### The Color Glass Condensate and Glasma

Elster’s it’s aligned to vin good evening ladies and gentlemen it is a great honor for me to open this lecture in memory of judaism break i had the privilege of learning physics from judah as a graduate student it was one of my best experiences as a student in this university and do this example as a teacher and a colleague later on has always been something I very much cherish and today we are very happy to have as our speaker professor Larry McLaren from Brookhaven National Laboratory I will first ask professor Muhammad Ali from Hebrew University to say a few words in Judah’s memory and later we will continue with a ceremony of awarding a scalp fellowship in Judah’s name and then we will move to the scientific part of this afternoon nealy acaba was professional when i came earlier today all of a sudden i caught myself asking why did they come almost a full hour before was it to evade traffic jams or perhaps as years ago when I used to come to discuss physics with you da I would come to have some extra time and we would just walk walking and hiking and exchanging views was one of our joint pleasures and I still miss him not only for physics but also for the lots of cultural activity that was developing during those walks and hives Judah was born in 1938 in Cincinnati USA his family moved soon to New York to force his suburb of New York City he studied in Columbia and later he did his PhD under Karen who hung in MIT Judah was fluent in Hebrew and Jewish culture he was perhaps the only person that I recall when talking to him I had to take guard how my hippo sounds and how I use it he got full wound education in Judaism because the tradition of his family the profession of his father and he was right in the sixties and in the beginning of the 70s to make aliyah I think that this decision to come to Israel to settle and to assume a professional career in Israel would with him for long period over the 12 years that he served as first assistant professor in Charlottesville rising after all ranks to become chairman around the age of thirty years old and when he was right for that right after the Yom Kippur War he came with a fact-finding mission of us professor for peace in the Middle East to Israel and he made a tour and I remember that day in December 1973 when looking over Jerusalem from the terrace in my home he said I think I wish to get an offer and from that point of on it was just a waste between Olivia beam and myself luckily for your people in Tel Aviv I was keener at that time I didn’t have this that influence and more author Aveda had one big advantage he had a young experimental group with him that attracted Judah and I think that this was one of the decisive factors the Judah went to Tel Aviv he spent the year of 7475 in Jerusalem and he made started lots of collaboration with Victor mother’s life with myself with other people from outside and then he moved in 75 to Tel Aviv he was a widely recognized leader in Payan nuclear physics in fact is entry to Pilon physics or curved couple of years before the seminal paper of the two Erickson’s 1966 that defined the framework of multiple scattering of

reactions in Low Energy prior nuclear systems and he was organizing workshops and leading informal groups in Los Alamos later in Vancouver also one summer in Brookhaven Larry long time before you came there and between the years I would say 63 and 1986 he was one perhaps of three or five leaders of intermediate energy physics notably polymer physics his wharfs are well known that and then typically he moved to a more novel field a field where he would applies method for dense and exotic matter using back reaction our calculation and Spearman’s fermions were is real of together with this ex student slick albumin he worked a lot on developing models of sermons and checking what effects they could lead in atomic physics Judah unlike many of newcomers to Israel develops a public career his fluency in Hebrew his grasp of historical and political processes enabled him very quickly to assume a role of leader and so he was it in the Tel Aviv University hierarchy to become a deal and later to become vice rector and if it were not for his untimely death in 98 he would become a retro and perhaps even assume higher positions his loss is lost his loss is a loss for every one of us for the Tel Aviv school of physics to the Israeli nuclear physics and atomic physics community and to his many friends as I said I mourn his death also from a personal perspective I miss the log walks with him the chats with him and in later years when he would become very busy with administration and I would call him on phone we would like to tell me something but he didn’t have time to he would say well let’s leave it to the desert of Judea vana she really needs Bollywood as a sequel a bit value though I think this is a good tradition and I will stop here leaving many memories that I can reform the value though I would like to mention that they speak allowing McLaren new Judah very well and so he say a few words about it my last long acquaintance or meeting with Judah when a personal basis was on a trip that nearly Judah and I had together the three of us to South Africa in 96 and Larry was there too this was a beautiful meeting in a place for paradise on the Indian Ocean and so Larry belongs to this community he came from high-energy physics and he moved into dense and exotic matter we came to Brookhaven and he was leading to look like a theory group which went for big metamorphosis and expanded and became one of the major groups in nuclear physics in the US and worldwide so thank you for your attention I would like to invite now this is nearly amid and the head of school of physics professor Owen oz to the award ceremony of a fellowship to an outstanding graduate student are you can you see the atom who is a graduate student in theoretical high-energy physics in string theory and we are happy to have this tradition of giving these fellowships to best graduate students every year and it’s a heavy burden you know people who got it in the past have done very well I wanted to take this opportunity to personally again to thank Larry for coming as I’ve already mentioned we’ve known each other for many many years and always such occasions when the lecturer is actually somebody who knew Judah was

his friend it sort of means a lot to me and I can welcome him personally and I also wanted to thank all of you all the physics department because when I see you I don’t need to tell you about Judah we was because for all the other places even at the University for people who knew Judah except those that were our close personal friends they they don’t remember him as well as you guys and they don’t know what really was in Judah that was so special and so unique so way whenever I’m among physicists I I feel that you you can identify was with our losses my personal loss and the loss of the family much more than anybody else and Shimon and fellow is not here but I also wanted to thank Shimon first of all for maintaining the rector’s lectures in Judas memory but also Shimon was the person that was so instrument instrumental in creating this scholarship in Judy’s name so also of course I’ll take the opportunity to thank you personally but I thought it was nice to mention that it was really he’s doing thank you very much so at this point so we hand the ceremonial parts of our afternoon and we’ll make a three minute break and then we will start with the scientific part where we will hear a lecture by Professor McClaren so we make Fourth Reich maybe even less than three minutes the people’s are some people who must be in other places at this point so hey once again I am very glad that I was speaker today is Professor McClaren I have personally known him for a very long time and always enjoy discussing physics with him he is currently the head of the Rickon theory group at the Brookhaven National Laboratory dealing this matter in extreme conditions which are being recreated that have an accelerator professor McLaren obtained his PhD from the University of Washington in Seattle later was a postdoc slack and and he was at the University of Minnesota also and is currently as I said in Brookhaven but he is indispensable in providing the theoretical guidance in these times which are very exciting as you would hear there is lots of exciting data and a lot of theoretical wisdom is needed and I think they are very lucky to have you there to help them sort it out so where you get to hear you okay can people hear me I guess oh yeah I first met Judah when I was in University of Frankfurt many years ago we shared an office together we were office mates up Judah was a person who was remarkable to me because he was one of these rare people is absolutely honest and filled with kindness okay he was also a person who by series of coincidences of water Barak hired some very good friends of mine into his group like dim-witted skate and like later with Anya Frankfurt and also was also at a department a people who have always been very good friends of mine who I like very much and this kind man nice man I remember very much the time we had together in South Africa in in and one of the things which we did together was we Judah and Nellie and I and much of other people went on a long hike into the on the inland mountains near the coast up to a waterfall and that’s just a wonderful time talking about all sorts of things we didn’t talk about physics but we had a night really a nice day he was a very nice man in this talk part of the talk is about some topics which are

related to things which do to thought about and did some work on actually do them down and it’s the critical work on and I’ll try to make relations to that when we get to that part of the talk so let me begin on ok Oh what about one of the questions I want to try to address in this talk basically three questions one is what is the high energy limit of QCD and other is one of the possible forms of high energy density matter and how do quarks and gluons originate and strongly interacting particles that is how do you calculate the distribution functions of quarks and gluons and strongly interacting particles and the best way I know of getting into this subject is to do qualitatively through art art and metaphor has advantages in science and disadvantages one is its visual and included the other problem is it’s very subjective that the subjective nature of art is very useful at times because as we know theoretical ideas changed as a function of time and sometimes the words and concepts we use and even the mathematics which we use metamorphosis into different ways of thinking about problems is time the balls an art has that property very strongly that in a case it provides a useful way of thinking about what we’re doing this is a picture of a heavy iron collision we begin with a color glass condensate it makes some thermal equilibration matter quarks and gluons that work well in plasma and then expands and eventually produces particles which go out in a detector and this is a picture of a distribution of particles which is seen in the star experiment I’ll call that the little bang the Big Bang is of course the Big Bang there you have an initial singularity inflation where the universe expands very rapidly it eventually thermal eise’s matters and density fluctuations in matter are generated which eventually are seen in the form of distributions of galaxies and ultimately hopefully will be seen in the distributions of dark matter in the universe these things have a formal similary and that one’s talking about expanding matter and in fact there are actually some mathematical singularities with what happens early on in the collision and what happens early on and they and if that’s some of the things you look for experimental e are related to the things which you look for experimental in the Big Bang but it’s metaphor and it’s art and it serves as an introduction to the way we think about these problems here’s another set of artwork if this piece of artwork is due to my friend Tetsu a hot suit at the University of Tokyo this one’s student my friend Stefan boss a Duke University this picture is two nuclei approaching one another which I’ll call a color glass condensate and I’ll define what I mean by that later in the talk they collide and when they collide I’ll call that the initial singularity that’s sort of the tip of the light-cone in this picture which isn’t shown and then after they collide in this initial singularity evaporates away one has GLE asthma which eventually forms a strongly interacting quark-gluon plasma which eventually makes a had run Gauss and had runs go off to detectors I’m not going to talk about these two latter stages of the collision I looked at the history of this lecture of this colloquium series before I came and they’ve been talks about this I’m sure this has been talked about this probably maybe has not been so much talk about in colloquia unless Genya gave a cochlear money either genuine no shame on you you don’t advertise our work here’s another way of thinking about this which is maybe a little more mathematical here are the initial nuclei going along lines with T is equal to Z and he is equal to minus C two thin sheets which are long the light-cone they hit at T equals equals zero that’s where the initial singularity is the initial nuclei as a color gloss condensator thought it has cold here on high energy density gluons the initial singularity at least at very very high energies will be a singularity and it will look somewhat like an event horizon from which their quantum fluctuations which there are some formal similarity to Hawking radiation evaporate and this matter is it’s expanding which is going to produce at this singularity I’ll call glaze no because it’s somewhere in between a color glass on and say cork gluon plasma but I will have to justify to you why this is qualitatively different than what precedes it and what follows it and I’ll do that and then finally there’s the quark-gluon plasma about which I’m not going to spend much time talking this picture has a strong correspondence with cosmology but their ideas and words in here which aren’t really the kinds of words that use in

cosmology so the question you have to ask are how can ideas be tested ideas about strong interactions so more generally about field theory and what are the new physics opportunities which you can find in this environment I always find them walking to the screen because I pushed on that use when these fancy Mouse’s work in the distance here’s a picture of the had run at very high energies here’s what happens in a detector this is a Phoenix detector this is a star detector this shows that in these collisions lots and lots of particles are produced thousands and thousands of particles from a few hundred nuclear arts and the initial collision how do they get produced will they get produced because in the wave function of this nuclei there are lots of gluons now you say that sounds silly because I know that a quark nucleus is made of nucleons and a nucleon is made of three quarks but that’s not really true sometimes it’s made of three quarks sometimes it’s made of three quarks plus one go on sometimes it’s me made even a three quarks and lots of gluons there are lots of difference states of this wave wave function of a hadron its wave function can be decomposed into states which have three quarks and very many gluons in it and it just happens in in high-energy collisions the states which have three courts and lots of blue on center are the important ones for these scattering processes it’s also true that if you think about this in a frame where the nuclei moves very fast this nucleon looks like basically a wall of gluons now this picture is perfectly Lorentz invariant I’m not saying that if I Lorentz boost this part of the wave function I get this it’s just that when I study high-energy processes it’s this part of the wave function which is important for this particularly Lorentz invariant picture um in fact if you talk if you measured the number of gluons as a function of the ratio of the energy of the glue on the total energy of a headline in a frame where the head was moving very fast it actually rises very very rapidly as X gets smaller that’s called the small x problem in high energy physics actually it should have been called the high energy problem okay because you see if you fix the energy of the gluon had some scale like a strong interaction scale and make the energy higher and higher the minimum of value of X gets smaller and smaller so what you really see is that the high energy limit of strong interactions is a limit where there are very very many glories inside I had one and this causes naively a problem because we all know from measurement no theory just from an experimental measurement that the total cross section over very very many orders of magnitude barely changes at all so what do you do with all the gluons okay they have to keep fitting into the same sized hadron and they’re gonna get squeezed and in fact what happens is kind of amusing if you try to pack more and more gluons of the same size into this disk at some point they’ll all be pushing on one of them you can’t fit any more in okay and really what happens is you have to put a water one over alpha stronger these gluons into this just because only when you power 1 over alpha is falling on top of one another through the interactive strength 1 coz alpha strong times 1 over alpha strong is immortal 1 so they act like hard spheres I should say the coupling constant gets small because the density of gluons is becoming very very large so it makes sense to talk about this when we coupling theory but now you can see what happens is you go to higher and higher energy so you fill up this disc with little balls of some fixed size you want to add in anymore what do you do you have to add in smaller ones so you add them in between the holes between the big ones they get all filled up and then you have to add in smaller and smaller ones ok so what does this picture tell you you say well why is he saying well what it’s really saying is when you use quantum mechanics the typical size of these gluons is related to the transverse momentum inversely small thoughts have big transverse momentum have big energy so as you go to higher and higher energies of course you fill things up first which have the largest size which have the smallest energy then you add in more and more high energy ones and more and more high energy ones and you get this funny picture saturation saturation is not the statement that you keep adding glue on to this thing and the number of gluons are stopped rising it’s a statement that gluons the fixed size stop increasing as you go to higher and higher energies you can always add in more and more gluons so the high energy limit is a limit of very very many gluons inside the hata neuron and the gluons up to some fixed size are filled up as much as they can be what do we mean by this well let me define the words color glass on and say

for you the word color is easy color is just a statement to the gluons carry color condensate I think we can understand now because what I was doing in that previous picture I was constructing a phase space density for you and the phase space density is just e n dy e to PPD to xt which quantum mechanically it’s just the occupation number of states of a given momentum or energy at at in in this box which has since izb which is associated with d2 x and the way this works is you have a condensation phenomenon you have an attractive potential which causes you to produce particles but then when you get high enough density every pulse of interactions cause you to stop adding more particles to the system and that always happens when the phase space density is the border one over alpha strong and that you’ve seen in many many contexts you’ve seen that in the context of superconductivity where you have the landau-ginzburg model and the condensate ends up saturating at some density involving inverse coupling constants you see it in the Higgs vacuum and electroweak theory where the Higgs condensate saturates at 1 over lambda it’s even true in these atomic traps at the density if you could keep highlighting things in in would eventually saturate at some density associated with the inverse strengths of couplings okay so I think we can understand the words condensates you should also recognize it because the phase space density is very high that means it’s a highly coherent object and has probably described by some kind of classical field where do we get the weird glass well that’s where you have to have a little creative imagination you imagine that you have very high energy had rocks moving very close to speed of light they have some very high-energy gluons with them and they make some lower energy gluons those high-energy gluons have their natural timescales the Lorentz time dilated because they’re moving paths therefore the slow ones would you make have their Lorenz time skills dilate and also because they’re produced by these fast-moving guards so even though these four moving folks we can see in the in the center-of-mass right slow moving means they have a glorious gamma factor of order 1 they’re still moving close to the speed of light but but they have their natural trying skills and interaction dilated by a gamma factor which is huge because they’re produced by these very fast-moving particles systems which evolve over very long timescales compared to their natural timescales I just call a glass ok that’s sort of the colloquial definition of glass glass is a liquid on very long timescales that it’s a solid on short time skills mathematically this also has the property that when you write down a theory of this stuff the theory you write down is the theory of a spin glass which involves an incoherent sum over external fields and that incoherent sum comes about because you ud cohered the system due to long time skill that’s technical details my definition of glass is just very simple it’s a system which is evolving very slowly compared to natural timescale okay but those of you who demand intellectual honesty probably got very upset and what I said in the last few seconds about fast and slow-moving because I didn’t define for you what was flat fast and what was slow by the way Jesus oh okay um I hope I didn’t do anything okay okay um you should feel free to ask questions during the talk I always like people who’ll ask me questions and give me a hard time because that makes me at least feel you know that I can maybe explain something okay is everybody with me so far everybody’s with me so far no problems anyhow a key if you all it is very important oh that’s a very good question you see if if if gluons were burning on his space based density could only be a water one but because their glory are bosons you can get them to be water one over alpha strong you can get them to be much larger than one and that’s really important because that’s what says that at high energies Hadron wave function completely dominated by gluons and fermions are playing a secondary role very good question okay but for first thing you have testicles what’s fast and what’s low on a hand Ron and I said that’s sort of arbitrary because they said the fast-moving poles make the slow-moving ones well in fact the picture is a little more complicated here’s a picture of experimental data a

trick where you plot the density of particles as a function basically the logarithm of the energy the produced particle from the beam energy the blue curve is what you get lower energies and you see if you go to higher energies the red curve is there and it looks just like the blue curve for the fast-moving pulse so you might think for the blue curve at this energy you can make a theory where these degrees of freedom were maybe frozen out and resources for the low-energy degrees of freedom and then when you wanted to go to energy he’d maybe have to integrate out degrees of freedom here and turn them into sources which are now on this red curve which generates the theory for the law energy degrees of freedom here and then when you went to get higher energies you’d have to integrate out the degrees of freedom here to make the black curve and have a theory which generates the thing at lower energies nerve that process is a renormalization group you’re just integrating out the higher energy degrees of freedom to make an effective theory for the lower energy degrees of freedom and there’s a one defying way to do that and you could do that for first principles in QCD and in fact the surprising thing you find is when you do that you find a spin glass pipe theory and that spin glass theory has the renormalization group which determines the density of sources in the system and that’s a theory as a universal solution and Universal is really important because Universal means no matter what had wrong you started from be it a pie on a nucleon a gold nucleus or iron nucleus the matter which you’re describing the high energy limit is universal and it’s described by one thing there’s not a color glass condensate which comes from a gold nucleus our color glass condensate which comes from a nucleon our color glass condensate which comes from a pond it’s one in the same object described by the same theory they you want to parameter this in fact the gluon field itself okay now now okay the problem is that in order to make the theory gauge invariant for the glass you have to average over all configurations and when you average over all configurations of gluon field density itself vanishes all over the square gets a moment on the issue is that in the glass it’s an incoherent sum okay it’s not as sum with an eye it’s an e to the minus something and that incoherent sum is really telling you you’re really summing over the individual configurations which have an expectation value you know one can quibble technically over exactly water the right precise words to call but that’s what it is okay and the gauge invariance is broken in each configuration which is restored by the incoherent average si can an ordinary glass if you look at an ornate glass which sits on a table okay you look at where the atoms are distributed and those atoms are distributing away which violates translational invariance but of course when you average over all glassy configurations you’ll have a theory which is which has no symmetry support but it is a bit bizarre thing isn’t this is something which is having a local gauge invariance which is almost broken is what this is about and so you can say is it really like a local gauge in local local order parameter it’s not like a ordinary both kind of thing which really has that order from there broken and it stays broken and has sort of Goldstone modes associated with breaking okay yeah anybody else is a good questions okay okay oh let me see okay this is just a propaganda slide read it read it fast okay it says it’s important because it’s up because it’s universal and that means it’s fundamental that’s an advertisement it’s a universal form of matter I use that because I often give this talk to my nuclear physics friends and they say it can’t be matter because it’s not thermal or something like that but to my eye then I asked back well if it’s not matter what is it pure thought ideology god yeah that would really be wonderful it was one of those things that you just start in physics but no it’s just matter it’s just you’re just a bunch of the ones which are all piled together inside a box and the none of the separation of gluons is small compared to the size and system you number gluons is large it’s just not a system in thermal equilibrium and it’s also a system which is moving very fast close to the speed of light okay but better but it’s matter sure not if it runs into you you will feel pain okay what does a sheet of colored glass look like here’s a sheet of colored glass moving close to the speed of light here’s what the fields look like this should look for Boop’s would that I do this should look familiar to you because if you took Coulomb field and you

boosted them close to the speed of light you make these fields which look like an electric field in one direction a magnetic field perpendicular to it have both perpendicular to the direction of motion and that happens when you saw the yang-mills equations and we coupling because fields look like blue own fields and they just got Lorentz boosted you can even do it by some fancy mathematics UI that’s minus BT minus C and then you say big components are big if they involve derivatives with respect to this that small components are things which have you know don’t have that small derivative and it said it so you can do all that and you find that you’re just generating these so these plane polarized electric and magnetic fields the tricky part is what’s the distribution of these things on the sheet and polarization in color and water what are the fluctuations from that distribution and it’s actually actually the whole structure this renormalization group is just determining that functional which gives us waiting to the system yeah I don’t know how you would do that in practice you know because or yeah but the problem is that baryon density spread out over you know it’s a good question you can’t do that in the central region it reca so you could ask the question what would happen in the fragmentation region the problem of the fragmentation reason when I formulate this I formulated this renormalization group problem so I don’t have anything to evolve I certainly don’t have universality in that region but I wonder if there’s a thought experiment what one could construct which would let you make such distribution of matter in principle that I don’t know there’s a practical matter No ok so the color glass condensates explains the growth of gluons a small X the renormalization group equation which you solve actually lets you predict the growth of the saturation momentum as a function y is logarithm of 1 over X and you get this power law behavior and if you write down and solve those renormalization group equations you actually get what seems to be seen it’s done mentally within the kinds of errors you can put on that calculation I’ve already explained this about how they pile off but this is kind of remarkable but not only did you find that having this identity gluons lets you solve the problem but then you can go back and calculate what that high density is and occupants on energy it also explains the growth of the total cross section I’ll give you a heuristic argument everybody in this audience knows what heuristic is oftentimes I tell people heuristic means it’s an argument which isn’t quite correct which is what it really needs ok but it means I can’t fill in the details of this argument I make an assumption that the density of particles as a function of energy goes like Q saturation squared as a function of Y times the transverse impact parameter distribution and it factorize this into this form if it factorize this into this form at large RT it has to fall exponentially like this that really proving this is hard but it’s plausible and anyhow heisenberg assumed this about 60 years ago he used to pretend come on we’ll get the growth of the cross-section which work like this and if heisenberg get it i can get away with it i’m sure but in any case this is where the assumption is that it has this form add together to measure a cross-section and high energy she takes some probe which has some typical interaction strength with this a pass through the distribution and you just require that the number of particles and encounters is fixed and that says that this is just equal to constant then you can you work out what this means this means our t squared goes like weiss worked as articles like why and that means that RT square goes like Weisberg goes like the log squared of the energy and that’s known as the force are bound which is in fact how cross-sections really behave at high energies so at least you you get consistency with an argument which is qualitative and maybe meets and polishing but it’s pretty good the colored glass condensate also explains features of electron Hadron scattering if you take electrons and you run them into had runs at very high energies you have a cross section for the scattering of a virtual photon off

the proton and that in general we tend depend on the q squared of the virtual Photon a typical momentum of the virtual Photon divided by the saturation momentum squirt because it has to have the right dimensions but in general it can also depend on on X but the dependence on X would say it wouldn’t be universal because that would mean this result would depend upon say what energy you started at and if it’s really Universal theory and only depends on hue saturation squirt you should have this form without any separate dependence on X and you can see whether or not that’s true by just taking the data for that’s less than 10 to the minus 2 this is when the gluon density inside of hadrons is really big at high energies and a watch ok the factor works too well it works fewer than you would think that’s another story to really are yep that get the higher Q square stuff to work you can do that in any case so we’re things and having a theory which works too well believe me I know I’ve had lots of theories which don’t work at all but in a case it’s it’s kind of nice that this works and it’s it’s it just seems to be true so now what I’m going to do is I’m going to shift gears we’re talking about the color glass condensate which of these two sheets the color glass – what happens when these two sheets of garlic color glass hit one another at the speed of light sort of the picture I’m going to have of what happens is again in this piece of art on what a what’s done here is given the particles measurements a final time in the collision you can make radically different assumptions about how the matter thermal eise’s as you go backward in time and you get these balance and what the energy density was and you can see at a time when you expect the color glass of condensate could be poured in a trick your energy density is about 10 to the 30 gb per cubic fermi and this is when after these collisions the color glass has formed a glass ma which melts into gluons eventually all the gluons that milk it out the system expands as forcing lawrence eventually formalizes and goes to detectors timescales feel pretty realistic there’s not much controversy now on what these timescales are there’s actually not much controversy on what these energy scales are i also marked for your interest energy density in the course of nuclei energy density in the course of neutrons start to convince you that ones that really high energy densities you go to LHC it’s gonna get better but you’re in the ballpark with energy densities sometimes skills at rec so what happens here’s my picture and i’m gonna spend the rest of the talk right got me okay I tried trying am i doing something wrong with it okay okay what I’ll spend the rest of talk is trying to explain what this picture means but all I’ll give you the 30 second explanation right now when these two sheets pass through one another and there are very high energies they’re very thin sheets they pass through one another instantaneously that means the time is to time the passage of this thin sheets after they pass through one another they get dusted with color electric and color magnetic Clark those are the red and blue and yellow dots on this thing and I couldn’t figure out a way of denoting magnetic and electric fields separately so some of these are colored magnetic charges the summer color electric charges and what happens after this collision is you instantaneously form longitudinal electric and magnetic fields and you can say I don’t believe that then I can stare at you right back in the face and say you have two and you say why and I say because the couplings look can you say so walk they say because the couplings weak I know everything and I can really calculate this thing from first principles and it has to be true and this has to be true okay there’s no cheating okay well almost none okay here’s a little bit better picture of what happens now I’m going to give a seminar on Thursday here for people who want the details about this but but basically the way this happens is you could actually construct the fields with salt in this problem if you have a like on where one source of charges on one like on and other source of charges on the other like own there’s a solution where the field is zero and the backward like own where it’s a pure gauge transformation is zero and either the side light cones and then very close to like on if you solve the equations you’ll find that the solution is a1 plus a2 so that you can satisfy the boundary conditions along these light cones the problem with a 1 plus a 2 us it isn’t a solution of the equations of motion so things have to evolve in time as you go forward but that’s not important at very early times because they’re very real times that really is a solution and then if you look at what that means your mind

gets boggled because if you have a1 and a2 there you have a trim a to say e1 which is the source of charge along this light clock or a 2 dot b1 which is the source of charge here so infinitesimally is to go into the Ford like on all of a sudden the topology changed and you generate launch Nielsen pills which were fairly transfers and that’s totally wild because also hit do to get you to that conclusion or show you some pictures instant apology and I didn’t even have to solve any equations and isn’t that neat that’s kind of mind-blowing okay I well I thought it was maybe you okay but whatever hey um okay now why is this weird well having both electric and magnetic fields in field theory Oh is actually kind of an interesting situation imagine that you have an electric field that an electric charge gets accelerated in that direction spirals this way around a magnetic field now take a positron it goes in the opposite direction that it spirals in the opposite direction so such fears always will generate vorticity in the fluid it will prefer certain kinds of chirality what I’m giving you there are sort of a 15 seconds of derivation and a tooth to normally which says these long fuels can produce particles of a particular olicity to get to be strong enough so these fields actually do weird things like locally they violate CP and stuff like that and parity and they do funny things to charge they also associated with things called anomalies in field theory and electroweak theory such a normally generous thought perhaps generates a video number the universe through the electroweak anomaly in QCD it’s associated with the generation of mass and masses of protons and neutrons and its enormous mass generation moreover an even more bizarre things happens the interactions of these evaporated gluons with the classical field is really big because even those even if ice cores have weak interaction strength the gluon field itself is strong has strength 1 over G and so it’s very strong so maybe these fields even generate thermalization of the matter in these collisions maybe maybe not but certainly the the the structure is a nursery so here’s a relationship with some of this work to this Cup which googa and an Eisenberg and statistic II Cooper motto law sort of pioneered long long time ago and I didn’t tell you that old but but the idea was the following they they postulated that one had an electric field and that that electric field spontaneously decayed by pair production and they actually solved that problem with a good deal of detail in electrodynamics in fact many of the scaling relations they derived in that that people actually follow for this things which relate dimensional scales one to the other the constants you can’t get that the dimensional scales you can for example relations between the timescales energy density scales and multiplicity all follow from this work on the difference here the essential difference is that we have a magnetic field and if you have a magnetic field de DT is d cross B and because there’s a non zero magnetic field in the problem the electric field can decay classically and that also works for the decay of the magnetic field it can also became classically so you don’t have to have quantum pair production to have these fields evaporate into gluons it can all happen classically that said we didn’t quite escape because it was discovered that in fact even though you have this nice classical solution of the equation before the collisions after the collisions the solution you write down which solves this problem is unstable alright that’s good because actually what happens again isn’t using the classical solution works to a time of water one of the saturation momentum at the collision that these small unstable fields are generated by quantum fluctuations around that initial singularity and in fact the mathematics which describes those initial fluctuations is now just the mathematics was described excuse me talking Unruh radiation the growth of the instability generates a turbulence in the system and that turbulence will have a spectrum of scale sizes which is presumably some kind of coma broad spectrum which is analogous to zeldo with spectrum in cosmology it

will generate fluctuations those fluctuations are like what happens in inflation which the late times become the seeds for galaxy formation and here they generate fluctuations in the density of the matter distribution produced in collisions which actually are measured and you can maybe even hope to describe this in this kind of picture I found it absolutely amusing actually that after trying to escape all of these quantum fluctuations and pair production stuff which I tried desperately to escape for so long then in the end it came back and bit me on the tail right you can’t get away from it these solutions actually do have the instabilities they grow and eventually become so big they eat up the classical solution I don’t know of any other situation where this happens except in cosmology when one describes inflationary universe cosmology sort of similar situation goes on but it’s kind of ok ah well the color glass condensate and the gods made some predictions for it and predicted the told Malusi this is an ancient blot it’s not reproduced very well because I wanted to remind you was ancient when they first measured the multiplicity we got it right and almost everybody else got it wrong and in fact nobody got it right for the dependence of the multiplicity on the centrality of the collision everyone else got sort of too rapid arise the reason why this is not rising so rapidly is if you have incoherent scattering sing coherent scatters caused a rapid rise as you increase the centrality the collisions but coherence cuts us all coherence actually puts in the direction of reducing the magnitude affect you would have from the incoherent scattering case it makes the system more opaque if you want that any case one can describe the spectrum of fluctuations quite well in this kind of saturation picture and even more or less get the constants of proportionality right there was also a test of these ideas when one had tried to describe the distribution of particles in transverse momentum as a function of say the X of the nucleus with generators remember we’re describing what happens for the smallest explore on standing in a nucleus okay and so as we go to smaller and smaller that’s our proclamations become better and better now suppose you take a proton and you try and run it through a nucleus classically you’d say just multiple scatter and you produce more particles that some PT of course probability is conserved so you have to steal particles from low PT to make them at high PT and an extremely high PT the kind of typical transverse momentum you get compared to the momentum of the particles really small so you characteristically get this kind of behavior at at small PT is relatively small Rises it has the quotient peak and then falls down as you go to higher and higher PT and that’s what people had expected but the saturation of color glass picture says something different says you also have to take into account as you go to smaller and smaller values of X or higher and higher energies that the gluons can’t quite evolve as as rapidly as you naive we thought they would because what’s happening you had the saturation scale where all the gluons are packed together and you can’t put as many down there as you know even thought you could and what that means is when you solve the evolution equations you don’t make as many glance as you thought you could because you can’t put them into these places or they’re really tightly packed together so that means that the number of the a distant curve should fall and magnitude as you go to smaller and smaller values of extra higher our energies and in fact for the surprise with these calculations which were done by these folks some of the folks who did these things were here and they found that a low energy saw you in fact had this nice balloon at peak he went to higher higher he’s disappeared and in fact on this play that happened very rapidly and of course saw what happened was they did the experiment and here is what happens when you’re in the forward region this is when you have a collision which is not so long Central and this is the most central collision first off you see that these ratios are less than 1 meaning they’re suppression not enhancement and the other thing you see which is dramatic is than the more central collisions where you would have thought there would have been no scattering out of the beam there are less particles though and that’s due to evolution in fact that’s what I do I do

something bad ok you can also see this another way from the Phoenix experiment the Phoenix experiment they can measure things simultaneously in the backward region in the forward region and and for not so central collisions they see the clone and enhancement the backward direction particles being scattered out of the beam at low X and it’s at high X and at the central region is sort of kind of about 1:00 in the forward region not too much is happening here things are about 1 but now you go to more central collisions secona peak is really enhance for the things which are in the fragmentation region of the nucleus the small that stuff has really gotten suppressed okay so that’s positively like what you expect in these pictures now of course the story is that you know all the betting was again you when you started okay but all the best change sign after the experiment came out okay so you know you can you make predictions predictions are good to carry some sociological and psychological value we got it right other people got wrong doesn’t mean it’s right I don’t know you know one has one needs more tests and requirement and ultimately in theoretical physics you don’t show that theories all right you show their wall okay and one can pass the number cows and this passes a number test but we’ll have to see as things get more and more refined ah I don’t know if I really want to go here I’ll go there just to this slide and I’ll leave out the mathematical cyclist I’ll maybe explain more in Thursday actually it’s more than this upper questions at this point before actually nothing other questions at this point people are reasonably happy well I don’t know okay so you can ask the question now if you want to very high energies you could imagine that there’d be two possible cases that’s when all the blue wants are packed together and they’re sitting on top one other than the system is completely black and you can’t see your way through it because all the gluons are really piled together and the other situation is where all the gluons are uniformly distributed over the disk of the object and that’s the other phase of the system and you can ask whether that’s true and the surprise is it does not seem to be true what actually happens is more bizarre actually at the very very high momentum scales very small resolution skills when the density of particles are small the gluons temped together in spots and these spots are highly coherent if you like spots of color glass condensate where they’re highly coherent and if you ask what this means for high-energy scattering you will be surprised because you will see that because these things are acting weak coherently and they’re sitting on top of one another this doesn’t factorize and in the ordinary sense so what factorization means if you take a very tiny probe and run it through the system at a very very high momentum scale you’ll measure the distribution of objects in this thing and then if you take another poll okay you should be able to calculate how that other probe in another scale on behaves for example a proton or nuclear and it back there’ll be no factorization between a glue probe like an electron and dense fog like a proton or nucleus which has a distribution of spots like this another way of saying this spot spot scattering it’s not the same thing as on taking in coherent guangwen scattering so factorization breaks down which is one of the sacred cows of alpha high-energy physics it’s a sacred cow that is a sacred cow which you can’t prove is true in the small x limit and what usually happens in physics is when you can’t prove something is true it turns out not to be true but it’s a surprise and maybe this is the case and it maybe can have some dramatic consequences for very high energies that’s very high energies yep no they’d be the obvious one is you’d have to compare electron have non scattering with with a nucleus nucleus scattering that would be the simple one – the simple one whose most direct and you find that the gluon distribution function measure and lepton nucleus scatter would not be the same you measure and have no nucleus Catterick nucleus nucleus compared to how our nucleus is more complicated because you need to know more about the details and a proton relative out of the nucleus ok this is very very new this story ok and what its consequences are it does have this consequence in detail what it is

it’s not been worked out ok ok so I want to finish so I finished here and just open it up for questions ok no it’s not obvious vvvvv issue is high art in fact I don’t I try to use the word strongly interacting popcorn plasma rather than strongly coupled strongly coupled in in this context is the intrinsic coupling constant of the theory is big strongly interacting can mean that there are strong interactions even though the coupling this week there are examples of that in physics a colonic system where you have a nucleus which has a very large Z even though E is small Z alphas big so when you scatter electrons off a very highly charged nucleus the interactions are very small so coherence and sometimes generate effects which look strong even though the intrinsic coupling strength could be weak okay now the issue of the strongly interacting quark gluon plasma is an issue which is one which is experimentally rhythm okay there are claims that when you do hydrodynamic calculations of these collisions that those psychodynamic calculations will describe the data quite well he set the viscosity to be small that said you’re also making very specific assumptions on the initial conditions for those collisions and if you change those initial conditions you can compensate for that by jumping furthest kospi so I you know I think it is true that it is quite remarkable the dieter dynamic calculations get you close okay the conclusion that it’s really strongly interacting or an intermediate strength interaction what’s really driving the dynamics which gets a close hydrodynamic limit I’m a little skeptical it may turn out it’s okay but screw it is strongly coupled but then it’s an empirical fact is not being drew lining strong theoretical prejudice one way or the other I was in the glossary you can’t because the glossners weekly couple thing and it has hi I call it colorful intensities and you know the color field density goes like bone over G squared okay so G is falling of course you won’t have that kind of coherence on in the quote glowing Ozma that’s a different story and and there can be in principle and I had sense an interesting question to try to sort that out and see what the truth is presumably that will happen yeah you want to see I’ll show you yeah you can figure it out the point is that those spots okay on that system okay those spots can be described by field Y of X which is basically the logarithm the saturation momentum scale this is a two dimensional system the gradient squared should go like the saturation limit is Gordon dimensional grounds ah therefore the Lagrangian for this theory has to be D to Eretz grad Phi squirtles that was worthy to the part that’s a conformal field theory okay however in order to get the saturation momentum averaged be nonzero got a source of the problem to break the symmetry now you say that’s a disastrous thing do you know what the funny thing about it is if you break that symmetry in the theory the theory was started out as a purely conformal theory was only renormalizable theory and it seems to theory when you had a source in to break the symmetry turns it into finite table 3 that’s bizarre because ordinarily that doesn’t happen but it happens here because the infinities that that 2 dimensional theory are driven by almost zero modes of the conformal field theory that is kind of neat you know whether whether this theory of what’s happening with these spots as to as much if you’re than whether those spots are true I think those spots are probably true they really are they’re this theory and whether really despise what without that distribution the spot may or may not be true but it is kind of interesting that a conformal field theory arises in this context in a nice way you know for what it for what it’s worth yeah you can come down here you actually

come down actually if you stand up at home no no no no the issues are falling it’s in the initial wave function the initial wave function exists forever and that’s the color glass condensate and after the collision it’s plasma glassman is not something which is the glass was not a glass glass m’a is as sludge which you made from this hot glass it’s like melted glass that he liked and in fact in fact when they talk about real glasses okay every material called the Glassman which is associated with this multi glass light I didn’t even really invent and the term there that the Glassman really is describing this state after the collision are congruent so partially melted some of its coherent but it’s evolving the natural time skills so what you’ve done an equation is somehow you shock the system out of this glassy state but before the time skills really are very much elongated and if the states which are contributing to the wave function of this had drunk our states which have this glassy property now technically does it have all the properties you get when you really saw for a real glass certainly not but it certainly has a party when you calculate these configurations the partition function for this like a stained glass partition function so mathematically has lots of analogies look one of the troubles you get into when you’re in debt no words which I like to do because it’s sort of fun is when you’re inventing a new words you’re inventing new words for a new thing okay and those new words are again like metaphor like art okay they’re partly correct that they’re also partly wrong but if they’re successful words they become words which have a life of their own and a meeting of their own which supersedes how they were invented okay and so you know please give give me some feet of some literary and artistic freedom to pick you know we need that as physicists once in a while we get to invent a word which is maybe not exactly correct but catches on and is useful and this is a useful phrase and much of the mathematics is kind of an allergen transferable that’s good oh I don’t know I don’t know it’s a good question I can tell you can tell you what happened I can tell you what I I don’t know how the rapidity correlations call which is part of this problem because we don’t know that the theory I wrote down for this is where the correlations in the transverse pace but it is interesting the transfer space that it appears that the correlation functions at large at small transverse distances are given by naive conformal dimensions which is kind of amusing but again the kind of structure you’re talking about for intermittency our correlations which are done over rapidity and this the theory I wrote down was the theory was supposed to describe dense locally in rapidity and you know one could go beyond distant principle that hasn’t been done yet yeah that’s what I refer to yourself well look no no no no what what happens first okay because there’s a nonzero E and a nonzero B that classical longitudinal feels can classically evolved a way to transfer skin like radiation fields when you generate radiation from an antenna there are coherent fields near the antenna and sources but far away from the antenna you have this purely transverse fields okay that’s what happens here classically unfortunately that solutions not quite correct okay because when you get when you get to there when you look at small perturbations around that and I eat classical solution a boost in a very classical solution you find that non boost invariant fluctuation is grown and eventually they become as big as the classical field you started with so the system which was nice and flat and rapidity and a rapidity distribution look like this after some time gets all sorts of legal team and those wiegel’s are generated by those unstable modes so

it in the end it is quantum fluctuations which are driving the system then in this bizarre way it could start off classically but eventually the quantum fluctuations catch up with it weirdo other questions status

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