electron, so this is a hard electron, because you're finding the W from the electron. So you look for events with one hard electron and two B jets, and then some other jets, and that is the largest cross section. So we divide the top decays into three regions. There's fully hydronic, there's semi-leptonic, and then there's fully leptonic. So what fraction of events are fully hydronic? We're both Ws decay to jets. I guess let's start on the other side. What fraction is fully leptonic? We're both Ws decay to electrons or muons. So from one W to decay to electrons or muons is 20%, so for two Ws, you have to square it. So you have 20% squared, which is 0.04, so 4%. So this is 4% of the time you get two leptons. So the fully leptonic channel, you're losing almost all of your tops. If you demand it, also when you have two Ws decay leptonically, you have two neutrinos. And with one neutrino, you can reconstruct the W if you put it on shell. So before we talked about measuring the W mass from MT and so on, but if you know the W mass, then you have an extra constraint that you can use to determine the neutrino momenta completely. So with one W decay to neutrino, that's okay, it doesn't really hurt you, but when you have two Ws, then you have missing energy as the sum of the two neutrino momenta, and you can't do anything with it. So the fully leptonic channel is not so useful, but it's very clean because you just have two B jets and two muons. Semi-leptonic channel, what's the branching ratio? 14%, 2%, 8%, 30%. So one decay is 20%, then we have the other one decay at 20%. 14%, where's 14%? Yeah, but there's also, right, so it's really 80 because we're not including the towels. So we want one decay to this and one decay to something else, right? So it's basically, it's 20% for one jet and then 20% for the other jet. So we just have to add them as opposed to multiplying them. So we get 40%. But 40% way of one of them decay and the other one does not decay. So we don't care, because we're using the lepton to tag the top. We don't care if the decay is the thousand or not. So we get 40% and then this is the remaining 56% is fully hydronic. So this is the messiest channel with the largest background. This semi-leptonic channel is the channel that almost all top physics studies are done because the top channel, the semi-leptonic channel is very nice because you use the leptonic side to tag that it was a TT bar event. Almost all tops come from TT bar events. And then you have this other side where you can reconstruct the top. So if you wanna measure the top mass, what you do is you tag that it's a TT bar event using this side, but then you use these three jets to figure out where the top mass is, right? You don't need to worry about the neutrino because we're not using this side of the decay at all to reconstruct the top. So it's convenient that we have two tops at the same time and that makes it very easy to measure properties of the top. So we have a huge sample of these semi-leptonic top jets that are useful for studying color connections between these jets for the decays, understanding properties of the W boson. It's also actually the best sample of W, hydronically decaying W bosons. So if you're interested in Ws for some reason that decay hydronically, you look at the TT bar channel because if you just look for a single W that decay hydronically, that would just be a dye jet event and that's a mess. So TT bar is a huge sample of tops and Ws that can be studied in precision or from the other standard model searches or things like that. It's a question. Well, it's the same. You just have to do one minus it because you want one to be leptonic and one not to be leptonic and then the other one can be leptonic. So you end up just saying 20% one's leptonic and then the other is 20%. Just count the, you'll see it's right. It takes a little thinking. Yeah, did I do the numbers wrong? What? Do you mean you're talking about towels? Yeah, let me include towels in this. So let me call this 80. The towels are basically a hydronic. So it's one minus 80. 80 bay is 64, yeah. I'm gonna try to conclude. Let's talk about this later. These are the standard numbers. Okay, there's more exotic top decays but let me skip those. We're doing on time. Let me wait for the time to come about again. Oh, we have an hour. Yeah, okay. So I'm gonna talk a little bit about top mass measurements because that's, as I said, understanding the top precisely is one of the goals of precision physics and we don't actually know it that well. It's one of the least well-known quarks despite the fact that it's heavy and so heavy means that we should get a better precision measurement of it because it's not sensitive to hydrogenization effects and things like that. The goal, what we'd like to get is around 100 MEV uncertainty or something like that on the top quark mass. This is what we need to determine vacuum stability and so on. Right now the uncertainty is around one GEV. But again, even the uncertainty is debatable because of issues like what mass scheme is it measuring. So there's the systematic uncertainty even the experiment and then there's the theoretical uncertainty and theoretical uncertainty is notoriously hard to assess because it's not statistical. It's more about what you don't know and how do you assess what you don't know. But let me just kind of summarize how do you measure the top mass. The most obvious way to measure the top mass is kinematic. And so here we can do dilepton, semi-leptonic and hydronic. So these have different advantages. The dilepton, the fully-leptonic channel has a very small branching ratio. It's relatively clean but you can't reconstruct the tops completely because you have two neutrinos. So it's not a very useful channel. It has good signal over background. There's basically no background for that. It's B jets plus missing energy. But they do the analysis anyway. So you have to do something like MT, the transverse mass and try to extract the top from the transverse mass of the leptons. There's some other related observables they use but you get around a delta MT of 1.6 on the dilepton. The semi-leptonic channel as I mentioned is the best way to do it. So this also has good signal over background and you fully reconstruct it. So fully reconstruct because you have the hydronic side you have everything the top decay to and you can just look at the invariant mass of it. So you just look for a peak and you fit this to a Breitwigner distribution and you extract the top quark pole mass from this and then you get a delta MT of around 0.5 GeV. And it's this half a GeV that's controversial. So this is sort of the experimental uncertainty on it but then it's not clear, as I said, the difference between pole mass and MS bar mass is 10 GeV. So sub-leading order differences between the two are hundreds of MEV, which is the same order of this. There's some controversy that the pole mass itself isn't well-defined. There's what's called a renormal on ambiguity and there's estimates of how big that would be and it's, again, in the few hundred MEV range. So it's not clear whether we can trust these results but nevertheless this is the cleanest channel experimentally. The hydronic channel has a huge background. Delta MT is around 1.5 GeV. So a lot of way to get around this huge background is to ask for the tops to have extra energy. So they're called boosted and then you can identify, you reduce the backgrounds by asking for boosted tops. So one of the results of a lot of this jet substructure development, the last 10 years, has been to use the fully hydronic channel to do interesting physics and you get the advantage of having more events. Anyway, the bottom line is the semi-leptonic decay where you look for the invariant mass of the top is the best channel in the kinematic range. Yeah. No, so in the leptonic channel? In the dilapton, so the dilapton you have, right, so you might have B, mu and neutrino, right? So you get two B jets and electron and neutrino. So if I just took the mu on and a B jet, I wouldn't reconstruct the top because I don't have this neutrino. In the same way here, so I have two neutrino, so you can't do it. You have to do something like with the top where you look for transverse mass and you look for an endpoint, right? So it's the same thing here where they'll have an endpoint of the transverse mass at twice the top mass. However, you generally fit the shape. So what you do is you calculate this in Monte Carlo and you fit the shape and you vary the top mass. So there's still Monte Carlo. Here you can do it a little bit more analytically, but it's still a fit to a shape. So you have the same sort of ambiguities of what scheme you're interested in. It's the uncertainty on the top cork mass, right? So there's a plus or minus here, right? Like that, I think I have it. I don't know what it is exactly, but it's around the GEV. So when you read these numbers, you'll see 175 plus or minus one GEV, right? And this is plus or minus I'm talking about, right? Anyway, so that's the goal of the LHC is to improve this. The prospects are, well, probably we're not gonna do better than this. This is sort of the experimental limit, but now there's theoretical considerations, which is an interesting topic on its own right. Okay, kinematic total cross-section. So the total cross-section is an interesting measurement because there you can compare directly to a theoretical calculation. I just count the number of tops I have. If I know the luminosity of the machine, I can extract the cross-section, right? And this is something that's been computed to three loops, I think, right? So this is a precision calculation and it is a precision measurement. And the advantage of this is you know what scheme you're in so you don't have to do these shapefits and you can do the calculation of the total cross-section in MS bar, right? So we know sigma total has a function of m top MS bar to three loops. So we have a very good theoretical handle on this. The thing that we don't have a very good theoretical handle is the part and distribution functions. So the dominant uncertainty here is determined by uncertainties on what the PDFs are and that limits the utility of this. Also you need to calculate, you need to count the number of tops very accurately. So you could of course count in the semi-leptonic channel and just multiply by the branching ratio, which is mostly what they do because the hydronic one you can't really count. Nevertheless, there's experimental uncertainties on backgrounds and so on. So there's issues involved in that. The bottom line is you get a Delta MT from this currently at around 1.5 GeV. The hope is by the end of the LHC to get that down below a GeV. And the advantage there really is that you're directly measuring the MS bar mass for the top. So that's a promising channel. The third way of measuring the top is through what's called a threshold scan at E plus E minus. So this is something you can't do at the LHC but you could do at an E plus E minus machine. The idea there is you change the center of mass energy and you look at the cross-section as a function of the center of mass energy. Well, it's just S. I'm at a Hadron collider. And what you imagine, so you're looking for E plus E minus to TT bar, right, through an intermediate photon. So it's gonna turn on in the same way as I showed up there at around 350, right? And then it goes up and goes down. So if you know the location of where it turns on, you can measure this precisely. But what's really neat about the top is that there's actually a bound state. It's a very unstable bound state but you can have gluons exchanged between the top. And so you form this metastable bound state slightly below the TT bar mass. So this is 350. What you'll see is there's actually a little blip here and there's a resonance from a TT bar bound state slightly below the pole. So if you can measure this shape very well, there's ways to know exactly what the mass of this bound state is. And that's very sensitive to the top quark mass. So if we can build an E plus E minus collider and run it near 350, which again is 100 GeV higher than what I was talking about in this plot, right? And again, it's very, very expensive. It goes like the fourth power of the energy to build one of these things. Then we have the potential of measuring delta MT less than, I don't know, 100 MeV, right? So this is one of the strongest regions to build an E plus E minus collider and to run it at high energy so that we can finally determine what the top quark mass in an unambiguous scheme. So again, these are theory calculations about the location of the pole where actually you don't use MS bar or pole mass. You use something called the 1S scheme, which is some non-relativistic QCD scheme that's also, has the nice properties of being renormal on free and stuff like that. Let me not get into that. The bottom line is that this goal is probably only achievable at an E plus E minus collider. And in a Hadron collider, this might be the experimental, the systematics limit. Let me write systematics. But it might be true that MT theory, you know, is 1GV. But depending on who you talk to, people will say there's an irreducible 1GV uncertainty from shape measurements from pole mass extractions at the LHC. Some people will say you can get down. I personally think that we'll be able to get it down. I think this is a reasonable goal for the LHC about half a GV, which may or may not, depending on the value, be good enough to exclude the stability of the universe. Well, we'll have to see where that goes. Questions about top? Yeah, it's like 10 to the minus 28 seconds. Right, well, so, yeah, great question. So the question is, the top is so short lived, how could it form a bound state? So what you're seeing is the effects of these virtual corrections on the existence of center mass energy. So it's not like you actually propagate anywhere. And there's a competition between the decay of the bound state and the weak decay. And they have the same lifetime. But those lifetimes, it's okay. From the point of view of the top decaying, you know, it can form a bound state. You can see evidence of this binding before it decays. And that's what shows up in this plot. So in the sense, you can think of this as I'm just calculating the TT bar cross section with extra gluons in it. And if I sum this whole series of ladder diagrams, what it does is it decreases the cross section and then increases it at lower energy. So it allows for, even if these decay, if I include the whole decay chain, right, you'll see these effect in the production cross section because of this binding effect. So it sort of factorizes off from the actual decay. That's a great question. These are beautiful physics associated with doing these calculations. But it's a well-established, maybe I shouldn't write so low over there, a field that was associated with an RQCD, yeah. You know, why is it so hard? We don't know anything to three loops. Yeah, the beta function is a two-point function, right? You just calculate the correctness of the gluon propagator. The TT bar is protons come in and you're on all these different channels and tops come out and you need extra jets and you have to do inclusive cross sections. So you have to sum over the phase space. It's very, very difficult. It's sort of a heroic effort to know it at NNLO, which is only achieved rather recently. But I don't think, again, the precision on the theory is good enough that we don't need to go to four loops. It's also an asymptotic series, so if you get a lot in three loops, it starts not converging and it's not helpful to go to high-roader. But it's really dominated by PDF uncertainties and other things like that. Interesting theory question, but doing inclusive calculations ends up being very difficult at high-roader. A lot of us do is just removing the infrared divergences from the phase space integrals in the loops, which is not something you can do analytically. Yeah, yeah, well that's what I was saying. So it depends on the value of the top quark mass. So right now, the thing that we might be able to establish is whether the universe is absolutely stable or it's lifetime is finite, right? It's, we've excluded the possibility of the universe's lifetime being less than 15 billion years, which would be the most interesting case. So that's already excluded to like 100 sigma for position measurement. But if we measure the top quark mass, so it's about two sigma, the stability boundary between absolute stability and metastability, we're about two sigma away, but it's non-linear, so you can't really quantify it. So the top quark mass comes out slightly lower. So the way it works, I mean, this is interesting physics. I don't know if it's gonna be covered somewhere else. We'll aside from what we're talking about. So you guys have all seen this Higgs potential that looks like that. So this is just V of H is minus M squared H squared plus lambda H to the fourth. Because quantum field theory is normalizable, you can calculate radiative corrections to this and you can trust the calculations all the way up to M plank. So we can figure about what this potential is and so you get these terms that look H fourth log of H over some scale, let me write V for the VEV. And so the coefficient here depends on what's going into the loop. So what you do is you calculate corrections to the Higgs potential. So the leading order thing is lambda, it looks like that, but I could have something with, say, a top loop going around or I can have something, so this might be a top or I can have Higgs is going around H and they go in different ways. So a Higgs is a scalar, it's a boson, so it has a positive contribution. So basically the lambda is inversely proportional to the Higgs mass if I fix the VEV. So if I increase the Higgs mass, the potential becomes more stable. So the question is, does it go over here like this? Does it come down? Does it go up? And you'd like to know if it goes below zero or it never goes below zero. So if it goes below zero, then you can tunnel from our vacuum to this and that's the instability. And so the bigger the top mass is because this is a fermion, the more of a negative contribution you have. So a higher top mass makes the universe less stable. But we know what the top mass is and you need to know what it is in the right scheme in order to be able to do these calculations. And it turns out it's sort of marginal. So if the top mass were, I don't know, a GEV heavier than we think it is, then the universe would be unstable, right? So you need to know the top uncertainty to be small enough so that it has to be a GEV heavier than what it is and the uncertainty has to be small enough so that you can say with confidence that it's unstable. So it depends on the value or what the top mass comes out to be, but if some result says the top mass is half a GEV heavier, you should say that's very interesting. If it turns out to be lower, it doesn't matter. If we resolve up another five GEV and it ends up being lower, then we're done, the universe is less stable. So that's sort of the open question. Nobody really knows why it's interesting. I mean, there's sort of cosmological reasons to ask, does the existence of a lower energy vacuum, right, sort of we're in decider space and this would be an anti-decider vacuum and there's questions about whether decider vacuum even exists, right? So there's this weak gravity conjecture that says that this kind of state can't exist. There's sort of interesting theoretical reasons to care about this, besides the fact of knowing what the fate of the universe is gonna be, which I think is sort of philosophically interesting, but there's sort of mathematical physics elements to try to resolve this question. Whether it's worth spending a hundred billion dollars to build a machine, I don't know, but it seems like a question that we can answer in our lifetime, so maybe we should, but I'm holding the purse strings, a question. Yeah, so this is zero temperature potential. So thermal effects you take into account to figure out how we got here in the first place, right? So you might wanna ask, as the universe cooled, did we end up in this vacuum or down here, whether or not it's heavier or lower than ours? And that's a totally separate question. We're assuming we're here because we see ourselves to be here and then we just wanna know if we're gonna end up there and the universe is basically at zero temperature, T equals zero from the point of view of now. So during the electric phase transition, there's other questions about the order of this transition. So at high temperature, this thing is stupid. It's just the parabola that goes like T squared. And as you lower it, you can ask, is there a first order or second order phase transition and how do we end up in this vacuum? And does inflation reheat past this plate so you end up cooling there? And those are a whole separate, other separate set of questions, which I mean, you can just say, what I know experimentally is that we're here and I can answer this question independent of how we got there. But if it turns out there's new physics that affects the potential at scale. So I should say the scale here is around 10 to the 17 GB. Well, 10 to the 17 is the relevant scale. This potential isn't really gauging variant. But so if there's scales that if you reheated too high, you'd end up, maybe we cooled into the other vacuum that could have happened. So the questions about early universe cosmology that might need to be resolved if you modify the physics at that scale. But from the point of view of just our universe that we have now, assuming the standard model, it's a well-defined question. If we find physics beyond the standard model, you don't ask this question anymore because a lot of other things contributed to that potential. But all of this is predicated on just having the standard model and nothing else. Which we would love to see something else, but that's what we have. And again, it's weird to try to build a collider assuming it's the standard model because you want to answer a question, but also to say I want to look for things beyond the standard model. But in some sense, that's what we already did with the LHC. We built it to find the Higgs in the standard model, but we were hoping to find something else. So maybe we'll do it again. Questions? All right, we only got through three particles. We got another half hour. It's on the middle ring. All right, let's do bottom next. The MS bar mass for the bottom is 4.5 GeV. So the bottom quark, unlike the top, patronizes before it decays. The top quark lifetime, I guess I should write this. So the top quark of the top is 10 to the minus 23 seconds. The lifetime for the bottom is 1.6 times 10 to the minus 12 seconds. So the top is much, much more unstable than the bottom. It gets to compare these two other things. The lifetime for the pion and the neutral pion is 10 to the minus 17 seconds. So this is because pionaut decays to photons, so the anomaly, so it ends up being very fast. And pi plus 10 to the minus eight seconds. This is just relative scale. So the top is very, very unstable. The bottom is sort of metastable. The pionaut is very unstable. So the bottom, so what is the, how do we think about these scales more physically? So the, so we talk about the decay length. Lambda is C tap. So if something is moving at the speed of light, we'd like to know how far it goes before it decays. So we multiply the lifetime by the speed, and we get 450 to 500. Microns, which is around half a millimeter. So the bottom cork goes around half a millimeter before it decays, and that means we can see it because we can measure micron level tracks and so on in a tracker or a tenth of a micron type resolution. So bottom corks are nice because they hydronize and then they move and then they decay. And they're kind of special because this regime is basically the size of our tracker. So we can basically see the bottoms move and then we see the decay products. And that's how we use, that's the basic ingredient to use for identifying bottoms. So how does the bottom decay? So, so kind of formula. So the bottom decay is to say a tau on. And the rates for these formulas have a, go like G fermi and then they go like VUB squared times some other numbers. And it's this V, it's the combination of VUB being small because it's a flavor change in decay. So remember a bottom, the top is heavier than the bottom. So the bottom will decay through a W but it doesn't have a top to connect to. So it has to connect to something else. So this B is a BU bar bound state. So you could think of the B going and decaying through a W to a tau and a neutrino. And then the U kind of comes along and forms another bound state with say the D or BU. So this would be a B meson decaying to a pi not and a T do. And then this pi not decay to gamma, gamma. So you have this, yeah, so this kind of decay, you have this VUB suppressed interaction which you need to have for all B decays. And that's sort of the origin of this lifetime of the top that involves this Kubevo suppressed off diagonal CKM element. So I want to say about Bs. Typically Bs have cascade decays. So what that means is that the B decays to something which then decays to something else which then decays to something else. So we might have a neutral B decay to a D meson and a muon and a neutrino. And then there's D decays to say a K on and a pi on by minus. And then the K on decays to a pi plus by zero and that decays to gamma, gamma. So you have, this is what we call a cascade decay. The result is that you get a bunch of charged particles here. So we'd have one, two, three, four charged particles. Typical B decays have five or more, we typical say four or more to be consistent with my example. So they have a large number of charged particles coming from this cascade decay. So they typically will decay to a charm and then the charm will decay and then you go down one flavor each time. And that's sort of the origin of what's happening here. Yeah, yeah, so that's what happens here. The D is a charm based on, yeah, it's still suppressed. Then this would be a D and then that decayed. No, it's still off the angle because remember B is third generation and charm is second generation. So this one was even smaller than that. So let me talk about how do you find Bs? So the way Bs show up at a collider is they have this particle, you're produced from the hard interaction and moves a little bit into Ks and then everything else basically decays promptly. So you see essentially one vertex for the decay that's separated from the hard vertex by something of order half a millimeter. And then you see a bunch of tracks converging at that vertex from the charged particles. And then they decay to a bunch of particles. And typically Bs will be accompanied by whatever else was produced. So you might have a B produced from a glue on decaying to BB bar, which is not unusual. So you would have a glue on jet with two Bs in it and so you just get a bunch of particles and we talk about B tagging where we try to identify that there was at least one B in the jet. And we can do this predominantly because of this displaced vertex. So B tagging involves a combination of different things. One, you look for a large impact parameter. So what does that mean? The impact parameter, so you only measure the charged particle tracks. So, and they all go off in funny directions. So you can't always tell exactly how far the vertex was from the B decay from the primary vertex. In particular, you don't know the longitudinal momentum. So if we have the B is produced here, this is called the primary vertex, a primary interaction. So the beam comes in here and produces a B. And then if the B is neutral, you won't see a track itself, but then you'll see some decay. And so what you see is a bunch of tracks that go off like this. And you can track those, you can figure out from each track, you draw a line and you point the path of closest descent and that's called the impact parameter. So for each track, you figure out what the closest it gets to the vertex. And so you look for, you count the tracks that have large D. So you can't always reconstruct this vertex, but you can see if you have a track, whether it aligns to the primary vertex or not. Because remember these tracks, you don't see like a continuous thing. You see a bunch of hits. Right? And so you might see something like that and then you try to reconstruct a line. So you don't always get everything. So what you try to do is take each track individually and look for tracks that have large impact parameter as an indication that there might be a B associated with it. If you can, you can try to reconduce the secondary vertex. If you have enough tracks that convert to a point, that's even better. So that's secondary vertex reconstruction. Then you look for a high multiplicity. Right? And again, this is coming from the typical B is decay to a large number of particles. You might have four or five particles. So you just try to count that there's a large number of particles in the jet. And that's an indication that it might be a B. You can look for the mass of the secondary vertex to be around 4.5 GV to 5 GV. Right? Okay, if I can reconstruct this vertex, I can take the invariant mass of all the particles that go there and see if there's somewhere close to the B mass. And that can be useful as well. And so basically the way modern B tagging works is you kind of take all these things and you throw them into a neural network and you get the output. And typical results are around 70% Bs and one over 50. These are kind of typical numbers. You can vary the point on the rock curve that you're using this, but the point is if you do B tagging, you should expect that you'll lose around 30% of your Bs and you'll keep 2% of your background. Right? So there's some contamination and if you have a very large background, this won't help. But if you have multiple B tags, this can be very useful. I think I had an impact parameter slide. This is like a pile up. I mentioned pile up before. I just kind of wanted to show you a picture from a collision, what pile up is. Remember pile up is we have 100 collisions per bunch crossing. And so these collisions, some of them you can reconstruct as separate points to these different yellow dots from the tracks. The neutral particles you can't localize to a point. The red is a muon and the blue is an electron. Yeah, here. So this is an example of LHCB secondary vertex reconstruction. So here we have, so there's the primary vertex where the beam collides. You have a lot of tracks converting here and they're not showing you them all. Oh, there's also, you also look for muons. That's another, typically B decays, around 30% of B decays will have muons and that's, they won't be very hard muons but they're also using muon as a tag. So what happened here is you had a B decay and a decay to a D, which is the charm meson and went over here. Well, I guess this is the, so the B came in here and the B decayed to a charm and then the charm decayed over here. So you have a tertiary vertex, TV is secondary vertex, SV, and the primary vertex is this pink thing. And so these are the bunch of tracks and you look at track and you catch an impact parameter, the distance between this track and the primary vertex. So in this case, they're able to reconstruct things pretty well. LHCB is an experiment designed for B physics. So it collides the same kind of stuff that are collided at Atlas and CMS but it generally runs at much lower luminosity. So they try to not have such a tight beam spot so they don't have a lot of pile up which really helps with identification. It's also only half a detector so everything tends to be boosted and they don't need to reconstruct everything, they just need to reconstruct half the things and that makes it easier. And they have very good silica, very good vertexing for identifying bees. Questions about bee tagging? How do you calibrate what? For bee tagging? Yeah, so you calibrate it on events that you know have bees, right? So if you had a top, for example, you know there was a bee from the top for bees are often produced in BB bar pairs so you'd have a clean tag. These are basically the tagging probe method where you have one that you really trust that is a very clean signal where you might have something like this where you reconstruct everything and then you ask on the other side how well am I reconstructing it? No one gonna have a bee. So almost all these methods are done entirely data-driven, right? So they need simulations to know how their detector works but they kind of simulate the separate components and identify it but they do everything they can to test this. I mean again, these simulations, the decays are pretty easy to simulate because they're on-shell particles de-haying so you just need to know the branching ratios and the lifetimes and then you can just, I mean, you can write a five-line code to do it, right? It's not like a part-time shower where there's all these QCD effects, right? You don't need to calculate nuclear matrix elements, you just need to know branching ratios. So you just have these bees and they move along and they decay and you can figure out how that works. So the simulations are pretty accurate anyway. Bottom, done, we did four particles. Charm. Okay, so charm is like bottom but it's lighter and so you get all the same stuff, less of it. You basically, so this is a charm. Charm engines are called D for, I guess, historical reasons. I'm not sure why they're called D. Where's Duval? Maybe he knows. You hear? All right, ask him. Anyway, so the capital D is a charm and the lowercase D is a D-quark. Charm. So the mass of the charm, this bar mass is 1.29 GV. These are these D-mesons. So we talk about D plus, which is a CD bar bound state in D zero, which is CU bar, D sub S is the strange one and these all have around one to two GV of mass. There's D star, which are vector mesons. C tau is around 300 microns. So it's about half of C tau or B. So that means the lifetime for tau is, so you can't see it in that picture because it looks longer. But typically D-mesons are about, they left half as long, so you need twice as good silicon to be able to identify them. So they're just, charm tagging is very hard because you typically won't be able to resolve the DDK. Also you have fewer tracks, so basically you start here instead of here so you get fewer charged particles than you would with B, you get fewer muons, you get fewer of everything. So charm tagging is very difficult, but with the advent of new machine learning techniques, actually charm tagging is improving in efficiency and it's becoming something that's becoming more and more standard. It still doesn't work nearly as well as B tagging, but it's something they're thinking about for upgrades, improving the detector performance and improving the doing charm identification. So otherwise it's sort of qualitatively similar to B's. Move on. The next one is Strange. Well I was gonna talk, Strange is interesting because you can't, Strange are the K-ons and the K-ons sector is interesting because you can study CP violation, parity violation, which were very interesting historically. I think I'm not gonna get into any of that or historical, but Strange is MS-93 MEV. We have the K-ons, a few bar. Now it is a T-bar. Bar, these are all around 493 MEV. There's also K-node bar, which is a TS bar. So these states are degenerate, they're not mass eigenstates and they're not CP eigenstates. What we generally write is there's, the physical particles are called K-short, which is K-1 plus epsilon K-2, epsilon K-1, where K-1 is K-node plus K-node bar over the square root of two. K-node minus K-node bar over the square root of two and this thing decays to three pions and this thing decays to two pions. So epsilon is some small number around 10 to the minus three. So to a leading approximation at a collider you can ignore this and you think of the physical particles as the K-short and K-long, the K-short decays to two pions and the K-long decays to three pions called short and long because the lifetime is 0.09 nanoseconds and 52 nanoseconds. That means this guy goes around one meter and this guy goes around one centimeter. So both of these, the K-long and K-short show up as particles that are sort of essentially stable on the point of view of the detector. That is, we see them before they decay. This epsilon business has to do with CP violation. I don't really want to get into it. You can read about it in the notes or in a book. But the bottom line is there's two kinds of caons that are commonly produced and they show up, you can identify them as caons before they decay. They often deposit a lot of their energy in the calorimetry before they decay. Sometimes you don't see them decay at all. But if they decay, then you just see pions. And then finally, we can talk about up and down. So these guys are producing pions. So you have UD bar, DU bar, UU bar, and DD bar. This goes to pi plus, pi minus, pi zero, and eta. But let's not worry about eta for now. They also form barions, so the proton. So you have proton, neutron, pi plus and minus. Our bound states. So the proton is UUD and then we have VDU and so on, and anti protons. So the bottom line is the particles that you actually show up at the detector that are considered stable, meaning we see them before they decay, are the proton, the neutron, the pi plus, the pi minus, the photon, the electron, the muon, the k long, the k short, k plus and minus, and then a few other more exotic things, delta and neutrinos. So basically, these are the set of particles that the LHC measures. Everything decays to these things. So we can reconstruct intermediate things like bees, but we're constructing it by actually seeing things from this list. So you can ask, how much of these things do we get? So I think I have, let me see. Oh, here's a different projection of that in the display. Yeah, okay. Here's an outfit from Pithya. How many of you ever run Pithya or another simulation? So there's a number of programs that you can just download and run. Pithya is the easiest one. You can download and run it in a half hour. There's other ones like Hurwig that you can download and run in about six months. And there's MadGraph, which you can also run. You can run it online. I'm not sure of Pithya. Pithya probably you can't unrun. But anyway, you run these things. It generates an event and you see what it looks like. And it generates these things called LHE files. And if you look at them, they have a set of events. So here's an event, so this is an event. And there's a lot of numbers. These are the momenta and the mass of the particle. So the zeros are mass zero. I think this is the decay width. I'm not sure. And these are the mothers. So ignore the column. The main things you need to look at are the particle ID, which is this first row, which tells you what you actually saw. So these numbers correspond to something you can look up in a table. So 21 is the gluons. These guys are unstable. And then you get down to stable particles, which are these with the zeros here. The zero has to do with the color connections. So 111 is a pi naught. And 211 is a pi plus. So you get a lot of 111s and 211s. And then here I get a 2,112, where I look that up, it's a neutron. You get a proton. But you can see from this that most of you are getting pions. And in fact, the typical event is almost all pions. So I think from this event, we have neutrons, particle, and number. Give you a sense. So we would have neutron. There were 25 neutrons, proton, 11 protons, a plus minus 18, pi zero, 124, and pi plus minus 387. So this is not atypical. This is actually a typical event that almost all of them are pions and you get a smattering of other particles. The pi naughts we write here as particles, but they're really very unstable in the decayed photons. And that's the dominant source of photons in the detector because the pi naught decays 100% of the time to gamma gamma. But the essential point of this is that the LHCC's pions. Sometimes you get more exotic things, but essentially the thing that it measures are pions. Andrea talked about pion as being this Yukawa's Maison that he predicted in 1932 and was discovered two years later. This was actually the muon. And it would have made his career to see the pion, right? I mean, it was his dream particle and it was very hard to make. It took another 10 years to make them in the lab and now we just make them constantly and there's sort of distractions from other things we want. So sort of yesterday's signals are today's backgrounds, but the pion's more so than anything else. So we know a lot about pion's because we've been southering them for a long time and they have a lot of interesting properties. Okay. So I have leptons and Higgs's and we have 10 minutes. Okay, let me talk about leptons. I want to talk about tauons because there were a number of questions about it. That's very collidery. There's not much to say about electrons and muons. Electrons. Well, the main thing is that they radiate a lot because they're light and you're bending them around the magnetic fields. They have synchrotron radiation and Brumstrahlung and they basically deposit all energy. Muons. Muons are heavy. Muon is 200 times heavier than the electron and so it radiates a lot less. It does weakly interacting and you measure its energy from momentum. So muon typically leaves the detector before it deposits all its energy. An electron will deposit energy in the e-column and stop. The muon will not deposit all its energy. You get a few hits and you try to bend it with the magnetic field. You measure momentum from the curvature of the track and from that you deduce its energy knowing that it's a muon. And that's why these detectors are so big because you need strong fields and a long way to bend them so you can start seeing them bend. Now let's talk about tauons. So I mentioned tauons before. Tauons are funny things because they're leptons but they look like Hadrons and that's because unlike the muon and the electron the tauon is heavier than the pion. So it can decay to pions and it does. Tau has M tau is 1.7 B. So it decays so the tau will decay to a neutrino and a muon or electron and the neutrino around 30% of the time and the rest of it will decay through a W, to a U and a D bar. I should say it's more, well, like 35. And again, so it's basically, we can do the same sort of counting, right? There's three colors of up and down that they can decay to here. So we get three, four, five so we get roughly 20% to each of the decay modes. So we get, there's some small corrections because the masses aren't negligible here so we can't just treat them as the same but roughly speaking you get 20% muons, 20% electrons and 60% Hadrons corrected to 35, 65. Tau will decay to pi plus and neutrino 10% of the time and that's like I've drawn here but also it can decay to a rho plus, so rho meson, which is a vector excitation of the pion and then the rho is unstable to decay to say pi zero, pi plus, neutrino and then the pi zero decays to gamma, gamma so we get gamma, gamma, pi plus, neutrino. So we get, so things like this are, we call these one prong decays and that's around 51% of the time. Alternatively you can have tau decay to the A meson so tau plus goes to A plus nu and the A will go to pi plus, pi minus, pi plus nu and this is 14% and this is called a three prong decay. So what does a prong mean? They're just number of charged particles so you see these towels the same way you would see bees you see a bunch of tracks, right? So towels are like they're leptons so you see you had a W that decayed leptons into towels you see just three particles it was a three prong decay or just one particle. It was just one particle that would be accompanied by maybe two photons and you could see the photons separately and the neutrinos you don't see so you either have one charged particle or three charged particles and those are ways you identify photons, towels. So you either have leptons or you have one prong decays or three prong decays and I can draw my pie chart here so we get 51% one prong, 14, 14% three prong and 35% leptons. So what do you look for towel tagging? You look for low multiplicity, one track, two tracks, three, one track, three tracks. You look for these kind of narrow jets with low multiplicity particles and the other thing you look for towels is isolation that because they're leptonic they produce from things like W decays which is also a leptonic decay. So unlike bees which are produced from hydronic activity from a gluon spring to BB bar pair you're not gonna have a gluon spring to towels. So if you have like a gluon jet it's not gonna have towels in it but it'll have bees and it'll have light quark jets. So towels you often see isolated. One of the main uses of this isolation criteria is in Higgs production because if you look for something like Higgs to towel towel which Higgs has a reasonable branching ratio to towel you would look for towels without any hydronic activity around it because the Higgs is uncolored and so is the towel. So you look for these isolated particles is one way to find towels and part of useful in towel tagging. But anyway, because they decay to pions they're considered hydronic objects. It's certainly not like a muon where you just get a clean track and you measure its form momentum completely. You always get neutrinos from towel decays because they always decay weekly and so you always have some missing energy and you can't reconstruct them completely. So when we say leptonic we always mean muons or electrons because those are the clean leptons and the towel on is kind of its own object that you have to do separate towel tagging for. It's kind of messy but actually towel tagging now has gotten to be very efficient. So towel physics is a growing area of interest with lots of applications, particularly to Higgs physics. Okay, so we didn't have time to do the Higgs but it would take another 20 minutes so I'm not gonna do it. But we did cover the rest of the particles. We covered all the particles up to 2012. Which I think is pretty good. That's all, I'll stop here. We'll get to you. Bye, see you.