 It's on it's on it's okay. Is it just for recording or is it also broadcast here? It's coming out of these speakers Just leave it there. I may use it. I may not Okay, that sounds good right so welcome back everybody. It's my pleasure to introduce the second Speaker the second lecture of today on collider physics is Matthew Schwartz from Harvard He probably you know already him is an expert in quantum field theory collider physics QCD You might know him of by start studying QC QFT on his book Part of part of you probably learn QC QFT from him and Well enjoy well, it's great to be here It's great to see that's such a lively audience. I enjoyed Yuval's lecture and I want to echo some of the points he made You know this only works if you ask questions, so if I'm saying something that you don't understand, please ask I'll also try to start from sort of basic things and And development sophistication depending on time and interest as we go along The goal the goals of my oh question already perfect You can't hear me. I could talk louder or we can move the microphone or maybe raise the volume Is that better yes, okay So again, I've heard that there's a sort of a mixed audience here people of different levels and different backgrounds How many people here are in masters programs right now? Okay, how many are in PhD programs? How many are in a bachelor's program? How many are not in any program? How many did I not mention? Okay, I Okay, so there's a good Mac most PhD students and some master's students I also want to get a sense of where you're all from. I've heard there's 50 50 countries represented here How many people here are from Europe? Okay, so that's maybe half how many from Asia How many from Africa how many free from North America South America? Australasia did I forget anything? Okay, so it's quite it is it's quite a mixed group and it's great to see all these people So I'm gonna give lectures. I was hoping my lectures is collider physics I'm gonna sort of give you an Overview of the interface between more formal things you might learn in a quantum field theory course or a particle physics course and how it's actually useful in practice to understand the where basically the sort of historically How we learned about the standard model in particle physics But but mainly what's going on now in particle physics? It's large a drone collider and how to think about Studying the large a drone collider from a theoretical point of view What are the kinds of things we can measure and what what can we learn about it? Which is really the interface between what we have now and hopefully what we'll have In the future And again, please ask questions as we go along. I'll stop at the end of course to take more questions But but the more questions we have during the lectures the better and and feel free also to ask me just general general questions about You know quantum field theory anything you want, but maybe those more general questions save towards the end of the discussion sessions Um So I have three lectures not seven So I won't be able to cover that much the the goal of today's lecture is to sort of give you an interview an overview of Colliders particularly the large a drone collider to talk a little bit about its design and why it's designed the way it is and how it works And then moving into the kinds of things that we can see at the large a drone collider And then I'll start talking about different kinds of particles We can see and how we see them and how to how to construct observables and estimate things that we're interested in So just some some references before we start the main reference for these lectures are a set of Lecture notes that I wrote for some of the Tassie summer school two years ago Oh This will cover a lot of what I'm actually saying Also, but give this to put on the ICTP a website, but you can look at here if you want more details About what I'm doing other other lecture notes. So this is there's lecture notes by tau han that I like And another good reference is the a book QC lighter physics Sometimes it's not a pink book because it has a pink cover. Anyway, this is a very comprehensive Summary of a lot of interesting ideas and collider physics like you have to QCD This is a set of lecture notes similar to what I'm doing with a slightly different perspective And this is more or less the kinds of things I'm gonna say Okay, so let's talk about let's get started by talking about the large a drone collider as you all probably know the large a drone collider is a Located on the border between Switzerland and France Near near Geneva. It is a 27 kilometer. It's supposed to the design the center of mass energy 13 TV It's gonna ramp up to 14 TV. It's currently on shutdown and ran until last fall Well, it was the second run and now it's a long shutdown until 2021 when it'll turn on again And what we'd like to understand is why is it so big? Why and and How would you design such a why was it designed the way it is? so To get started the most important concept in collider physics is the notion of a cross-section You guys know what what are the what are the appropriate units of cross-sections that we use in collider physics? Bar right. So what is a barn? So one barn and to the minus 28 square meters Do we know why it's called a barn? Don't know what barn is a barn is that big red thing that I haven't done farms And there's a saying that you couldn't your aim is so bad. You couldn't hit the broad side of a barn But this this unit comes from Enrico Fermi who was doing nuclear physics and trying to make Nuclear fission and a lot of it is bombardment of neutrons on Uranium and he had a problem that he couldn't keep the neutrons from hitting the uranium So sort of the opposite he couldn't hit them So the point is you have a neutron a uranium was enormous thing like the broad side of a barn That seemed to have a very large cross-sectional area But that's one way of remembering what this unit is. It's roughly the cross-section for Proton uranium 235 So it's basically there are neutron So it's basically the cross-section for a neutron to scatter off uranium with a kind of inelastic collision To kind of form something else So Using this can we figure out what the cross-section is the main thing the LHC is colliding is protons So if this is the cross-section for a neutron to scatter off of the uranium 235 What is the cross-section for a proton to scatter off a proton? well, well So a neutron from the point of view of scattering mostly it's done through the strong interactions So you can't tell the difference in a neutron And a proton and uranium you could think of as 235 quions, which are photons or neutrons So we can have this picture of a neutron coming in and scattering off of this blob of 235 nucleons and What we know is that the cross-sectional area which is roughly the the area seen by a neutron that's coming in Is is given by this unit of one barn So if there's 235 of this you could say that the The volume of this goes like 235 So then the area goes like 235 To the two-thirds So we want to know is what's the cross-section for a single nucleon scattering off of a single nucleon? So we're only sensitive to the cross-sectional area. So from this we can say that the proton proton cross-section should be the Neutron uranium cross-section times a relative area factor. So if the neutral cross-section is the cross-section for a Proton scattering times 2 a gen 35 to the two-thirds then we put the 235 on the other side to the minus two-thirds So what what is that? Well, this is maybe a hundredth. So this is maybe a 10 so we can work out the numbers here and it's Roughly so this is one barn times 0.0 3 30 millibars So this is the typical scale for proton proton cross-sections It's a little bit less than a barn so a barn is a neutron scattering off of a proton But for proton proton cross-sections were down by you know one and a half water to magnitude 230 So this is the typical cross-section at the LHC of course it changes a little bit with energy But roughly this is the scale for proton proton scaling it it changes logarithmically with energy But this sort of sets the units for for collisions So another way to estimate this is just to think about a cross-section So what's this when you know the size of a proton is how big is it like what's the radius of proton roughly? Point 8 Fermi what's a Fermi? So the radius of a proton is around let's drop the point 8 1 firm femtometer Which then to the minus 15 meters? the radius of a proton So roughly speaking the the area the cross-sectional area of a proton is going to be pri RP squared Which is 3 times 10 to the minus? 30 meters You get roughly the same the same number Calculating those different ways right so this really should think of it just classically as the cross-sectional area of a proton And of course cross-sections quantum mechanically represent a generalization of that because if it's a cross-sectional area When you when two things collide if this was within this area, it'll scatter for sure The quantum mechanically you only have a probability of scattering But that probability to have the same the right classical limit should be interpretable as a cross-sectional area So we generalize the idea of a cross-sectional area to the more abstract thing called a cross-section But physically it represents the same thing we just calculated in a different way So you can think of it as basically the cross-sectional area Of a proton So how do you think about this so now if we have a beam So the the large edge on collider will collide protons and beams Right, it's kind of individual protons, but you don't know exactly where it is what you have is the sort of the width of a beam Which is typically around Ten microns which is ten to the minus five Meters so the area of the beam is around ten to the minus ten Square meters and so if the the cross-section of a proton proton scattering is ten to the minus 30 meters What that means is if I have a beam and I have a proton coming in and say I have another beam The chance for the protons to scatter off of each other is if I know that it's somewhere in this area Which is the order ten to the minus ten then the probability of scattering Just classically is going to be the it grows with the cross-section. So ten to the minus 30 Square divided by the area of the beam That's the minus ten meter squared, which is around ten to the minus 20 So for the typical beam size, I'll need to have ten to the 20 protons go past Before one of them scatters, but that means that I need to put a lot of protons in the beam So typical broke protons will have Bunches of protons typical beam will have bunches of protons around ten to the eleven protons in a bunch And if you're scattering two of these you'll get ten to the eleven squared Which is ten to the 22 which is bigger than ten to the Always the minus ten to the minus 20 so you'll get around a hundred protons scattering when each of these bunches cross That's typical design of the LHC, but let's try to understand that a little better Why what how many protons do we need? Why should we like a hundred protons to scatter off of each other? What is the design because it's very difficult to get a lot of protons together so you do have a lot of scattering That's called the luminosity And so the question is how much what luminosity should we need for a collider like the LHC to be productive? That is what kind of cross sections are we trying to probe? So this is just the total proton scattering the total inelastic PP scattering cross section But of course, we're not interested in just scattering protons and breaking them apart We were once but now we're interested in more exotic things like producing W bosons or Higgs bosons Or tops or supersymmetry or all kinds of things and so to do that We want the probability of scattering we replace the total inelastic proton-proton cross section with the cross section for the thing We're interested So for example, what is the cross section for a proton-proton? Scattering into a W boson Anyone know what this is? Can anyone estimate it? No, I just tell me the answer but use something, you know So this is a weak process, right? This is the W boson represents the force for weak interactions of beta decay is mediated by the proton What is the rate for beta decay? I don't know the constant used to describe weak interactions Your G Fermi So what is G Fermi? You have to speak up. You don't have a microphone 10 to the minus 5 GEV to the minus 2 Right, but roughly what it is is it's it's you have proton-proton and you have a W boson being exchanged So you get a couplings here So it looks like G scared over Mw squared and that's that this is G Fermi up to some factors of 2 Which is also you can write it as 1 over roughly 100 GEV squared So this is 1 over 100 in GEV squared and if we try to convert that To units of cross-section into the minus 6 millibarne Which is 10 to the minus 9 bar For the subacutus which is also known as one nanobar Right, so that's a typical weak scale cross-section again to see this by eventual analysis. So this We said a proton is determined by the scale of a Fermi right a Fermi is the size of a proton Which is 10 to the minus 15 meters? It's helpful to think of that also as a scale. So this is the scale associated with it is 200 MeV inverse So 200 MeV should think of as the strong coupling scale So a proton is a GEV, but it's of order 200 MeV But this is a useful conversion that a Fermi is around. Oh, this is the board. I shouldn't write on because it's dark But anyway, this is a useful thing to remember a Fermi which is typical size of the proton is around 200 MeV inverse Which is the typical size of lambda QCD or the strong coupling scale And so these are these are useful units and so how we're going from 200 MeV to 100 GEV So we get a factor of 10 to the 3 and then we square it so we get 10 to the 6 So that's this 10 to the 6 right so the the cross-section for a weak process It's typically down from the inelastic proton-proton cross-section by a factor of a million So what does this mean? This means that we have to collide a million protons To get one W boson every time we collide protons together So so every time we have a bunch passed by we get about a hundred proton-proton collisions And we need a million proton-proton collisions in order to get a single W boson Now this was exciting at previous machines that you know UA1 UA2 in the early 80s were producing W bosons for proton collision But we want something rarer, which is Higgs boson So there's different ways to produce a Higgs and we'll get into them And maybe Yuval will get into them in his in his lectures So you have to know something about how to produce a Higgs boson to estimate this But this is also the Higgs boson is essentially a weak interacting process this the dominant production for a Higgs boson is A loop process through a top cork And then you get a weak interaction and generally when you have a loop things are suppressed compared to leading water Not because of factors of H bar, which is one but because of numerical factors of order pi So you get something of order 1 over 16 pi squared times sigma We scale me write this as G for me Typically so you get something like another factor of a thousand ten to the minus three nanobarns order of pico bar Again, these are just rough estimates They can be all by factors of you know ten or something and in fact there's other production channels the the the real cross-section Closer to 40 pico bars But it's a reasonable estimate and the cross-section with W is also a little bit bigger than a nanobar And again, it depends a little bit on energy and so on but but but the point here is we're down by another factor of 10 to the Three another fact of a thousand what this means is we have to collide a billion protons to produce one Higgs boson All right, and this is known I mean this was known for a long time it depends of course on the Higgs boson mass So before the LHC turned on we didn't know what energy to make it and we didn't know exactly what the cross-section is but no matter how you how you No matter how you do it no matter what the Higgs boson mass is Roughly speaking you're gonna need a round you want to design the machine to be sensitive to Things that are produced by one part in a billion so one in a billion proton collisions has to be an observable process so that roughly that roughly Gives you a sense of what we need for the large hydron collider so So given Okay, so we want There we want a hundred Higgs bosons All right, that might be a typical goal. So say we run for a year. We should be able to discover the Higgs boson What how many protons okay, so we already said that when we collide well So we have a 10 to the minus 20 Chance of the protons scattering when we when we collide them in a typical beam size Now of course one thing you can do is shrink the beam size to increase this number You can also put more protons in the beam We want to kind of know how to put together these factors to know how many protons we need to get close enough to each other To scatter that is what is the and then this amounts to the luminosity of the collide Okay, so let's just do some more dimensional analysis. So we said so we said Thanks to the nine Proton collisions One Higgs That's what we just calculated. That's because proton collision cross-section is around 10 millibarons and a Higgs cross-section is around 10 picobarons, so that's a factor of 10 to the 9 So typical we need to also factor in things like branching ratio of the way we actually see it So one of the Higgs discovery modes one of the most important one was Higgs to gamma gamma Which has a branching ratio of 10 to the minus 3 That means of every Higgs every we have any a thousand Higgs Produced in order for one of them to decay into this way that we can see it The dominant way that Higgs decays into B quarks and B jets and those are very hard to see and have enormous backgrounds So this was sort of one of the design goals of the LHC is to be sensitive to this, right? So we want a hundred Higgs is we need a hundred times 10 to the nine, but now we need a hundred times 10 to the twelve So let's say There's also efficiencies So efficiencies are things like you don't see all of the production So the Higgs might take a photons, but they go down the where the beam was you don't see them Or most of the time the LHC is not running right it only runs for some fraction of the year So you can estimate this and just you know we say it's maybe 10 to the minus one or 10 to the minus two something like that Right, so what we have we have a hundred Higgs bosons so Say 10 to the minus two for the Higgs bosons say 10 to the minus three for the branching ratio and To the minus two for efficiencies so we get 10 to the minus seven So we have to pay this the hit of 10 to the minus seven So this is roughly compensated by so there's roughly 10 to the seven seconds in a year so So this says that we need So here we said we needed 10 to the nine protons to produce a Higgs now. We're saying we need 10 to the 16 protons in a year Right 10 to the second year means we need 10 to the nine protons per second Right, so we have to design the machine to collide around a billion protons per second Okay, this is the key unit here, which is around one gigahertz All right, so so 10 to the nine is a billion so gigahertz is 10 to the nine per second So this is a typical design when they design the LAT. This is what they needed they needed to set it up such that they can have 10 to the nine Protons collide per second 10 to the nine a billion inelastic proton collisions every second which is a lot There's a question This is like how much the detector is running So for a typical year most of the time it's not running and it has to speed up you have to have the beams Scale them up so you only get 10% or you know 1% of the actual Time in a year actually running to produce these things But also it also includes other things like detector efficiencies and the detector not being on when you take experiments But also photons look good down the beam. It's just an estimate, right? There's some number of order that so maybe it's maybe we're down by an order magnitude here Maybe we're up by an order magnitude. We're just trying to get a sense, right? You want to be conservative about these things in order to make sure you don't miss the thing Okay, so how do we achieve this? Well, as I said the the LHC collides Protons and bunches so the way it works is you have this big beam, which is 27 kilometers around and It the way it works is you have protons and bunches where there's around 10 to the 11 protons for bunch So it's not continuously colliding close protons. It's climbing them these bunches and the bunches are separated by 25 nanoseconds so every 25 nanoseconds a bunch passes by another bunch So they have bunches going this way and also bunches going that way And there's interaction points of different parts of the detector. So atlas might be down here EMS They're around here and LHC B Would be over there and Elise might be over there. So there's around the ring. There's four four mean detectors With with slightly different designs But so the so what happens is these bunches of beams go around and then the beam is focused down to this 10 micron scale at different points around the beam normally it might be a millimeter wide and then it has its accelerating and then they'll focus it down using a Special magnets to collide them at the shortest possible scale And of course the smaller the beam spot is if you can get below 10 microns you can increase luminosity And so the goal is to do that at different different places So 25 nanoseconds. So this is 25 times 10 to the minus 9 seconds, which is also One over 40 megahertz So the rate for the beams to the the bunches to pass each other is 40 megahertz and what we're looking for is a gigahertz rate so the rate the beam crossing rate is 40 megahertz so 40 megahertz differs from 1 gigahertz by around a factor of 100, right? This means we need a hundred collisions per Bunch crossing Okay, so this is the typical design ideology and this is basically how it works You have these beams around 10 to 11 protons they collide in these Beam spots around 10 microns and each time they collide you have this factor of 10 to the minus 20 from the beam crossing And you have so 10 to the 11 squared. So we have 10 to the 11 squared times sigma Pp divided by Area of beam was around 100. So then you get 100 Pp per This is the calculation we did before Let's basically how it works. So you collide the proton. So, you know that maybe the early runs of the LHC You'd only have maybe one or two collisions per bunch crossing But when it ramps up you get to around a hundred the high luminosity LHC might see as high as 500 Collisions per bum crossing keep in mind that the higher this number gets the harder It is to actually see anything because you have a hundred collisions all at the same time that are basically indistinguishable So you get all this enormous background from the thing you want It's not just backgrounds you can calculate from this the same collision They're not like you know background to Higgs to two photons might be Just you know to a pion decaying to two photons But these backgrounds are you produce a hundred different pions from different protons colliding and you have to figure out Which photons came from which pions and that's a that's a big mess so When you increase the luminosity to get to get this high you also have bigger backgrounds from pile up from non from protons colliding from Different protons colliding in the same bunch you also have what's called out of time pile up where 25 nanoseconds is Short time it's short enough time so that you could have a bunch crossing and then things basically move out at the speed Of light right so but by the time 25 nanoseconds later You have the next bunch come in and your other collision hasn't left the detector the detector These these detectors are as big as this lecture hall or bigger right there are a hundred meters tall Right and so at 25 nanoseconds you can go around 10 meters So you go 10 meters and then the next collision comes you go another 10 meters So in a hundred meters you might have 10 different collisions populating through the detector at the same time So it's an incredible Computational challenge to sort this all out figure out which came from which time But but they have great timing information in these detectors to sort it all out So units so so typical unit that you don't always write a hundred collisions for a bunch crossing the typical units for luminosity are We talk about different kinds of luminosity they talk about the instantaneous luminosity so It might be something like two times ten to the 34 one over Centimeters squared per second so these are these are funny units and You could also write this as 20 Hertz for nanobar These are weird units have never seen them before it takes a while to process what's actually going on I think the easiest way to write this is 20 inverse nanobar per second So we've taken inverses of various things In fact, let me write it as 20 nanobar inverse So we typically talk about Integrated cross-section so the total luminosity Integral over time of the instantaneous luminosity And so this might have a unit of something like a hundred inverse femtoparms Right so in 2018 the experiments got around 60 inverse femtoparms either each these are typical units So this would say that you get 20 inverse nanobarms per second So a nanobar is 10 to the minus 12 and a femtobar is 10 to the Minus 9 and a femtobar is 10 to the minus 15 So you got to have to have a million seconds so roughly runs for a million seconds and you get 20 inverse Femtobarms 100 femtobarms you run for Five times 10 to the six seconds something like that which is down by you know I mean order magnitude from the number of seconds of the year But anyway, these are typical scales So this is people used to use this unit a lot more now you see this more commonly But you can translate between them without too much work. It's when you when you'll see them a lot you get intuition for it But this is a typical I think this is the peak. This was the maximum instantaneous luminosity at the LHC So but roughly I think 2018 they got around 60 and they got maybe 50 the year before So each experiment got maybe a hundred and so there's maybe 200 inverse femtobarms as the total amount of Luminosity recorded at the LHC and once you know this number you can translate back into cross-section So if the Higgs boson production cross-section is of order 30 picobarms There's something like that. So if if the if the cross-section for pp to Higgs 30 picobarms then in a hundred inverse femtobarms so a hundred inverse femtobarms is a hundred times 10 to the three first picobarms So it's 10 to the 4 10 to the 6 times 30 picobarms 10 to the 6 1 over 30 So that means we produce about a million Higgs. I'm so far at the LHC Right and of which so if the Higgs to gamma gamma is factor of 10 to the 3 We produce about a thousand Higgs to gamma gamma events right most of the Higgs is decayed a BB bar a lot of them We didn't see at all, but these are typical numbers, right? So we're well in excess of the hundred we needed to produce To see it but not that much next So the LHC is kind of doing what we expected if you have a process with a cross-section Three orders of magnitude smaller than the Higgs production cross-section of which there are plenty, you know producing I don't know Resonances and extra dimensions or or gluinos or something like that We're the cross-section to say an out of barn and a femto barn So something has a cross-section of a femto barn then with a hundred or some two barns you might have produced a hundred of them If it's an out of barn you haven't produced any yet, right? And so the goal for the high luminosity LHC is to accumulate around 250 inverse femto barns a year But maybe finally at the end of the LHC we might get two out of bars something like that a total of Then we need a new machine There's only so much you can do and again as you increase luminosity pile up becomes a problem these extra collisions of the same bunch crossing And so on so it becomes a map Wanted to say about this. Yeah, good. So So we have this this collision rate so they actually achieves around a gigahertz collision rate So gigahertz So you guys are familiar with this unit of gigahertz right probably from like the processes on your computers, right? Anyone know how fast your computer runs? What are the units megahertz gigahertz Hertz? gigahertz Right, okay. So so what is a gigahertz on a computer mean? It means it does a billion processes a billion operations per second, right? So that's like adding two numbers they can do that a billion times a second, right? But here we're colliding we're we're producing we're having a billion inelastic proton collisions a second, right? So you want to be able to process that with your computer that could do one addition a second, right? and that seems kind of challenging because you you could either have a lot of computers all working in in Common, but you need to do the computational challenge of Understanding the LHC data is significant. So we have roughly a one gigahertz a collision rate a Typical event is around one megabyte Right so that but one megabyte is a million bytes, right? So basically the information that you get out of an event which means recording where all the particles go the best you can Takes about a million bytes to record that information So if we have a billion collisions a second We need a million billion bytes recorded to disk a second if we're going to record all of that Which is of course impossible So we have a problem that we need to reduce the gigahertz rate down to something that's More manageable, right? Um So what we can record what can you estimate it like from your computers? How fast can computers transfer information? Can you do a megabyte a second? Can you do a million megabytes a second you do a billion megabytes a second? No, so what? What do you think the best computers in the world could do? If they do a billion megabytes a second Don't think a lot of course you had a billion of them you can right? But we don't have a we don't have room for a billion of them because we have the same detector Producing the same information you got to connect all the wires and be able to record that data coming from each individual wire So you can you can try to paralyze it about as you can but you can record typically around 200 megabytes per second Which is a lot faster than your computer can do but again this is within the context of the LHC So we started off producing a billion megabytes per second And we have to reduce it to 200 megabytes per second and that's called the problem of triggering so we need to reduce From 1 gigahertz 200 Hertz right So each collision is in so the units of megabyte are the units of events so we grant from producing a Billion events a second and we can record 200 events per second So how do we decide which of the billion events? We want to record to this and we have to do that at the hardware level mostly because by the time we recorded it we do the analysis We must have reduced it before we could do that So this is called the triggering problem. I don't know it's a problem But it's just something you have to do when you decide designed An experiment so the way it works is we have a trigger table And so you have to put cuts you can't record everything and you have to decide what you record and to the best possible You have to be able to decide that on the spot Locally in the detector because it's hard to process global information about the whole event at once So there's things like we look for one isolated electron PT Greater than 25. Sorry about the squeaking. So this means we can't record every event that has an electron in it But if we record we ask for a single electron to have more than 25 GeV Or we can look for two isolated electrons So together these add up to around 40 Hertz Right, so we get a billion out of the billion collisions per second of protons. We have 40 of them satisfy these criteria We can ask for one Photon greater than 60 GeV on which is another 40 Hertz But we can ask for muons and cows and jets And so on and so you figure out for each of these how many how many you get and the total should add up to around 200 and again it varies with luminosity so at higher luminosity you need to have weaker triggers Right, so for example if we're running instead of one gigahertz two gigahertz Then we have to cut these by a factor So we might say at so for example looking for jets Right that the LHC you have to require jets to have PT greater than 400 GeV Right if they're less than that then you have more than then you can handle right so already this gives you something like a 20 Hertz But if I run the LHC to run at 2 gigahertz or say I don't know 8 times 10 to the minus 20 minus 34 Inverse centimeters per second Then you might get you don't have to increase the cut on jets to be I don't know 600 GeV so these these trigger tables all scale with luminosity Anyway, so the lesson here is that you can't record anything and you need to know when you're doing analysis of the LHC You can't just make up some process and say LHC go find it because if it doesn't satisfy one of these triggers It's not recorded because they're just incapable of recording Everything and so the first lesson is when you're trying to see if here I have this model of supersymmetry or whatever can we see it you have to know that it's actually going to be seen and that Requires the LHC to satisfy some of this trigger and actually over the last ten years Theorists have come in and said listen you guys how you're not recording the right things And you need to modify this trigger table to find my model of beyond the standard model physics Whatever, but but there's what a sort of more active discussion among the experimental community who picked these triggers based on ideas from the 80s to adapting to more modern ideas from from theory About what should be seen and what what what can't be seen Are there questions about this? Well, I didn't write them down, but there's some so this is a you know two muons. I Just didn't write them, you know greater than 10 GV know a tau five GV I Mean they vary by experiment and they keep changing them with time so I don't have up to date The cuts on the transverse momentum. How are they decided? You want to take them as low as possible so you can keep as much as possible And you have to trade up so all these numbers have to add up to 200, right? So if I made this 5 GV this might be 500 hertz and then everything I recorded would be electron And I want to also be able to record other stuff right so the tradeoff is you want to record as much as possible and you know the guy working in the Electron group has to fight the guy working in the QCD group Fill over triggers and some compromise was made to record a little bit of everything Constantly questions that everybody always wants to lower them and you have to use physical what's most likely what's most interesting Based on the goals of different physics groups Yeah, good question Other questions about that So during the whole during a run Different triggers will be being applied to the detector Yeah, yeah, so during I mean even Right during When the LHC is colliding these every every 25 nanoseconds a bunch collides right most of the bunches they won't record anything right, so that's 40 megahertz already of Glitching rate so so you have to throw out almost everything from every bunch crossing In order to see to see anything but then out of the 40 megahertz you have to get down to 200 hertz So that means that one out of every I don't know million or so collisions You record and then you save everything from the whole collision. Oh, no, I mean wouldn't different groups want different triggers for Like these like a different trigger table for each one, but do they just run different ones throughout the no No, they're all running at the same time So if any of these are satisfied the whole event is recorded, right? So you set these once and for all and again this makes it so you record one in every, you know Million bunch crossing so you get down to 200 200 hertz right so remember the LHC is colliding a million protons every second By these beams coming in a million bunches every second and out of those you can only take two every second 200 every second of Events can actually be safe Right, so they have this set of table and some of them are done at hardware level So very low level using the silicon where the you know See if there's tracks for displaced vertices for be tagging triggers And some of them are high level things where they can reconstruct jets and look for the invariant mass of two jets to Be higher than something and so the lower level triggers have to be that the biggest reductions have to be done earlier on So it's sort of a staircase of escalating triggers of increasing complexity and now actually the new run when they're the redesign of the LHC They're putting new more sophisticated hardware triggers in so they can do things in the low level and look for more interesting But there's a lot of there's a lot of science and technology that goes into doing this at all And of course as computing capacity increases we can increase this from 200 Hertz to You know killer Hertz right and that helps a lot too and there's also the data storage right LHC records a water of a petabyte a Year of data and you have to analyze that I mean I didn't really talk about the storage requirements But maybe it's worth knowing so the LHC the data There's one copy of everything that's ever recorded at the LHC that stays at CERN and then another copy is distributed to Tier one centers all over the all over the world and then from those tier one centers There's tier two centers which are level of say at the city. We have a few universities in the same area We'll share and then there's tier three which is an individual university So it's a distributed level where you have one copy local as at CERN one copy distributed And then that data gets picked out for certain certain processes of someone at a university is doing you know A dime you on search they'll ask for the ones that satisfy the muon trigger and then record those so they don't need to deal With the petabytes of data all on their own And and you know transporting the data is actually a formidable challenge also When you treat when you trigger what actually gets written to tape at the end of the day The whole event so every part of the whole bunch crossing Like all collisions in the same punch crossing. So again, what you're recording. So, okay, what is a detector? So what do they actually see in so? So you'll have so here's a kind of a sketch of Atlas that has these kind of things at the end And then it's a big tube like that and then has these other end cap things So Atlas kind of looks like that So the beam will come in here One beam coming this way one beam coming in this way and again just for scale This is around a hundred meters and they'll collide right in the middle of Atlas, right? So again, there's these tensly 11 protons right and you might have a hundred of them collide within Punch and you have particles and most of these collisions are called minimal bias So the protons don't necessarily collide head-on and you don't have some hard scattering within the proton You just kind of it smash of the part and produces a bunch of soft pie It's a low-energy stuff that just kind of circles away in the magnetic field and nothing interesting happens But sometimes you'll get something interesting, you know, one out of one out of a billion times We'll get a Higgs boson and you might get something hard And so the way these detectors are designed is close to the beam. They have the silicon And silicon there's different levels of this There's the pixels which are the highest resolution silicon which is very close to the beam line So the idea here is that you measure charge particles you measure tracks of charge particles And so this is the most useful information because you'll see it then you have strong fields near the beam And you can see where the particle is you can measure what the charge is It's positive or negative but also from the curvature you can measure the momentum And there's a cascading level of complexity. So there's the pixels and then there's the transition radiation tracker And there's other silicon trackers all close to the beam that measure different things Outside of it you have the calorimeter. So you'll have what's called the e-cal Which is the electromagnetic calorimeter. So that measures charge particles basically it measures photons and electrons Minus and protons and so on anything charged Will show up in this electromagnetic calorimeter and then the outside of the detector is the well Then there's another layer here, which is the hydronic calorimeter. And so this measures protons and neutrons anything and pions Anything that has strong interactions and in the final stage this the reason it's so big is the muon system The muons are very weakly interacting and to see them at all you need well to measure their momentum You need to have a big enough field so that they come out straight and they sort of bend a little and you're looking for that curvature And that's you can tell the momentum of muon. So the problem with the muon everything else deposits all of their energy before it leaves the detector So so mostly well Mostly what the LHC produces is pions, you know, nine out of ten particles at the LHC are pions pions are either pi plus pi minus Which are essentially stable from the point of view of the detector They show up in the electromagnetic calorimeter about a third of their energy is deposited there and the rest of it deposit in the Hadronic calorimeter and they don't get out of the detector And they produce some set of protons and they produce electrons Electrons leave tracks in the silicon then they show up in the electromagnetic Calorimeter, but they don't show up in the Hadronic calorimeter But they're strongly interacting from electromagnetic point of view because they're light and so basically they deposit all of their energy to the Ecal the muons are weakly interacting and they usually produce hard So they produce some energy in the Ecal But mostly they just go out of the detector and don't interact at all in the Hadronic calorimeter and leave the detector So you try to measure their you figure out their energy because they leave you don't get all of it So you can't measure it from a calorimetry. You have to measure it from the track So you need a big enough system to see the curvature of the track especially for very energetic So that being said what the experiments trying to do is measure everything they can So the experiment is mostly pions with protons photons muons protons neutrons Things like that and you try to see for every particle identify it if you can figure out exactly what it is That's hard, but at least you can get all of its energy So the output this megabyte of information is every every Detector response right so every time a particle moves on the detector lights up They have timing information when did it happen and you need the timing information to separate one collision from the next And the energy information so how strong with the signal in different regions of the calorimeter So each calorimeter has its own circuit that determines what's going on there And the information recorded once any of the triggers past is all of the signals recorded from all the detector components of the whole detector Right, that's the signal the event and then offline You can process that and reduce it down to a set of you know four vectors or whatever you want to represent the information from the particles But but the thing that's actually recorded is the raw detector information from the different electronics used to measure the particles So either either record all of it or you record none of it. It doesn't make any sense to record some of it And that's the point of a detector like the LHC Can I ask where the bottleneck is in recording only 200 megabytes per second because we have storage media that are much faster Is this just because it has to be on tape or something? well, you have so How fast do you want right? I mean we don't know things that from a quarter gigahertz, right? So a billion megabytes per second. We don't have anything that can do that We have storage media that can record like two gigabyte per second two gigabytes per second Okay, so two gigabytes per second is still a factor of a million below what you need Yeah, sure. I was just wondering how it off and it's not it's not necessarily the latest technology It's a technology in the mid 90s when this thing was being built, right? Okay, of course electronics is upgraded and and you also have to be able to put it in the in the system right so you have to record the information locally so you have to be able to distribute it around you know I mean they need things for the timing information, you know the length of the wires that that's going through detector So so it's a challenge and there's a historical element to it, right? It's certainly for new designs. You can use the latest technology, but there's limitations as you know It goes exponentially with technology So you're you're stuck with the things that you have and the practical components of where you put it And what is the actual information that's coming out, right? I mean you're you're You know idealized processor that can transfer from your USB drive to your computer is a much more controlled system Than a Hadrona calameter where you can't have them any wires because that'll block the production of particles, right? So it's a complicated very constrained system that limits it to around To enter her. Okay. Thank you. So usually these experimental plots are Plotted on my son why a x axis and event on y axis, right? So what that mass and even what's an event is? I'm not sure I understand the question. What would experiment shows mass on the x-axis and events on y-axis usually the plots, right? So when they say events events is cross-section, right? So this is usually differential cross-section with respect to that To that observable so the question is what is When an experiment when an experiment plots something, what are they plotting? So typically you might have mass a mass square mass on this axis and events Right, but events you should think of as this is the cross-section Differential cross-section is back to the thing in the x-axis so events and cross-sections So the bigger the cross-section the more events they're directly proportional So there's some units here, which is usually the the total cross-section say the total pp and elastic cross-section Or the total number of vents when you just integrate over the plot So if you have something like this for a resonance when I sum so this will be a histogram Right because I put them in discrete bins When you sum over these number of events you get the total number of vents Which is the same as the integrated differential cross-section. So if I normalize this so so this integral is equal to 1 Or it can be equal to the total number of heads So the thing you calculate to figure out what this plot is is the differential cross-section And then up to a rescaling it gives you the same curve as they measure where they count the number of events and put them in bins And we'll talk about a number of examples of this when we talk about observable But that's the thing they're measuring. So this is the same thing I was talking about the total cross-sections, but then you can also ask the differential cross-section, which means Suppose I want the total cross the total cross-section for Higgs to gamma gamma might be a nanobar I'm sorry a femtobar and something like that But then if I asked for the photons to be have the the invariant mass of the photons that be within a hundred twenty-five GeV so this might be you know 125 to a hundred twenty-six of this bin And this would be a hundred and twenty 121 will be this bit so then I just count how many events did I get where the invariant mass of the photons was between 121 120 and that's the same as the differential cross-section with respect to the Two photon invariant mass for Higgs boson production, which I can calculate on a filter And then I would integrate that from the left side of the bin to the right side of the bin as my theory prediction And compared to the data, which is the number of events in that bin so up to a normalization That's exactly the same But we'll see some examples of this Questions Okay, so the next topic is what are the kinds of things that we Measure so this is this now. We know how that what the experiment can do. We've talked a little about triggers We want to know what is it what do we want to look for and how do we find different kinds of theories and different signatures of Different systems, so let's talk about Let's talk about the kinematics of a proton collision so protons come in Proton is roughly speaking three quarks Right, so you might have an up up down in a proton and then I have another one here, which is up up down But of course, it's not really three ups and a down. There's all the stuff holding it together Which are these gluons? So you can think of like gluons as kind of being there, too Right and you can also have virtual particles, so I might have a strange quark and an anti strange quark and there's some probability that anything's produced because it's it's a Roughly speaking a bound state of three ups and downs, but you can also scatter the gluons that are binding it but also virtual production of Strange quarks, right? So a strange quark is around 100 MeV Which seems like a lot. It's a significant fraction of the energy of a proton but it's not a significant fraction of the energy in the collision so for colliding things at 13 trillion electron volts the fact that you have 100 million Electron volts isn't a big deal and so that energy can easily turn into the production of Strange anti strange pair. So essentially you think of a proton as a big soup full of lots of particles some are some are More more likely to be found than others But but anytime you collide two protons what you're expecting is that not the whole proton collide, but you're hoping that that one Particle say it up from here, and I don't know a strange from there My collide let me let me pick a different particle. Let me say up bar There's an anti up quark that might my collide So anytime the proton collides basically a lot of things are colliding at once But almost all of that carries a negligible fraction of the proton's energy But sometimes there's a probability that you get a hard scattering where some particle in the proton carries a significant fraction of it But in a significant fraction doesn't have to be very significant So if you want a hundred TV Higgs boson out of a 13 TV collision, right? That's a factor of a hundredth Right, so it only has to be one out of every hundred Of the energy of a proton goes into this And this together, but it could happen, right? And so what you end up having is two quarks might scatter And then you have whatever your your Feynman diagram is for scattering of the partons within the proton And the thing that tells you the probability of finding a Corp really given energy is called the parts and distribution function I'll get to those In a minute, but the main point is that What you're doing is you're picking out some particle within the proton that carries some fraction of the proton's energy, right? So the proton might have momentum Pz is six point five TV going this way and energy would also be six point five TV and this proton would be coming with Pz is minus six point five TV and energy is six point five TV But this this quark inside it would only have some fraction of that, right? So this guy might have Pz is a hundred TV Right and energy is a hundred TV something like that, right? And this guy might have Pz From my science here is say minus 50 TV, right? So this is a hard collision. This is a very small fraction of the proton's energy is in that particular quark Yet from the point of view of the partonic vision. It's a very high energy collision With the center mass energy of well a total energy of a hundred fifty TV But the point is typically these are not going to have the same energy, right? And they're not going to have the same component of momentum And so that means most collisions in at the LHC will be very asymmetric so most of the time the net momentum of this so the total as Pz is 50 G Right, so the whole thing is going off this way. So what that looks like is you have proton collide And then you might end up with two particles going off like that Right, so they're very often asymmetric, right? So a typical collision. Well, I should draw it in the frame So you might have particles one going this way and one going that way, right? So it doesn't look like momentum is conserved But that's because you're having an asymmetric distribution of the momentum of the original proton going into the parton that collided And then when these partons collide momentum is conserved here But the net momentum is still is still boosted in a particular direction All right, so so the point of view is That this frame what we're not so I'm interested in is the collision in the in the lab frame What we want to do is instruct things that can measure this independent of of the relative fraction of the protons energy that went into it But all I care about is a partonic if I know what the energy is of the partons that were colliding I don't really care anymore about what happened to the rest of the proton So what that means is that I want to construct observables that are independent of this of the net component of Z momentum in the partonic process right in other words we want observables That are boost along Z direction, I guess I should also mention my coordinates here, so Typically we use Z this way and we'll use theta is the angle with respect to Z And then there's the azimuthal angle, which is around this way, which we call phi So this is the polar angle the azimuthal angle and and z so we decompose things into that direction right So some of these things are already boosted variant along the z direction particularly the azimuthal angle It doesn't matter what if I give the whole thing more momentum in the z direction the azimuthal angle will be the same But then the polar angle will change so and of course the z component of momentum will change Okay, so what do I mean by this what is boost invariant? What is a boost? So a boost is So I have some momentum a for momentum and under a boost in the z direction I have to act with a boost generator So what is this boost generator so K? Kz is like a rotation, but it's a four by four matrix that looks like cosine beta zero zero hyperbolic sine of beta Zero zero that tells me how things transform more explicitly the energy goes to energy times cosine of beta plus qz times inch beta and Qz goes to Z crash beta inch beta So the energy and the z component of the momentum mix up and the x and the y component of the momentum say the same okay, so Okay, so what this means is that? Qx and Qy which are the components of momentum in the transverse direction Say this is y and this is x the components of momentum in those direction are boost invariant So you can just measure those and it doesn't matter the how much fraction that the part on how to the original proton energy It's independent of that right there they're boosting variant But the z component and the energy are not so we want to do is take a different combination of the z component energy That isn't variant right so it's not qz and not e but because there's a relation between hyperbolic cosine sine cosine squared minus squared beta Is one the the there's some combination of this that's invariant so let's see let's see what it is So motivated by this what we do is we construct something called Well, let me just write an equation so if we consider e Plus qz divided by e minus qz How does this transform? So this goes to e Let me write Call this c and call this s So we get e goes to e times C and then qz with qz plus So So we get a c from here and an s from there so c plus s plus qz times C plus s On the other term right so this is again. I'm just e goes to e. Yeah, I shouldn't get entangled e c plus qz s plus C plus e s divided by the difference between them e c Plus qz s minus qz c minus e s So the top is proportional to the product of e plus c plus s and the bottom is the product of e Minus qz Minus s Now let me multiply the top and the bottom by C plus s and then I get c squared minus s squared, which is one in the denominator So again, I'm just gonna multiply by c plus s over c plus s. So I get this is equal to e plus Qz divided by e minus qz I'm c plus s squared Right so what that means is that this quantity this ratio of these different combination Scales by a constant independent of what e and qz are so no matter what they were originally I know if I boost I'll just have a factor that I can compute based on c and s and In particular if I take the ratio of this quantity with this quantity for say a different particle Then that ratio will be entirely boost independent, right? So the ratio of these things are boost independent rather than taking ratio what we like to do is take sums and differences So if we take the logarithm of this A ratio becomes a difference So this modes it motivates us to define Rapidity y is defined as One half times the logarithm of e plus qz Three minus qz so under a boost y goes to y plus A half of logarithm of c plus s squared so then people log of them through the square it is just the logarithm of c plus s All right, so just shifts under a boost the rapidity shifts and therefore Differences of rapidity So y1 minus y2 Also known as delta y Right so what that means is if I have two particles in my then say I have an electron in a muon If I ask me what their angle is their their polar angle in the z component momentum It's not very useful But if I take the difference between the rapidity of the electron the rapidity of the muon that becomes a more powerful Kinematic quantity because it's independent of the longitudinal both that is independent of what the fraction was of the original proton Their momentum that went into it So I don't care about the overall z component of the electron muon pair And therefore distributions of this will be much more representative of what's going on in the underlying physics So we almost always use rapidities to describe the angular distribution of particles At a drone collisions, but keep in mind the rapidity itself is not boost invariant It's only differences in rapidities that are boost invariant But often it is differences in things that we're interested in anyway So a typical process thing we might calculate is if I have two particles here say Right, so I this one would have I can defy bit by say PZ and theta and Phi And this one will be one one one and then PZ two theta two Phi two What I do is I change two coordinates, which is PT Which is the transfer momentum, which is PX PY Because PX and PY themselves are boost invariant the transverse momentum is boost invariant So this is just a two vector for orthogonal to the beam We also can talk about So we can talk about Delta Y and we also talk about Delta R Which is the square root of Delta Y squared plus Delta Phi squared so the azimuthal angle is the angle between So 10 Phi is PX over PY So Phi is the angle the azimuthal angle in the XY plane So that's boost invariant because P and X and PY are boost invariant and rapidity is boosted differences and rapidities They're boost invariant so this Delta R becomes a kind of angular distance between two particles in the in the transverse plane So this is a very useful quantity because it's boost invariant So we'll often talk about the if you want to know how far apart things are an angle The what we mean by that is the difference the root mean square of the rapidity difference in the azimuthal angle So that's a quantity we'll be using a lot as well So Excuse me Yes I saw in some analogies of So the rapidity Okay, so now let's talk about a special case which is massless particles So the massless particles Have their energy is equal to the magnitude Of their momentum remember M squared is E squared minus P squared So if the mass is zero then the energy is the magnitude of the momentum So then the rapidity for a massless particle is one-half log of E Plus Pz over E minus Pz How do we think about this? So let's draw a little triangle here So we have our our polar angle here Pz and the transverse momentum and the energy is the magnitude of The total momentum so the magnitude of the total momentum is Pz squared plus Pt squared So that's P the magnet the length of the hypotenuse of this triangle is Is the total momentum which is also the energy So remember Pt here is squared of Px squared plus Py squared So that means that cosine Theta is Pz over E so here I can write this as One-half log of 1 plus Pz over E Over 1 minus Pz over E So I can translate it to cosine theta Which is one-half log of 1 Plus cosine theta over 1 minus cosine theta Which is one-half log of Two cosine squared theta over two over two sine squared theta over two Which is log so I've squared the two's cancel and the squares I could pull outside and cancel the half So we get log of the cotangent of theta over two Okay, so for massless particles We have this special relation that the rapidity is in one-to-one correspondence with the polar angle, but this is a little weird, right? because We said the rapidity is boost invariant, but the polar angle isn't boost invariant. So how is this consistent question for you? It's like we have a contradiction because this thing changes under boost but the rapidity doesn't if it has massless particles Well, that's one possibility It can what's that? Invariant The difference is still boost invariant. That's right. The difference is still boost invariant, right? So I never said rapidity was boost invariant, right? Well, we said it was the differences in rapidity or boost invariant So there's no contradiction here because rapidity isn't boost invariant and neither is theta, right? But the differences in rapidity is will be well, they're not gonna be differences in Theta's They're gonna be some complicated combination and that complicated combination happens to be boost invariant So what that motivates us to do is Define another quantity So we define pseudo rapidity rapidity Ada is defined as the logarithm of the cotangent of Theta over 2 Right, so massless particles Implies that Ada equals the rapidity, but for massive particles, they're not equal But importantly this so this quantity, so Delta Ada Are the changes let me ask you are the differences in pseudo rapidity boost invariant So in general, they're not the differences in rapidity are boost invariant for massless particles differences in pseudo rapidity are boost invariant for for massive particles differences in pseudo rapidity are not boost invariant is Boost invariant Only Or m equals zero, otherwise, they're not so you should so But nevertheless at the LHC almost all the particles are effectively massless as I said They're almost all pions and pions are really mad you can think of them as massless I mean the mass is so small compared to their energy typically that we can treat them as massless So pseudo rapidity becomes practically equivalent to rapidity in almost all situations except when you talk about something like the rapidity of the Higgs boson the rapidity of the W boson right which their mass is Significant or the pretty of the top quark and then you have to be careful mostly we talk about the rapidity of their decay products So we won't talk about the rapidity of the Higgs itself We'll talk about the rapidity of the photons to which a Higgs decays And then the rapidity and pseudo rapidity are used interchangeably But the important point is that rapidity Is a kinematic quantity while pseudo rapidity is Geometric quantity right so pseudo so rapidity is defined this way in terms of Have things having to do with the four momentum the energy and the momentum While pseudo rapidity is defined in terms of the polar angle as measured in the lab, right? So people use them interchangeably. They're only interchangeable in the context of massless particles For massive particles are different but things are effectively massless. So it's usually a good approximation To give you a sense of what pseudo rapidity looks like so we define at theta equals zero Actually, we usually call this data is pi over two right on the one that you can't see So typically so this will be eta equals zero theta is pi over two while over here is a theta equals zero Eta equals plus infinity and this is eta equals minus infinity Theta equals pi so theta is going this way And rapidity kind of goes out from both directions Right, but so typically you'll have something like eta equals one So rapidity of one pseudo rapidity of one corresponds to theta is 40 degrees. So this is 40 degrees Eta equals two This theta is 15 degrees and then down here Eta equals four Theta is two degrees the electric detectors only go up to pseudo rapidities of five Which is around one degree or less than one degree so even though five maybe doesn't seem like such a big number In terms of angle is actually very very close to the beam line less than a degree The best calorimeter is go down to eta of three, which is about ten degrees. So the the the tracker for example only can measure particles in the in the region up to a rapidity of around a pseudo rapidity of around three, but typically these are the units we're using so so most of the The highest resolution information is between rapidities of plus one and minus one Which is angles around 40 degrees, which is you know about half of everything you can you can see But keep in mind that most collisions with the LHC have one small X and one large X that is they're very very boosted So you'll have most of the stuff going this way or most of the stuff going that way However, the highest energy stuff will be more likely to have be roughly central So like digest production at a TV will almost all be in the central region and we'll get into some of that more when we Talk about parts and distribution functions Okay, so that's all I wanted to say about the kinematics of the detector. I guess next time we'll talk about some more observables and Get into how we see different kinds of particles So let me take some some questions in the last few minutes and we can continue it in the discussion session as well. Yeah Would we show it? What about pseudorapidity? Pneudy is equivalent to angle the relation between pseudorapidity and polar angle is this one So you know exactly where something is in the detector. You can tell me exactly what pseudorapidity. It's at This is you just take the logarithm of the cotangent Which is roughly linear in the angle near 8 equals 0 for example? Pneudorapidity equal to 2.5 There is that over here Yes, in a detector in end cap or barrel Or the middle of detector. What's the question? That's true. 8 of 2.5 has a region in the middle and also goes into the end cap Yes, I want to draw a detector and You want to see where the different regions are? Well, let's try to sketch that. I mean, I it's hard to draw But I can show you a slide of it. We can take one up. Actually, I might have one here Let me see if this thing is still working. That's not working Think my battery died It's right. I'll show some slides next time. Nope. I'm out of battery No, it's okay. I'm out of battery. It's not gonna work I mean, what can I say? The central region goes up to ability around three is the is the kind of cutoff for the highest resolution stuff Right the barrel, I think 2.5 starts starts probing the end cap for Atlas at least boost generator Why am I finding boost to me? Boost generator because we're interested in Lorentz and Berench quantities, right? Yes, it's a relativistic collider. Yeah, we want to know under a Change in the overall Z component of momentum How does it affect the energy of the particles, right? It changes by Lorentz boost. That's what I mean Actually just wanted to understand like why you were using hyperbolic functions. Why why do where do they come from? Yeah, so they they're they're their variances of the so if I look at something That's Lorentz invariant like the momentum or the differences So suppose I want something like the the invariant mass of a quantity So I have the two photons and I want to look at the Higgs So that's the momentum of one minus the momentum of the second one squared Right so that difference in mass squared is Lorentz invariant quantity Which means the invariant under exactly that transformation that I wrote down with the hyperbolic functions so it's a generalization from rotations, which have signs and cosines to Variant when you have energy transforms with an opposite side because it's a the signature of the Macaulay metric is different from the Yeah, so I see that the definition here angular separation squared is like delta phi squared plus delta eta squared And I was wondering if there's like a good theoretical reason to weight them by the same number because it is like some complicated So it's not really it looks complicated But but actually if you expand in the central region, this becomes theta minus pi over 2 Plus higher out of things so this is it's really in the central region it becomes linear Right and that's mostly where we use it. It's linear over much of its range and it starts to get non-linear near the end But it's basically the same right I mean you could take any other function of this and it would be also a very right, but we choose this function so that It has a nice property Yeah, great question. I should have mentioned that there's a question over here. Yeah third from the top Tracker and Ekel have coverage up to eta equal to three So can I say that charged particles are measured up to rapidity three You can say that the tracks from the charge particle I measured but there's also sensitivity to other features of the charge particles Like the energy right so the calorimeter depends what they are like a proton will show up in the hydronic calorimeter Which is higher rapidity is also the forward end caps which have which have calorimetry information as well Which go to rapidity of five? Okay, so we can't measure the tracks so we can't know the Momentum we can't see the curvature in the magnetic field, but we can still measure the energy but we just don't we can't tell necessarily if it was a Neutron or a proton right they might have the same energy deposit, but we can't tell if it was charged or not because it doesn't leave a track We just have less information also the resolution the spatial resolution is less the best spatial resolution I don't know exactly where it went to help that I have a track they'll eat cowl grids are like this big right So it depends where you are in the forward region. That's that's a very large region of rapidity coverage Right, but in the central region you have very fine resolution because of the tracker, you know Usually for photon rapidity is taken to be around five Usually photon rapidities are given Usually we take it to be around five for photon well photons only tracks right so you don't have to worry about the limitations from the silicon on the photon Right, so that again the photon is all from the electromagnetic parameter Which we do have sensitivity up to rapidity of five and roughly speaking everything works up to infinity five except for the Tracker, which is basically rapidity of three, but it's the strongest in the sense of region rapidity of one You have the highest resolution a minute to grades as you go out And again, this is because we're mostly interested in high-energy stuff, which is mostly central And so we can we can compromise tough in the forward region, but for really inclusive processes We need the forward region and you can't do everything any more questions No, I just wanted to ask like how is this concept useful like just relabeling of the coordinate theta How is how this concept useful like it's just like a function of theta So I can just measure measure the angles right why use rapidity instead of theta Yeah, because it's boosting very because differences in rapidity of boosting very and differences in angle art When you take this nonlinear function, then you can take a difference between two things and that's boosting variant But the difference in polar angle is never a boost invariant. Oh, it's useful for like making plots and distributions, I mean suppose I You know so if I have two particles that I look at their difference in an angle, right? So this would be say theta one and theta two Right that difference in Delta Theta if I plot as a function of Delta Theta. Yeah, I mean, I Don't know what it's gonna look like might look like that or something Right some crazy thing, but if I look at the rapidity difference, this might be sharply p'd right So I might have the same plot for Delta Eta Might have a you know localized in one difference if they came from say it was a decay of a heavy particle They had w decay to two particles or a z right if I look at the the angle between the two particles that doesn't give me very useful information, but if I look at the the Rapidity difference this might be sharply p'd so if I if I knew the energy of the z the pizza transverse momentum This rapidity would give me very clear information, right? And because it's boosting variant this thing would change if the z was produced with more z momentum Then this thing would get shifted. So this represents that smearing due to taking a longitudinal momentum fraction But there's no smearing here because it's invariant of that boost So this becomes a much more powerful quantity. It's the same with differences So the the typical distance between these I look at Delta R between the decay That's a useful quantity and it's peaked around a certain value just like this. Well, the theta's not I don't focus if I instead of this if I looked at Delta of Logged in log of tangent of theta it would be right because that's just the cotangent of theta So if I take a nonlinear function, I get this nice structure Since you mentioned inclusive cross sections Okay, maybe briefly comment on the difference between an inclusive decay rate cross section an exclusive one and a differential one Well, it's just that the inclusive one is integrated over the differential one over everywhere it can go So the useful for different purposes, you know, if you want to know How many Higgs bosons I produce I can just calculate anything that has a signature of a Higgs boson But if I want to know the spin of the Higgs boson I have to look at a differential cross section in the angle of the decay products And that might tell me about the spin the total number of Higgs bosons wouldn't tell me that so depending on your purposes You sometimes want exclusive processes where I put restrictions and sometimes I'm on Inclusive processes where I just count and we say that exclusive ones are harder these days or harder Yeah, harder well to calculate, but I don't calculate. Yeah. Yeah, well, I'm not talking about calculating anything yet It depends sometimes exclusive ones are easier to calculate because you're doing one less integral And so it's often easier to calculate something Differentially than it is to calculate inclusively, right? If it's differential enough that I could just evaluate the matrix element, and that's fine I don't do any integrals at all. That's the easiest thing But it's not very useful because it's just differential in all the possible phase space points so typically doing phase-based intervals as hard and The more you do the harder it is, but it's a trade-off You end up introducing more scales, and so you have sometimes they get logs over those scales that make it hard So you can do the integral for the exclusive process But just not a good approximation to the all-outers thing because perturbation theory is breaking down So there's a lot of challenges involved in both All right, now if you calculate a total cross-section with a simulator like mad graph, right? It'll calculate the total cross-section by calculating the exclusive one and integrating, right? So there obviously it's easier to do it exclusively because it does one less integral I don't know what you're doing. All right. Okay, this tank met again