The Secret Life Of Quarks ▸ KITP Chalk Talk by Will Detmold

so thank you thank thank you for having me here for this talk so yeah as Greg was saying you should feel free to ask questions now or later and I can put my email here if you want to ask them offline that's fine um sorry I'm gonna spend the next 45 minutes or so telling you about the secret life of quacks so I'm going to tell you what quacks are and I'm going to tell you why they're extremely weird things they are very very quantum things and there the way they behave is very current counterintuitive but over the last 40 to 50 years we've managed to really piece together what what the reality at the scale of quarks is so so to set the the scale for this talk I have this picture here that really shows ok we're living up here at kind of macroscopic scales and we go down beyond microscopic beyond molecular scales down to atomic scales where we have a cloud of electrons zooming around a nucleus the nucleus is made of protons and neutrons and those protons and neutrons have substructure themselves so it's really this sub structure that we're going to spend today talking about and so this is a very simple picture of what a proton looks like it has it's not just a single thing it has things inside it and those things go by the name of quarks and this is you I hope you see in this talk is a ridiculously simplistic picture of what a proton looks like that it just has these three things inside it's in fact much more complicated so we're down at scales I should put a unit on this ruler actually this is a very nice logarithmic ruler and it's in units of meters so we're talking about here down about what are called femtometer so 10 to the minus 15 meters extremely small the dynamics that happens here these these things inside the proton moving essentially at the speed of light so really the dynamics that's happening here you can take this distant scale 10 to the minus 15 meters and ask how long does it take a quark to go across this nucleus this proton or a nucleus and it's traveling at the speed of light and that gives you basically 10 to the minus 25 seconds so these are extremely fast moving things extremely short time scales that are involved and that's the that's the world we're going to talk about today so this is the world of the standard model this is really the way we understand matter rotates at its shortest distances we have a theory of that and this is called the standard model and the standard model is something called a quantum field theory so you've mentioned most of you have heard of quantum mechanics so quantum field theory is sort of a generalization of quantum mechanics and this particular example of a quantum field theory is called quantum chromodynamics or QCD plus another quantum field theory called the electroweak theory and what these theories describe is really everything we see around us so they're made up of particles so that's the outer rim of this this nice pie chart here so we have various types of quarks so up quarks down quarks strange quarks charm quarks bottom quarks and top quarks and the order I went through that is kind of perverse but is really related to how big those quarks are and then down the bottom we have what we call the leptons so we have electrons and neutrinos and then various cousins of electrons called muons and Tau's those particles interact with various different forces so there are electromagnetic interactions these are governed by the photon which we have a simple gamma 4 and there are the weak interactions so the W and the Z bosons telling us about weak interactions and then the strong force or QCD is the interactions they are determined by gluons these are the things that hold quarks together is why they're called gluons so as well as that I'm sure you've heard recently that the Higgs particle was discovered about four years ago now and this Higgs particle what it does is it gives mass to all of the particles in this in this chart here except for the gluon and the photon those particles remain without any mass at all but the Higgs provides the mass for all of these however it doesn't provide mass for for everything in this room that actually predominantly comes from the strong force from QCD so what we're going to do today is really focus on QCD so we're going to talk about quarks and gluons because those are the only things that participate in the strong interaction okay so the first thing that we can you can learn about quarks is that we never see them okay so when we build very very large particle physics experiments we try and look at the smaller scales that we can and we try and probe nature at its most fundamental level and we get these we get building very complicated and expensive particle detectors we get in the 1970s at least we've got pictures like this from what are called bubble chamber experiments and these lines here correspond to a particle moving through through some region of in this case a superheated high liquid hydrogen and as it goes through it basically forms little bubbles and that's what this this is and then you can take a photographic image of those so this each of these lines corresponds to some particle moving through the region that this camera was looking at so this was in the 1970s nowadays we have the Large Hadron Collider in CERN and there they expect the experiments that that look look at the shortest interactions or even more complicated this is the CMS experiment and and this is basically a computer readout of what the CMS detector sees as there is a collision of particles each of these lines corresponds to a reconstruction of where the particles came after us being after the two protons were smashed together however none of these lines is a quack yes right so the scale of this one here so this is basically a picture of the entire is sort of a picture of the entire CMS detector which is something that is about the size of this room actually completely filling this room the CMS detector may be even a bit bigger and yes so this so this blue region is that the actual physics that we're really interested in the very microscopic physics is happening right at this point here and then the particles are streaming outwards and the detector itself is big but everything is really focused down on this tiny little region so over here these this is somewhat smaller this region so this was done in fact this experiment here happened before I was born so I would say this is of order and a meter scale basically these these the type of detectors they were a big tank of liquid hydrogen that was heated up by using a piston that basically made it go supercritical so that if something came through it would form but it would basically form bubbles okay and so you have a big tank of liquid hydrogen making it even bigger is pretty dangerous because hydrogen has the problem that it burns so so really this this kind of technology turned off pretty quickly and we use a very different technology in current detectors okay so yeah as I was saying none of these lines are actually quacks okay what they are is either leptons so the electrons or muons or they are complicated combinations of quarks so because the strong interaction is very strong what it does is it takes quarks and gluons and kind of clumps them together and all we see is these bound what we call bound states of these things these things that are stuck together and over the over time we've seen many many many different types of these bound states many hundreds of them and in fact every two years what's called the particle data group releases a book which is about 1,500 pages now there's a catalog of all of the particles that we've seen in all of their properties okay and this is the guide to the zoo of particles so one of the triumphs of modern physics or physics in the 1960s at least is that this zoo of particles many hundreds of them were able to be classified in a much simpler structure and so this was done by Murray gell-mann and various other people and this this is this classification of all of these particles was based on thinking that the protons and the other particles soap ions and neutrons and K ohms and things these were all made up of more fundamental objects and these are what where the name quark first came from and the way this classification works is that all of these hundreds of particles you can think of them is in two categories you can think about nez ohms which are quark which are a combination of a quark and an antiquark and baryons which are combinations of three quarks so just this one example we have what are called the hyperox so these are baryons and you can see two particles which this is the proton and this is the neutrons so these are ones that are probably familiar but they come along with six other particles there are sigma baryons lambda baryons and then these fiber ions which are commonly called cascade baryons so what what go man and others realized is that these particles say for example the proton and neutron are very similar so the mass of the proton and the neutron are almost the same so the mass of the proton in kilograms is one point six seven two six two two times ten to the minus 27 and the mass the neutron only differs in this fourth digit okay so these are very close to each other similarly that the three different sigma baryons all have masses that are very close to each other and these two have masses that are very close to each other and then if you look kind of not along the rows but along these diagonals of this of this picture each of these particles have electric charge one these have electric charge zero these have electric charge minus one so there's a lot of symmetry in this arrangement here and it's really the symmetry prints all that led Gillman to actually be able to classify a very complicated book of stuff into much more much more simpler units so we'll come back to these these different these Neutron and proton masses in a little while I just want to convert them to units that are more convenient for particle physicists really these these units here are basically kilograms but they're called mega electron ports over c-squared and these are just units that we more commonly use so in terms of this there is a small still this small difference between the proton and neutron masters and I will come back to this so well I said at the start that a proton was not this very simple picture of three quarks and then I just told you well protons are three quarks well it's sort of right and it's sort of wrong so let's let's try and ask this question and we can actually do this using experiment and so to do that I need to introduce something and this is called a a quark distribution function okay and I'll introduce this very slowly I hope so this is something Q of X okay two function of how much momentum a quark inside the proton is carrying and we write it in terms of a momentum fraction X and so X is going to be something if a quark is carrying all of the momentum of the proton it'll be one if it's carrying a tiny bitter to be almost zero okay so X goes between zero and one and what Q is going to tell us is if I look at a proton how likely is it that I that I do an experiment and I see it I see a quark inside there carrying a particular fraction of the momentum so let's think of an analogy for this and it initially is kind of a looks like a bit of a silly analogy but it's actually not too far from from a good analogy so here we have a fishbowl with a bunch of fish in it sitting on a skateboard okay and so if we give it a push it will start moving so we're going to think of this as our proton so I'm going to call this proton momentum so if we have this moving with some velocity this way then momentum is just the product of the mass times velocity right and so this this fishbowl has momentum in this direction and what we're going what we really want to ask is how is that momentum made up of the components of this fishbowl system okay so this this fishbowl is not just a one thing right these fish are going to be moving around inside the fishbowl so what I'm going to do is is basically neglect all of the the actual water in the bowl and just talk about them the mentum of the fish but so let's say this fish here was swimming in this direction inside the bowl and then we make the ball move okay so now this fish is going to be moving quite fast in this direction and so it's going to have it's going to have a significant component of the momentum of the whole thing is going to be because this fish is moving this way so we can write this as saying that this fish has a momentum and really I only need to talk about momentum in one direction here so I'm just thinking about going across the screen so the momentum of this is some fraction of the total momentum call it x1 okay and we can do the same thing for all of these other fish this guy swimming backwards so his momentum is he's swimming this way but moving this way even faster so he's just got a little bit of a momentum in that direction okay but now we've really broken down the momentum of the whole system into the components of it okay and if you think about it you see that okay if this is all of the Constituent and remember I'm neglecting the water if this is all of the Constituent then all of these momenta should add up to the total momentum right and what that means is that sum over all of these X's x1 plus x2 plus x3 plus x4 plus x5 has to be 1 okay so that we get the total okay so we can do this we can do this little experiment once we can basically take our take our fishbowl set it moving and then look at what the fish are doing and then we can do it again and the fish we're doing something else right and we can keep doing it many many times and we'll get it basically a distribution of what fish like to be doing in fish bowls on skateboards which okay not a question that you would normally ask that's what we're doing okay and so that let's just make a histogram so basically what I'm gonna do is say okay this this guy has x1 maybe he's got x1 and say point 6 okay he's carrying quite a lot of momentum so in my ex range I'm gonna say around 0.6 I count one okay and then I take the next one and he's maybe 0.3 so I put something in this column and then I keep doing it and I do it over many many versions of this fishbowl and I basically build up this histogram of just how many how many fish do I find carrying 60% of the momentum or how many do i fire and carrying 10% and I build up this picture and then what this function Q of X is is basically the thing that in the limit that I have many many copies of this and do a large statistical sample I will map out some function Q of X okay so Q of X is really telling us if X is point three then that means that well quite a lot of those fish are carrying point three of the momentum of the part of the bowl in this case but really I mean proton okay there are any questions about this right okay so what we want to do is do the same thing for a proton now okay protons are different than fish balls obviously and so to actually do ask the question of how fast the Constituent if the proton are moving we have to do much more complicated experiments before we get to those experiments one thing that we can we can ask from this function Q of X is how many quarks there are in a proton right I've just told you I have to redo whoops I have to go back no I've gone back too far sorry we've just built this histogram and what this does tells us that this number of fish inside the fishbowl carry momentum fraction 0.3 right so if we want to know how many total fish there are I should ask how many are carrying point one how many are carrying point to how many carrying point three and so on and just add them up and that'll tell me the total number of fish okay so what I want to do is is calculate that sum now X can take any value it doesn't have to be point one or point to be point one one three seven nine right and so instead of a sum we have what's called an integral but really you should just think of this is a psalm over all of the possible momenta that can be carried and so if we just sum them all up and over the range 0 to 1 which is the allowed values that X can take we'll get the total number of fish or now and the total number of quarks inside a proton yes yep yep right so the surface to a proton is is really set by QCD by the strong interaction basically as you try and pull a take a quark outside it you'll see that it gets pulled back in it's basically everything confined itself to some little region and it's it's really through the through the fact that these quarks are talking to each other by exchange by exchanging gluons between them and they're glued together so there is no physical boundary but just everything keeps together okay so in order to actually calculate this we need to know what Q of X is for a proton so we can't use that analogy anymore we have to go and do what I call deep inelastic scattering experiments so we need to go to a big particle physics accelerator and do something that this the following thing so we take a proton and we can think about this sitting at rest as a target in this experiment and then we take a very high-energy beam of electrons coming in and they interact with that proton target V expire sending off a photon and knocking something in here okay and they get scattered off and by measuring how they're scattered you can actually learn about these these distribution this quiet distribution Q of X inside the proton so these these experiments were first done in the late 1960s at Stanford and they really set the scale for set the stage sorry for understanding the structure of the proton so in this figure here I'm showing this distribution Q of X and I've made in fact I've put a factor of 2 here because I also wanted to show not just the distribution of quarks but also the distribution of anti quarks and if I didn't have this factor of 2 these would be on top of each other and you couldn't see anything okay so I've just offset them a little bit so here we have this is a function of this X variable going from zero to one but again I've made this a logarithmic scale so zero is infinitely far off that way and this is just these these distributions and in fact this these lines here have error bars on them coming from their extraction from experiment then they're very precise in fact so what this tells us is that well out here so if X is say 0.5 there are very few quarks in the proton carrying half the momentum okay if X is point zero zero one so here we are carrying a tenth of a percent of the momentum of the proton well there's actually a substantial number of quarks that carry that momentum similarly with the anti quarks you also find that there are quite a lot of them carrying very small fractions of the momentum now we can we can do these experiments and map this distribution of Q of Q of X out and we actually find that it has the following form so it I don't want to scare you with this this formula but it basically has it goes like X to the minus one point two so as X gets very small this is basically 1 over X so that gets very large okay so that's why this thing is going up very fast as we go towards x equals zero and then as X goes to 1 well this term gets very close to zero and so Q of X goes to zero okay so it's a in fact fairly simple form but what it means and for those of you that remember integration or deep integration you can think about this function and say well this is actually something that when I try and do it integrate it try and count all of the all of the area under these curves it's actually going to be infinity okay and while that's telling us is that there are an infinite number of quarks inside the proton not 3 how you can look at this cute this distribution of anti quarks as well and that basically has a very similar form and well that also the total number of anti quark inside the proton is also infinite so that seems a little odd because I told you before there were three quarks so what am I talking about well to piece that together what we need to do is just think about this function a little bit more and I'm going to reap lot it but I'm gonna plot not Q of X but basically X to the one point two times Q of X so that will make something that doesn't explore it as we go to x equals zero okay and so things look much nicer there so this is Q of X or X to the one point two times Q of X and X to the 1 point 2 times the anti quarks and now we actually see there's quite a difference between the two of them ok and what we can do is actually say okay both of these become very very large as we take it X goes to zero so but in fact they become large in exactly the same way which is why these two curves come together here so as we go toward zero these become identical and so in fact that region if we ask not about the number of quarks and the number of anti quarks separately but ask the question the number of quarks minus the number of anti quarks then that that infinity will actually cancel between these two things and so it's in fact the number of quarks minus the number of anti quarks which is related to this area here between these two curves which is perfectly fine ight thing this is 3 ok and so the proton okay when we say there are three quarks we really don't quite mean that we mean on average there are three quarks inside the proton but really it's much more complicated so I can make a quick analogy with quantum mechanics so I'm sure many of you have heard of Schrodinger's cat for those that haven't this is a thought experiment that when Schrodinger came up with where we take a cat and put it in a box with a radioactive source which is a very quantum thing and will decay or not if it decays it will force this hammer to smash this vial of nasty nasty stuff that will kill the cat okay if if it decays but we don't know if it the case so we make this up we close the box and we say well what state is what state is the cat in and either either this thing decayed or it didn't okay that happens all the time okay either it's either it decays or it doesn't and so either the carrier is dead or not but we don't know because we haven't opened the box right and so we think about this cat from outside the box it's it it's either it's both dot a little dead and alive so quantum mechanically we say we have a superposition of a live cat and a dead cat and that's the state of that cat that we know until we open the box when we open the box we see two either dead or alive right but this is really what what the state it lives in quantum mechanically in the mean time so now let's turn to the proton and ask what Schrodinger would think about a proton so he would not think that it's three quarks it's really much more complicated it's it's three quarks but it's also three cats very it's also four cats and a dead cat or five cats and two dead cats and so on okay and yes so this is really the difference between quantum mechanics and quantum field theory is actually that even the number of cats in this box is not fixed anymore right it's kind of pretty weird okay so now let's talk about the quarks themselves because they're even weirder than protons so what is a quack so this is kind of complicated and it really depends on how you ask the question how you look at it so we can do a little for another thought experiment where we take two experimental physicists I like I'm a theoretical physicist so I like doing thought experiments using experimental physicists but let's let's do this so they're both experimental physicists so Zack makes a particle accelerator and this is a picture from a famous particle accelerator that was at Lawrence Berkeley Lab it's now decommissioned and he does these deep inelastic scattering experiments and so he learned something about a quark inside a proton so this probably happened in the 1980s and now Alice comes along later in the 2010 and builds a much larger accelerator this is now the LHC at CERN in Switzerland and doesn't it does the same kind of experiments but with much much higher energy collisions and she looks at the same proton and she sees not a quark but actually a quark and two gluons and remember gluons are the things that carry the force between quarks so how does this make sense well I need to tell you one thing first so the reason we try and build bigger and bigger particle accelerators is because the scales at which we can probe things are direct inversely related to the energy with which we do collisions okay so the LHC is a much much higher energy collision than the other experiment I showed you and so this comes from this relationship here which is basically tells you that for a photon the energy of a photon is inversely proportional to the wavelength so if we think about light light comes in many different wavelengths so red light has a longer wavelength than blue light and so the energy of a blue photon is actually somewhat higher than that of a red photon and if we go beyond the visible spectrum down here you have x-rays and then gamma rays which are getting shorter and shorter wavelengths and getting higher and higher energies and if you think about taking some some object here and taking this wave and impinging on it if the object has structure that's smaller than the kind of undulations in this thing you're not going to see it but if you come down here where the undulations are much faster you'll be able to resolve that smaller structure okay so by going to higher high energies we're able to see smaller and smaller details of the picture of particle physics okay so we can then think back to these two experiments so here we are with Zacks experiment so here this is this is meant to be the proton Zack is working at some relatively high energy e1 okay and he sees a quiet carrying a particular fraction of momentum in the proton we can go to higher energy and let me do both of these and we can go all the way we can go to a sort of an inter me energy and here what happens is that we've gone to a higher energy and we resolve structure inside of this quark and that structure is actually in terms of of a quark and a gluon okay so there are quarks and gluons inside quarks which is sort of a little counterintuitive to say the least so what is what happens though is that this this quark hero is carrying the minton fraction X now this quark is carrying less momentum and this gluon is carrying some momentum and the sum of them is still the original momentum of that Kwak momentum fraction I should say now we can go to Alice's experiment which is at an even higher energy and she resolves even more structure inside here so she sees a quark and not just one law but to gluons but again all of these momenta add up to the same as this original momenta so what we see what we think of as a quark at one resolutions go so one energy scale that we're probing the system or a length scale that we're probing it is actually a more complicated thing when we go and look more closely so now a picture of Schrodinger's proton gets even more complicated so we don't just have cats and anti cats or live cuts and dead cats we also have dogs and these are the gluons okay so the picture of the proton gets more and more complicated now amazingly we have a theory that actually tells us exactly how what we see should change and so this is QCD on an chromodynamics and it predicts this and it predicts it in a fairly complicated way there's a set of equations called the docs it's a Gribble of lopata alpha really per easy equations which given me a long name they probably are pretty formidable equations and indeed they are and this is mr. Leaphart over here who when he's working at blackboards never raises anything he just keeps writing over the top of stuff makes it very hard to follow what he's doing but he developed some pretty amazing things so what these equations actually do is take us from a quat the quite distribution function measured one energy scale and allow us to work out in a complete a predictable way what it will be at another energy scale and then to another energy scale so this picture that I had no no no sorry this picture that I had here is actually completely calculable and under the control of these this guy and friends okay and it's also completely verified by experiment so this is a pretty complicated plot here so I want to explain it carefully so this this is a plot of this quiet distribution function and this function is a function of the momentum fraction and also the energy scale so what's plotted here is the energy scale and then each of these little curves corresponds to a particular value of x okay so large x is down here and small x is over here we don't need to think about all of these but let's just focus on say x equals point zero zero eight and here we have a bunch of data points and a curve with an arrow bar owner and the the curve is actually a prediction from these evolution equations that if you measure the quiet distribution at some particular energy scale you can predict exactly whether it will be other scales and then you can do your experiment you can do an experiment here you can do an experiment at this higher energy or you can go to the LHC and go to really high energies and that's what the data here correspond to and so this these predictions of QT are completely verified by this data here and so this is actually probably the most compelling piece of evidence that QCD is really the theory of the strong interaction okay yes yeah so let me come to that in a second actually because I will I won't derive them because but I will tell you a little bit about how they're derived how what kind of a mathematical way we get to them is okay so so this was really talking about just the the shortest distance structure of the proton asking what the quarks are doing inside it but really we should if we think we under Stan reality we should be able to describe the proton itself everything about it alright we should also be able to describe more complicated things we should be able to describe nuclei and we should also be able to describe macroscopic things like neutron stars because basically the same physics that determines the structure of the proton determines how protons form nuclei determines what happens in neutron stars if there's also gravity involved here but let's ignore that for now so yeah we really have a much more complicated task ahead of us than just trying to understand this very short distant structure inside the proton we really have a much bigger thing to do so the simplest question that we can ask that is not about quarks is well what is the mass of the proton or in this case the neutron so you might think this is a pretty simple question to ask but it's basically taken 35 years of hard work and lots of people working on this and lots of big computers to actually work work out as theoretical physicists what the value of the neutron mass is so the timeline for this is basically this this theory QCD was discovered or invented in 1973 very soon after that a technique called lattice QCD was invented or discovered and so this is what actually going to let us solve this problem and I'll tell you a little bit about this and then people tried to calculate things like what is the mass of the neutron and so the first actual attempts to do this were in 1979 but they were very far from being able to do anything that would tell you anything about that the neutron and it's taken from there until 2008 until the first what I would call complete calculation of the mass of the neutron from the fundamental physics that we think describes the neutron actually happened and so this appeared in science in 2008 so we'll come back to this in a little while unfortunately at least unfortunately for theoretical physicists there's a thing missing in this timeline is that in 1930 to 1932 James Chadwick in the paper where the existence of a neutron was first demonstrated measured the mass of the neutron to much higher precision than we'll ever be able to calculate it from key CD okay so a little humbling for a theoretical physicist okay so why is this so hard and this is really because this the the QCD is the strong force and the interactions between quarks and gluons are very strong okay and so we can contrast what happens when we take electro dynamics so we take a a positive and negative charge so we say an electron and a proton and forget about the proton has structure to it but just say take a positive and a negative charge well they interact through exchanging photons but they do it in a way that if I take those they elect the positive negative charge apart the force between them which is attractive gets less okay and it falls off in fact like one over the distance squared so if I start with them here move them twice as far apart the force they feel is down by a factor of four and so I can take them off and it gets less and it gets less so I can pull them apart QCD is quite different so the analogs of a positive negative electric charge in key severe a quark and an antiquark and because the force carrying particles in QCD which of the gluons are very different than photons they actually interact with themselves not just not just with the charges of the theory and so what happens is that all of the gluon structure likes to sit between these two quarks it doesn't go off like these lines tell you that the photons are kind of going off everywhere for blue ones they really stay together and so if you think about this well you can calculate what the force that the that is required to pull these quarks apart is going to be and it basically becomes independent of the distance so as we try and pull them further and further apart we have to pull higher as just as hard to move things away and so if we want to take this quark and the antiquark and we want to we want to get just one quark we have to take this anti quiet all the way off to whatever is in that direction off infinity and each time we move up we need to do the same amount of work so we move it 1 meter we need to some work move another so if you get that way over there it essentially costs an infinite amount of energy which is why we will never see a single quark by itself would cost infinite energy to do that yes yes that's right so yes so that's what I will explain next okay so this is really this picture here which is a Nobel prize-worthy picture and a particularly important nobel prize here so this is david gross and company's Nobel Prize in 2004 was really the prediction that the well if I go back here was really the prediction of what should happen down here so what what's showing here is the interaction strength between these two quarks as a function now of energy not distant but remember energy is inverse of distance so high energy means very short distance and low energy means long distance okay and so what you see is that the strength of the interaction is going down as we go to high energy okay and if yeah as you saw that's what's happening down here the force between things as they get very close to each other closer than the size of the proton that goes away okay and that's this going out here and I should point out that the curve here is the prediction of quantum chromodynamics the prediction of gross polar Terim will check and the data points correspond to various experimental ways of measuring this this strength of interaction okay so this is actually very nice so if this becomes small we can think about some quantity that we want to calculate which I call Oh and think about it as an expansion in powers of this of this strong coupling alpha R s so if alpha R s is 0.1 well this term here is small compared to this one and this one is even smaller and so on all right and so if I want to calculate this this quantity whatever it is to some given level of precision I can basically say okay well that's enough the next term is going to be 10 I'm smaller so I can forget about it okay and so this is what's called a perturbative expansion basically you do an expansion in a small number and this is actually in fact how these pockets agreeable apart of out early Parisi equations are derived they're something that works at very high energies and works because the strength of the interaction is turning off so unfortunately the other end of this curve is that as we go to low energies and so one is basically the mass of the proton in in these units this this coupling strength becomes very very large and so doing an expansion here and it's basically expansion in something that is basically 1 and so it's not an expansion at all so such a method is just not going to work so this is really where things stood for a long time so we've we've been able to do many many calculations at high energy and basically verify QCD by doing these calculations on pen and paper doing fireman diagrams which you've probably heard about but at low energies this is just not going to work so we did a new tool that new tool is lattice QCD and i'm not going to tell you technical details about this I'm really going to think of it basically as a black box although we'll open it up very briefly because it looks kind of cool inside and let me just tell you why it's called lattice QCD and why we have these nice pictures here so it's really just a way of dealing with these quarks and gluons when the interaction between them gets very strong it's called lattice QCD because in order to calculate things mathematically we have to think about not a continuous space-time we think about a discrete set of points so we only think about things that could exist here or here or here or here not anywhere in between them okay and so we have what's called a basically have a four-dimensional space-time grid of points where we define our equations and then we can solve them of course reality is not this discrete system but this is really the origin of the name lattice it's a set of point so now this picture here this animation here and this is due to a person from University where I got my PhD this is a picture of one of the ways in which these quarks and gluons like to arrange themselves so in order to actually do a calculation what we need to do is think about what these quarks and gluons could be doing on this funny grid of points okay and we have to think about all possible ways they could be arranging themselves and moving around and doing things and this is a depiction of just one of those possibilities so remember I'm thinking about space-time here so it's a four-dimensional thing so this sort of three-dimensional volume rendering the fact that it's changing in time this is really just one of these configurations of what the quasi Lorentz want to be doing and look the colors mean something but not not relevant from what we want to discuss right now this is so you can see this grid here so this is this is showing each point of this of this lattice so you're basically asking what is the value of this gluon each point in in space-time okay and the way we do this is by the way we do calculations is by generating many many ways in which those quarks and gluons could be arranging themselves and then doing averages over various things of those things to extract quantities that we want the hardest part about this method is actually not doing either of these things it's actually understanding what you've done by deciding that space-time is not continuous but is a discrete set of points so what you have to do is then take this separation with it between these points off to zero right and understand how that happens and here I say we're going to average over many representative configurations and in our calculations many might be some number some number of thousands but strictly speaking the correct answer only emerges in the limit of the infinite number of these samplings of what quarks and gluons want to do so understanding that limit is also very complicated and both of these contribute to this being an extremely computationally demanding thing which is why this has taken so long for this to be a problem we can solve so it's basically taken 30 years of working out algorithmic and computational details of how you should do the calculations in order to be at the state we can do this and remember this is 30 years riding on the back of the Moore's law increase increase in the computational power that you can use right so computers have got exponentially better over time in fact our algorithms have got even more exponentially better over time and it's taken both of these to get to a state where we can do proper calculations of these complicated quantities so just to give you a scale from what we do in 2015 all of the people doing lattice QCD calculations in the u.s. used about 10 to the 10 billion CPU core ELLs which is kind of a large number if you think about that that means that essentially 1 million CPU core hours were running continuously for a year and that happens every year in fact now of course CPU is now have multiple different maybe 10 cores in them and so that means we actually only have a hundred thousand computers working on this problem continuously for a year but that's what it takes to do these calculations and these are some pictures of some of the very large computers that we use ok so now I want to say one thing about how we calculate a mess because here again is something where I think there's a pretty nice analogy we can make and this is an analogy with dropping rocks into water ok so if you think about dropping a rock into a water what's going to happen is that well the surface is going to change and there's going to be a pattern of ripples coming up from where you drop it and that pattern will depend on what the rock was right if I drop a tiny pebble I'll get a small ripple if I drop a rock as you'll see here a large rock off a bridge there'll be a bigger response ok so what we're going to do is drop a rock in here and then I'm going to sit out here and measure how the surface of the water goes up and down as this as this ripple comes and passes through here so here it is coming up going up and down and up and down again okay and so I want to I want to look at that and they don't want to do it again and so now I'm gonna drop a much larger rock and I'm gonna sit the same distance away and obviously the the riffle it passes through the point the same distance away is going to be very different for this big rock right and so you can actually just by measuring that response of the fluid that we're sitting in you can measure about what the what the perturbation or what the disturbance you imposed on the system was okay yes yeah and basically I'm what I want to do is think about sitting at some particular point so here was this the center let's see say a meter away and as a function of time measure how the surface the water goes up and down right and that mapping out that dependence will tell you whether it was a big rock or a small rock essentially okay and basically in lattice QCD to measure a mass of the proton we were a neutron we do the same thing so we do it in a funny space-time lattice and what we think about is basically taking a configuration of taking kind of the vacuum and then exciting it and this is basically dropping the rock and what we do to excited is plate is is force it to create three quarks here and three quarks have the right quantum numbers to make protons and then I want to sit with my little measuring stick measuring the height of the water some distance and I do it in time in this case away from where I disturb the system okay and what I want to do is move this this measuring point forward and backward in in time and okay you could do something in space as well but let's not worry about that and the nice thing about these lattice QCD calculations is all I have to do is get the quantum numbers of this system right I don't have to actually work understand exactly what a proton is the averaging over all of these configurations of the quarks and gluons actually puts all of the an antiquark pairs that really should be here and all of the gluons in automatically for me sorry now what I'm going to do is is basically as a function of the distance T have some correlation between the disturbance I'm putting in and the measurement I do a distance T away okay and by measuring that I actually extract a response so C is that response as a function of T and it basically goes down and up in this case and it depends on the mass so if the mass was 0.05 it goes down like this if that mass was point two it goes down like this and so by measuring by calculating this what I call a correlation function in in lattice QCD and finding this versus this I can actually extract what the mass was okay and this is how we calculate the mass of the proton okay so that's at least a little view of what we do I certainly don't expect you to understand all the details but basically we've we've done this and so after 30 years we actually get to this plot here which is from this science paper where we look at the spectrum and various different states so the the mass of various different states I should say so here is the neutron and the blue point corresponds to the lattice QCD calculation and then the white lines correspond to the non experimental values for these masses so we have the neutron but we also have lambda barrier on the sigma bearing on the cascade bearing on some other stuff and some maisons down here and you can see that these calculations are able to completely reproduce experiment here and so we say we can now calculate the mass of the of the proton from the underlying theory of the strong interactions okay so this is pretty important in fact because previously we had really only verified that QCD was the theory of the strong interaction at very high energies where we could do these these calculations expanding in a small number but now this plot here is basically demonstration that QD describes strong interaction when they're strong which is kind of where you want to describe strong interactions okay so this is really the kind of the main thing I want to tell you about is that we we really now know that well QCD is at least to the level at which we can test it experimentally and computationally is right so there may be things beyond it but we wouldn't need more precise experiments to see differences okay so that being said now we get to the interesting part so because as I said Chadwick measured the mass of the neutron in 1932 so great we took a long time to calculate it so there is a clock here I should finish pretty soon right yeah okay so let me just say one thing I've got a couple of different examples of ways in which actually having the ability to do these calculations and verify that QCD is right we can actually calculate things you can't get a experimentally so let me just turn back to this to the neutron proton system and back to the fact that these masses were different okay they're very close to each other but they are different the neutron is heavier than the proton and that actually means that the neutron can decay to a proton plus an electron plus a neutrino and this is a very important thing this is basically how it's very important for many reasons so experimentally we can just measure these numbers and that's it okay however these numbers come from two different places so the proton is on average two up quarks and a down quark and the neutron is on average one up quark and two down quarks so the difference in these masses can come from the fact that the up quark is lighter than the down quark but it can also come from the fact that the proton has an electric charge and the neutron doesn't and so what having an electron charge mean electric charge means that if you are moving along you basically have a cloud of photons that follow you along okay and they they like to raise them of a charged state so a proton is actually heavier than it would be if there were no if there were no if it didn't have a charge now experimentally you can't make a separation between these you can only measure the neutron proton masses okay however having complete computation and control over over the theory that we know gives these numbers you can actually ask more detailed questions so this is another calculation very recently of these mass differences so this one here is of the difference between the proton Neutron this is differences between other mesons and baryons but let's just focus on this one here and the line is again the experimental number and the and the Green Point here is the lattice QCD plus QED calculation so this is a calculation of including Q city and also electromagnetism and you see that okay well we verify an experimental difference but now we can do an interesting thing we can take this calculation and we can do it again but not have QED there right so we can just have this difference between the masses but not this piece here and we can ask well of this number of 1.3 MeV difference what fraction is coming from electromagnetism and what fraction is coming from from the difference in the quark masses or we could do the opposite thing we could keep electromagnetism but make these white masses equal they're just parameters in our theory right so we can change them and you could then see what part is coming from electromagnetism so this is okay might seem like a fairly abstract thing to do but it's actually really important for our existence in fact so here I have a plot that shows the fraction that the difference in mass between the neutron and proton coming from this piece of it and the neutron the difference coming from electromagnetism QED in this case and so with these calculations where we can play with both of these pieces independently you can actually pin down what's coming from what bit is coming from each source and we find that there's a point sitting here so if we ended up sitting up here somehow right if we if if electromagnetism was somewhat weaker okay that would mean that the the mass difference from QED would get smaller and so we would actually move up here and if that happened well we'd be in big trouble because now the mass difference between the neutron and proton would be so small that when we try and do fusion taking neutrons and protons and forming a composite thing called deuterium from them releasing energy that wouldn't happen okay also if the other thing if if we made this mass different smaller moving across this way we will move into a regime where where we would not have stars as we know them right because hydrogen would automatically fuse into wood very very quickly fuse into helium and all we would have in the universe is helium and so we would have helium burning stars instead of hydrogen burning stars which would be a very interesting universe to live in I'm sure so yeah these these questions of well what the value of the bursts of the QED interaction is and what the value of this mass building is they're really important for our for understanding what the universe could have been like we actually know now that the universe it's right here and fusion works as it does that's great but if it wasn't we can sort of ask the question well why is this value here and we can ask really quite deep questions about why as I universe like it is and let me just leave you with one last thing so to actually understand these questions you need to do a little bit more than just playing with the masses here and this is some work that I've been involved in recently and this is actually trying to understand these fusion processes where we take a neutron proton smash them together form this this thing called the deuteron which is a bound state of these two it's basically hydrogen but with an extra Neutron right and giving off energy through a photon right so this is a fusion process something similar to this involving two protons is actually what powers the Sun but this process here in particular is critical for the evolution of the universe this essentially the first nuclear reaction that goes on in something called Big Bang nucleosynthesis and if if it didn't happen how it happened we would just wouldn't be here we wouldn't form the deuteron we wouldn't form heavier elements and we wouldn't form carbon and well we wouldn't be here so let me finish there and please feel free to ask questions in these LCD calculations you describe the lattice how do you decide on the scale of how small right Yes far do you go until you say so okay so you can sort of think about it as okay we're trying to describe the physics of say a proton right and a proton we know it has a size that's roughly 10 to the minus 15 meters and what we want in order to sort of describe the dynamics of that system with with reasonable fidelity we need that the discretization scale is very small compared to the scale at which physics is happening okay so that really tells us how how small those lattice spacings have to be to be sort of close to being right answer and then what we do is we do calculations for a range of different scales and extrapolate to zero spacing we also have to think about the size of the space-time we need that to be big compared to the proton and this is sort of why the computation will cost is so big brilliant place if we have a hierarchy of scales that we need to impose in these calculations that's not easy I have a fundamental question when you take a quark and an antiquark and stick them in something as small as a maze on what presents what prevents them from just annihilating that's a very good question so quacks come in different types okay so we can think about like I talked about up quarks and down quarks and strange quarks and things so if I take two quacks that are the same type indeed they can annihilate but if it takes a up quark an anti down quark then they don't they can't annihilate basically because the so what happens if i take a saying up an ante up they form they can basically turn they can turn into a gluon right but the glue on carries doesn't carry what we call a flavor quantum number so it doesn't have any up Nisour down this or strangeness okay and that the strong interaction actually preserves up nurse and Downers so if I have something that has has two up quarks in down quark it's never going to have four it's never going to have it's never going to turn into something with just three up quarks it can turn into something that is two up quarks and down quark and an type and another up but not in it just can't do this so in order for changing flavor you need the weak interaction and that's it's also a very important part of things but so I didn't get to talk about it today I think you mentioned that the quarks were moving at the speed of light yeah very very close to it but don't they have mass and so they do so how does that work right the Jerry good question yes so quite the the quarks they have a very small mass so the proton mass in these units was 938 MeV okay so if we ask what the masses the up and down quarks are they are something like 383 MeV for the up quark and 5 MeV for the down quark okay so you can see that two up quarks and a down quark doesn't make a proton right it gives you something like 10 MeV out of a thousand MeV so that those masses are very small and so yes they're not quite moving at the speed of light but they're moving very close to it compared to say a proton moving it's very close I'm not sure how to ask this I'm always wondered how do you know if you keep finding particles inside particles and particles is there it seems to me that the only way that you would know if you're done yes is if maybe time is discrete and not continuous is it relationship yeah so the question of when you would know when you're done I think you can strictly you can't answer that you never know you're done what do you do all you have from experiment is information that at the in the experiments that I've done I can describe what I see right now it could be that that there's something much more fundamental going on but and it's almost certainly the case that the standard model is not the final thing for example standard model doesn't tell us why neutrinos have mass it doesn't tell us about dark matter so there's things that we don't understand so we most I would say almost all theoretical physicists think that we're not at the final thing but for these experiments that I'm talking about here this theory is really is describing what we see okay and in fact you should think about the what I said about quacks right quarks have quarks inside themselves right if you look harder at a quark you see quarks and gluons inside it so it's kind of a tautology to even ask what what's inside a quack because the answers are quack yeah so there's many things that could happen I mean there are people that think that in fact if you go to very very high energies so energies where gravitational forces become relevant then in fact space-time could be discrete right and yeah but but to get to experiments they can actually prove that we need to invent some extremely powerful new technology to be able to do that a couple questions over here yeah what's the difference between like a strange quark and all the other ports yep okay it's so strange why is it called strange yeah so it's historian too it's a historical reason why it's called a strange quark basically people people look at these first experiments where they started to see that there were lots and lots of things lots and lots of particles in their experiment and they said hmm that thing's strange and so they discuss their first discovered one of these funny baryons called the lambda barium which now we know contains a strange quark and they thought well that's a pretty strange thing it doesn't behave like the protons and neutrons they'd seen before so the difference between quarks different types of quarks really is two things firstly they have different electric charges and they also have different masses so the strange quark is a little bit heavier than the proton than the up in the down quarks and the bottom and top quarks are even heavier yes the graph that you showed were the little loop in the graph when the quarks are at their closest the animam energy between them at that point you can hit them with very high energy and blow them apart you can blow them apart a little bit but then I'll pull back together so so no matter how much energy you put in at that low energy state between the quarks they don't turn into pie maisons or anything um yeah that's actually a very good point yes I tried I wanted to go us over this but yeah what will happen is if you try and pull them further and further apart there's so much energy stored in this what we call a flux tube between them that it becomes energetically favorable to create new particles all right so basically somewhere in the middle will create another quark and an antiquark and so these these two that were at the end will basically snap together with the two that got created and you will get back to me that's that's pretty weird yeah thank you all right on that note thanks will yep thank you thanks for listening [Applause]

Channel: Kavli Institute for Theoretical Physics

Views: 23,868

Rating: 4.776 out of 5

Keywords: Quantum field theory, High energy physics, Nuclear physics, QCD, lattice QCD, quarks, gluons, baryons, mesons

Id: H_PmmMkGyx0

Length: 65min 57sec (3957 seconds)

Published: Tue Jan 03 2017