Ian Moult: Unveiling QCD Dynamics with Energy Correlators

What this episode is about

Ian Moult discusses recent advancements in quantum chromodynamics (QCD) and how they bridge the gap between theoretical frameworks and experimental observations at collider experiments. By focusing on observable phenomena like confinement and QCD flux tubes, he emphasizes the potential for new experimental insights that could enhance our understanding of real-world QCD systems.

Key takeaways

• Bridging theory and experiment in QCD could finally unravel the mystery of confinement phenomena.
• Recent advances make previously elusive experimental observables now relevant to real-world QCD studies.
• The complexity of QCD observables mirrors the challenges of deciphering a botanical labyrinth; every layer hides secrets.
• As we celebrate 50 years of QCD, let’s not forget: theory and experiment need to tango closer.
• Energy flux measurement may just be the QCD Rosetta Stone, revealing truths hidden in collider chaos.

Who speaks in this episode?

• Ian Moult (Host) · 44 min speaking

What is discussed, and when

1. 0:00 – 5:00: QCD, asymptotic freedom, energy flux operator, George Sturman
2. 5:00 – 10:00: George Sturman, Hoffman and Maldina, David Simmons Duffin
3. 10:00 – 15:00: Pluto experiment
4. 15:00 – 20:00: Yanji Lee, CERN, LEP, Pluto experiment
5. 20:00 – 25:00: George Sturman, E plus E minus alliance
6. 25:00 – 30:00: Pluto experiment

Notable quotes from "Ian Moult: Unveiling QCD Dynamics with Energy Correlators"

• Is interested in from the theory side. and this makes me optimistic that we can actually learn things about confinement phenomena in the real world from experiment. so as…

  about QCD · at 0:47

• And so this is something which you can directly measure in real world QCD and it can actually tell you something about the dynamics for example of confinement. and so this idea was.

  about George Sturman · at 4:40

• Observables were resurrected about 30 years later in this important paper by Hoffman and Maldina. and so they really emphasize kind of two important key things. So the first is…

  about Hoffman and Maldina · at 5:56

• I showed as Pluto where it's measured as a function of the angle between the two detectors but this is now done at the higher energies of LEP. So this is now at a center of…

  about LEP · at 16:42

• Bit disappointing because of course as you know LEP is now retired and so in particular you can go to CERN and this is a particular detector from the LEP experiment. In…

  about CERN · at 17:42

• And so Yenji really started this program to kind of resurrect this data to be able to do precision physics and in particular study aspects of QCD using all this beautiful data. and so.

  about Yanji Lee · at 19:22

• Currently. and so the kind of outcome of this is there's now this nice group of experimentalists from quite a few different universities which go to the name of this E plus E minus alliance which are really kind of serious.

  about E plus E minus alliance · at 22:17

Who and what is mentioned in this episode?

People

• Yanji Lee — Person · Collaborator (experimental lead on data resurrection) · 2 mentions · first at 18:50
  Described as the speaker’s collaborator and an experimentalist who led efforts to resurrect and modernize preserved LEP (ALEPH/DELPHI) datasets for precision QCD/energy-correlator measurements.
• George Sturman — Person · Referenced expert (historical originator) · 3 mentions · first at 3:54
  Credited with introducing the energy flux operator (a foundational idea behind energy correlators) in the mid-1970s, framing the talk’s historical arc from theory to collider observables.
• Hoffman and Maldina — Person · Referenced authors (revival paper) · 1 mention · first at 6:00
  Cited as authors of an influential paper that resurrected/modernized energy correlators, emphasizing their applicability to generic QFTs (especially CFTs) and their relation to local operators like the stress tensor.
• Steven Ellis — Person · Referenced expert (method generalizer) · 1 mention · first at 4:54
  Cited for generalizing early energy-flow ideas to multi-point energy correlation functions, connecting collider event characterization to higher-point QFT correlators.
  Significantly generalized in the kind of late 1970s by Steven Ellis and collaborators who said one can measure just like you do for example in the CMB instead of measuring kind…
• David Simmons Duffin — Person · Referenced expert (illustrator/communicator) · 1 mention · first at 6:26
  Credited for a picture/illustration used to explain energy correlators in a conformal field theory setting, supporting the talk’s bridge between collider observables and general QFT/CFT ideas.
  And you can consider an example. And so this picture was made by David Simmons Duffin. And so his favorite conformal field theory is the icing model. And so you can imagine that you have some 2 plus 1D sample of the icing.
• General Thomas Sarsfield Power — Person · Referenced authority figure · 1 mention · first at 18:00
  Mentioned as the (then) CERN director via a book preface about LEP’s legacy, used to contextualize LEP’s retirement and the motivation to revive its data for new physics studies.
  Some plaques about how nice this experiment was. And you can also get this book which has this preface by Rolf Power who is the director of CERN where it says the kind of LEP…

Companies & orgs

• LEP — Company · Referenced organization · 2 mentions · first at 16:45
  Mentioned as the experiment where early measurements of energy correlators were performed.
• CERN — Company · Referenced organization · 2 mentions · first at 18:00
  Mentioned in the context of the LEP experiment and data preservation efforts.
• E plus E minus alliance — Company · Referenced organization · 1 mention · first at 22:27
  Group of experimentalists working on resurrecting and analyzing old LEP data.
• ALF — Company · Referenced organization · 4 mentions
  Mentioned as one of the experiments that invested in data preservation.
  And use this early data to study confinement. and so one thing which is very nice is that two of these experiments Alo and Deli actually invested significantly in data…
• Deli — Company · Referenced organization · 1 mention · first at 17:50
  Mentioned as one of the experiments that invested in data preservation.
  And use this early data to study confinement. and so one thing which is very nice is that two of these experiments Alo and Deli actually invested significantly in data…

Concepts & topics

• QCD — Concept · Core topic · 1 mention · first at 0:13
  Central theme of the episode, discussing the connection between real-world QCD and its underlying field theory description.
• asymptotic freedom — Concept · Key concept · 1 mention · first at 3:49
  Fundamental property of QCD mentioned in the context of early theoretical work.
  Flux at some particular angle is actually calculable in perturbation theory. and so this is very important because unlike things let's say like scattering amplitudes this object actually has a smooth infrared limit.
• energy flux operator — Concept · Key concept · 1 mention · first at 3:58
  Introduced by George Sturman as a way to connect theory and experiment in QCD.
  Underlying theory. and so what he showed also in his early work is that this expectation value of this energy flux at some particular angle is actually calculable in…
• CMB — Concept · Referenced concept · 1 mention · first at 4:58
  Mentioned as an analogy for measuring multi-point correlation functions.
  Late 1970s by Steven Ellis and collaborators who said one can measure just like you do for example in the CMB instead of measuring kind of multi-point correlation functions of…

Places & events

• Pluto experiment — Event · Referenced event · 3 mentions · first at 11:58
  Early experiment where the energy correlator observable was first measured.
  These plots more in more detail later for the actual measurement but this is similar to the measurement which I showed as Pluto where it's measured as a function of the angle…

Full transcript with timestamps

0:09 Um so today I'm going to be talking about some work that I've been doing with a number of uh excellent collaborators on trying to sharpen the connection between real world QCD in particular at collider um experiments with its underlying field theory description. Um and so particularly when it comes to phenomena such as confinement or QCD flux tubes, there's often a kind of big gap between what is done in the theory world and what is done um in experiments. Um and so we what we wanted to do was to try and um sharpen this connection. Um and I hope to be able to convince you that due to a lot of recent advances, it's now possible to actually study on the experimental side observables which are much more closely connected to what one is interested in um from the theory side. Um and this makes me optimistic that we can actually learn things about confinement phenomena in the real world um from experiment. Um so as everyone

0:58 here is very familiar in the last several decades there's been tremendous progress in our understanding of gauge theories which has been driven both by amazing um numerical simulations as well as by insights from a variety of um simplified uh toy theories. Um and so this has led to a qualitative and in certain cases quantitative understanding of many simplified observables. So things like expectation values of Wilson loop, certain correlation functions, etc., etc. Um but sharpening this picture for real world QCD and relating it to observables of interest in real world QCD remains an extraordinary challenge. Um but as you've heard at this meeting, there's been a lot of exciting progress um from this collaboration. Um and so at least for myself, so one of the most beautiful aspects of real world QCD is that it is in fact real. Um and so this is also what makes a lot of the goals of this collaboration um very important. Um and

1:54 so one of the nice opportunities that we have because QCD is real is that much like in condensed matter, we can in principle try and study some of its phenomena experimentally. Um and just like in condensed matter we can hope to be kind of inspired um on the theory side by what we observe experimentally. Um but of course in reality this is much more complicated because of the time scales which are involved. Um and so one of the major difficulties which is important to appreciate in trying to learn things from experiment about real world QCD is not just that real world QCD is a very complicated uh field theory but it's actually that a lot of the observables that we have access to experimentally are very complicated observables. So for example, very complicated collisions like this. Um and so if we could actually go out and measure for example some correlation function or some kind of Wilson loop

2:39 expectation value even if we couldn't understand it from uh first principles calculations we could at least compare it to similar observables which we understand um in our favorite um toy theories and this would provide a lot of insight into phenomena that we don't understand in QCD and then we could try and um improve and kind of sharpen our understanding of these interesting phenomena. Um and so this is really one of the uh major difficulties in this field. Um and so what we would like to try and do is to kind of sharpen this relation between what we can actually observe experimentally and things that we can um understand kind of very sharply at least in toy theories to try and draw um general conclusions. Um and so because of this kind of lack of um connection in the last several decades, I really think that this is what has kind of driven um experiment um and theory apart um particularly when it

3:26 comes to QCD. Um and so this kind of idea of trying to connect theory and experiment and collider physics experiments has a very very long history going back now about 50 years to the um kind of beginning of QCD. Um and so I wanted to highlight um at the beginning that because this fall is actually the 50th anniversary of some of the first attempts in trying to connect theory and experiment um in QCD. Um and so in particular in um 1975 a little bit after the introduction of asmtoic freedom um George Sturman who was inspired by kind of what you actually do um in experiments introduced what we now call the energy flux operator. Um and so this is motivated by what you literally do in an experiment. Um and so he wanted to define an operator which is just like a calerimeter cell and it's kind of measuring the flux which comes off in some particular um direction. Um and so what he proposed is that one could

4:14 measure or one could compute um expectations values of that energy flux operator which as I'll show in a second are kind of related or are directly related to threepoint functions in the underlying theory. Um and so what he showed also in his early work is that this expectation value of this energy flux at some particular angle um is actually calculable in perturbation theory. Um and so this is very important because unlike things let's say like scattering amplitudes this object actually has a smooth infrared limit.

4:40 And so this is something which you can directly measure in real world QCD and it can actually tell you something about the um dynamics for example of confinement. Um and so this idea was significantly generalized in the kind of late um 1970s by Steven Ellis and collaborators who said one can measure just like you do for example in the CMB instead of measuring kind of multi-point correlation functions of temperature fluctuations you can do this also for these multi-point correlation functions of energy flow. Um and so in particular he proposed that you could kind of characterize um events in QCD um by measuring multi-point correlation functions which again in the underlying field theory would correspond to like four five or higher point functions um in QCD and then this would tell us a lot about the distribution of energy in QCD and ultimately of the underlying field theory. Um and so this was something

5:30 which was pursued vigorously in the kind of late 1970s going on into the late 1980s and it was very important for establishing um the theory of QCD as the theory of the strong interactions. But then as that was kind of established people lost interest in like this kind of direction and these things were kind of left um for a long time about 30 years um as just kind of something which people do um in QCD and that nothing kind of beyond that. Um and so these observables were resurrected about 30 years later in this um important paper by um Hoffman and Maldina. Um and so they really emphasize kind of two important um key things. So the first is that these observables which I'll refer to as energy correlators are kind of interesting observables for characterizing generic quantum field theories. So they're not something that you just do in QCD. And in fact, they're very natural in, for example, conformal

6:20 field theories where you don't necessarily have a standard um Smatrix. Um and you can consider an example. And so this picture was made by um David Simmons Duffin. And so his favorite um conformal field theory is the icing model. And so you can imagine that you have some 2 plus 1D sample of the icing model. And you can excite it at some particular location and then kind of measure the fluxes um which come out um to infinity. Um and so this is some natural set of observables which you can measure in just completely um generic theories. um much like you do in um QCD.

6:49 And so this is very helpful in trying to connect what people do in the specific case of QCD with what you can do um in more generic quantum field theories. Um the other very important thing which they it was already kind of known but they really re-emphasized um in this work um is that you can directly relate what you're actually measuring or what you're measuring at infinity to operators in particular local operators of your underlying field theory. So in the simplest case if I'm just interested in measuring for example the energy flux at infinity I can write down this calerimeter cell which earlier um I showed this picture of George Sturman had written in terms of the action on kind of particles coming off to infinity but you can really write it as a particular integral of the stress tensor of your underlying theory. So you kind of dot it into some particular direction take it off to infinity and so if all

7:34 the particles in your theory are massless you really just integrate it along um future null infinity. Um and so this provided a nice kind of connection between um what these detector operators um and the kind of local operators of your underlying um theory. Um and so this was extremely important because it really provided a direct relation between what you can do um in experiments namely measuring these asmtoic fluxes and the kind of spectrum of local operators of your theory. Um and so instead of being functions of the kind of positions of these um operator insertions like you would have for a normal um correlation function. So instead of being just functions of position, these are now functions of angles on the celestial sphere. Um and so I'll often denote these angles. So instead of doing in terms of the literal angle, I'll often write in terms of this variable zed, which is just related to

8:22 the angle like this. And so in particular zed goes to zero as these two detectors become on top of each other. and zed goes to one as these two detectors become um anti-totally um separated um

8:41 good absolutely so yes I'll be more careful about this um later and so of course in real world QCD we are measuring massive particles and this has an important distinction um and so the way that I've written um this shown here as this actual limit can be done properly to um incorporate the fact that in QCD things have masses and I'll actually show this of course as you would expect has an actual impact on the distribution and I'll be more careful about that um later on um but in the case that it is a CTF it really reduces to this very simple integral along null infinity and some often I'll kind of draw that schematically but I'll highlight this later when we do it in real world QCD perfect um okay and so this kind of had two very nice um uh impacts on the field so the First is that just at a practical level, it enables us to use properties of these local correlation functions to compute

9:33 observables which we can measure um in collider physics experiments. So just from a purely practical perspective, this is extremely useful and often these are much better understood than what we might be trying to do um in collider physics experiments. Um and so the second um thing which is in some sense much more important is it made us able to connect um to calculations in our favorite toy theory. So this is a perfectly well um defined observable. you can take whatever theory you want and you can compute it. And so this really provided a very nice connection between what we want to do in the real world um or observables that we can study in the real world and observables that we can study in um simplified uh theories. Okay. And so the other thing which I've already emphasized but I just want to make very clear is that we can actually directly measure these observables in the particular case of

10:18 electron posetron colliders. So here we have a literal map um between what we would like to do in this kind of picture and what we can actually do in experiment. Um and so in particular in this case we can really excite the QCD vacuum with a local operator which is just the electromagnetic or the electroeak current. Um and we can measure the asmtoic fluxes which are coming off to infinity. And in particular we can do that as a function of the angle between the particles. And so we can really map out the behavior of this correlation function over its complete um kinematic range um going all the way from this kind of backto-back limit which I mentioned all the way to the limit where the detectors are so-called colinear or on top of each other. Um and so this is extremely satisfying because this really provides a very sharp relation between what we can do in experiment and where we can literally study um QCD um and four-point

11:06 functions in particular of the stress tensor. And so it should be clear that one is under no illusion that we can really understand this non-perturbatively in real world QCD. And we're very familiar that there's huge distinctions between the complexities of QCD and the complexities of these toy theories. But just h establishing such a mapping is a good first step towards understanding this. Um and so this really enables us to identify observables where we can go and then compute them in other toy theories and then try and sharply understand um distinctions in particular related to confinement um in the real world. Um and so of course this was an observable which was proposed very early on and so people measured it at very early experiments and so I wanted to just since I've been highlighting some of the experimental aspects to kind of show um this measurement and this will also familiarize you with what you're going

11:53 to be seeing um later. So this observable was first measured actually in 1979. So a very long time ago at the Pluto experiment. So this is when experiments were quite um small. And so this is running at 13 Gev. So it's quite a low um energy. And so they made this plot of the distribution of this energy correlator observable. And so again just to kind of orient you. So it always ranges an angle between 0 and 180° going from this regime where you have the two detectors literally back to back. you have some kind of middle region where your detectors that are at kind of 90 degrees and then you have this limit where the two detectors um are colinear.

12:27 Um and so you get this nice um kind of distribution um which comes out. And so because I emphasize that this is something that is really um calculable in QCD, you should be able to directly compute this um and compare with what you get um in real world or in the data. Um and so this was done very early on and there was actually a huge amount of kind of theoretical firepower which went into trying to make this first kind of theory data comparison. So in particular it was computed in this limit of the kind of two detectors coming back to back by Parisian collaborators. And so the reason why there's kind of specialized calculations for the different limits I'll come back to. It was then computed by Konishi and Venitziano in this um small angle or colinear limit and then it was combined with this calculation which I mentioned earlier um by Ellis and collaborators um in the middle. Um and so what you can

13:13 see is that you have quite horrible dis or agreement between um the theory and the data. But nevertheless, this was kind of a first attempt at actually making a comparison between descriptions of energy flux um and correlations in QCD and trying to learn something about um QCD by comparing it with this type of observables. Um and of course this is not unexpected because this is at very low um energies. Um okay, sorry. So this is E plus E minus. So this is actually the center of mass energy.

13:53 It's high compared to the QCD scale and so I should say so it is high but it's not that high and so you have quite large non-pertive corrections and so I should also emphasize so this is done with like leading order calculations. So from a modern perspective we can get much better agreement. Um and I'll I'll show later. So we can now go very much much better. Um but for this level of calculation it is not a bad a bad agreement. Um and so exactly related to your to your question um one thing which is will become very important in going forward is to understand the scales which are actually probed by the measurement of this correlation function. Um and so in particular we're very used to for um correlation function or for example uklidian correlation functions that the scale which is being probed is just essentially proportional to the inverse of the distance between the two operators. Um, and so as you

14:38 bring the operators together, you probe the UV and as you bring the operators apart, you probe the IR. Um, and so because these observables or the detectors are placed at infinity, you essentially flip this relation. Um, and so this is actually very nice or this can be viewed as advantageous because the scale that you're probing is actually dependent on the um or the angle between the two detectors. And if they're at some generic angle just for example 90 degrees where zed is generic you're really probing the scale at q ^2 which is related to your um question but as you bring the detectors together as zed becomes small you actually probe the infrared of your theory and you're probing a scale q ^2* zed. So this is why in these experiments you're actually probing also much smaller angles. And similarly as you bring the detectors exactly back to back you're probing a scale of q ^2 um* 1 - z. Um, and so one

15:28 of the reasons why this is very nice is it's just like as if you actually had a correlation function of the local operators and you can kind of dial their positions and probe this theory at different scales. And so in particular, if you have just a single collider at some high scale Q ^2, then by varying the angle between the two detectors, you can actually sweep out the energy that you're probing the theory at over, for example, multiple orders of magnitude. Um and so in particular if you had for example infinite angular resolution you could really perform this measurement all the way from a kind of very high scale Q^ squ where you're probing the dynamics of the kind of parts in your underlying theory and you can sweep this to sufficiently low angles that you actually have kind of subconfinement resolution and you can kind of really image the transition from parts to hadrons. Um and so this is this nice

16:14 advantage of doing things asmtoically is you can kind of really in one experiment sweep out a kind of huge range of scales in QCD. And so this is very nice because we now have both an observable where we can actually understand what is probing in the theory and we can also use it to study the kind of confinement transition or to sweep out the dynamics of QCD as a function of scale. Um and so this was attempted early on and I'll explain these plots um more in more detail um later for the actual measurement but this is similar to the measurement which I showed as Pluto where it's measured as a function of the angle between the two detectors but this is now done at the higher energies of LEP. So this is now at a center of mass energy of about 90 um Geb and you can see that what happens. So what again what we wanted to or what we said that we wanted to do to study for example the dynamics of

16:58 confinement was to study these two asmtoic limits either when the detectors become perfectly on top of each other which is this side or as the detectors become very backto-back which is on this side. Um and you can see in the data that essentially what happens in those limits is things just go completely crazy. Um and so you kind of lose control over what's happening um in your experiment. And so as a result, these were kind of the best um measurements which were ever performed and they were performed in essentially the late '9s.

17:24 Um and there's been no kind of experiments um since then. And so as a result, the kind of direct measurement of this confining transition where you could really kind of use this to learn something about confinement in QCD was kind of always left murky and was never really um uh performed. Um and so this is kind of problematic or a bit disappointing because of course as you know LEP um is now retired and so in particular you can go to CERN and this is a particular detector from the LEP experiment. In particular, this is the um Delelfy detector. And so you can read some plaques about how um nice this experiment was. And you can also get this book um which has this preface by um Rolf Power who is the director of CERN where it says the kind of LEP experiments have published their last uh papers, but it will live on um in textbooks. Um and so this is a little bit disappointing for trying to actually

18:10 study um these kind of nice properties of confinement. Um and so actually I I kind of attended a number of the early workshops of the Simon's collaboration on confinement and QCD strings. Um and so we were really motivated to kind of go back um and actually use this data because of the recent interest in confinement to really kind of bring it back to life and try and focus on understanding aspects of confinement in these energy correlator observables. Um, and so this will be a little bit of a detour, but it's kind of an entertaining detour on trying to actually go back um and resurrect um the data from these early LEP experiments to use it um to have improved insight into confinement.

18:46 Um and so, as I said, motivated by um this recent interest in confinement um with my collaborator um Yanji Lee, who is a very good um serious experimentalist, um he wanted to go back and actually try and use this early data um to study confinement. Um and so one thing which is very nice is that two of these experiments Alo and Deli actually invested significantly in data preservation. So they stored all their data that was taken um at that time. But of course there's a very different thing to just having some of this data and using it for for example educational purposes versus trying to actually do kind of precision um physics with this.

19:22 Um and so Yenji really started this program to kind of resurrect this data to be able to do precision physics um and in particular study aspects of QCD using all this beautiful data. Um and so one of the reasons why this is still actually possible is that these collaborations still exist in some very uh reduced format. And so you can go for example to CERN you'll find this room where they actually have for example some remaining um ALF members. Um and if you go into it you'll actually find so at that time they um had event displays apparently printed on transparencies. Um and you'll find this actually just fused into the wood of the table. Um and so this suggested that there was going to be a big gap um between really trying to um extract this data and using it um for modern purposes. Um so as one continued things got even worse. Um um and so in particular one thing which I had not appreciated um is that all

20:14 this old data of course they don't use kind of modern um computers but is all stored on very old floppy discs. And so in particular you actually need to find the original computers to be able to run this. Um and so even after that was actually done, some of these had even um just kind of dumber problems, namely that some of them are password protected. Um and so you have some of these very old uh Windows computers where you actually cannot extract or run in particular certain of the detector simulations. Um and so this really took an immense amount of effort from these experimentalists. A lot of it is just not even physics but just kind of detector work in going through kind of old notebooks from this time to kind of extract um all this data um and get into a form which is manageable. Um and so the outcome of this is after this huge amount of effort which took um several years we actually have the kind of fully

21:01 modernized versions of the ALF and Deli um data sets um which we can use to study aspects of QCD. Um yes

21:10 so the good so so far has only been done for LEP one. So there there is also there is the data for LEP 2 but it has not yet been analyzed because this is a little bit more complicated because you go above the WW threshold and so this needs to be treated a little bit more carefully but the data is there it just has not been reanalyzed um and this is in particular an issue because for some of these detector simulations um so there's one experiment so this one is password protected and so you can't you actually can't do the detector simulations and that prevents doing more sophisticated things for this deli experiment you actually do have the higher energy data And that's being analyzed right now. Um, which will be very nice. Um, yes. Yes.

21:51 Can't you like crack the passwords? Is it really old? Yeah. Yeah. Yeah. So, so yes. So, I think that will be that will be done, but that has not been done yet. Um, yes. But yeah. Um,

22:00 the scope. It's outside the scope of this talk. Yes. Um Um, but yes, I mean. Yes. And so that would be very nice because then that would enable the full um leptu data set. And so you'll see that I'll I'll only have things at the Z pole. And so the LEP 2 would be very nice to go even higher energies and and that is underway currently. Um um and so the kind of outcome of this is there's now this nice group of experimentalists from uh quite a few different um universities which go to the name of this E plus E minus alliance which are really kind of serious experimentalists trying to use this um data. And so kind of another fun um anecdote is that this entire LEP one data sets the LEP 2 one is bigger but the LEP one which I'll use here is 28 GB. And so for like eight dollars you can have your own um copy of this and can easily analyze it um very nicely. Um okay so one question which you should

22:52 ultimately um have about trying to do something better with this old data is that these measurements for example of these um energy correlators are going to be fundamentally limited by the detector resolution. Um and so this is something which is famous in cosmology that to really kind of get these beautiful pictures that one sees one had to really update from the kind of kovi to w map to plank. Um so a question one should ask is if we have these kind of very old and outdated cameras how can we do better without having a new detector. Um and so to understand this it's a bit of a technical detour but I kind of wanted to emphasize it because it's really what enabled um these measurements to give um a lot more kind of power than they used to. So one thing which is important to know is that charged particles which leave tracks can be measured with very very good resolution in particular using

23:35 tracking detectors. You can think of them as being able to be measured with these kind of very modern um detectors. Um whereas neutral particles are what are measured by these giant detectors out here and these have very poor um resolution. Um and so in all these old calculations and in particular the statement of George Sturman which I um cited before require that you sum over both the charged and the neutral particles and so this is because of this KLN theorem which requires that you sum over all states to achieve an infrared red finite answer which is computable in perturbation theory. Um however in the kind of 30 or so years um since these early measurements um there's been a lot of progress in our understanding in particular of effective field theory um and so using kind of modern effective field theory and reormalization group techniques we can actually do something for these detectors which is very much

24:21 similar to what we normally do in the study of local operators namely we can just use kind of matching um calculations and to match between UV detectors um and infrared detectors which measure the hadrons um and so in particular you can think of these infrared detectors is actually literally measuring the hadrons and so they can incorporate properties such as charge or other properties of the hydrons which you might want to um um incorporate and then you have UV detectors which kind of reach in um and actually measure the individual um quarks and gluons um and you can derive and I've written it very um schematically but just like you would for local operators you can actually have some matching equation between your kind of nice um in this case infrared detectors and your UV detectors um over here um and so the the very nice aspect of this is that we can actually do this kind of very um or systematically. Um

25:09 and this really enables precision theoretical calculations for measurements using these tracking detectors. Um and so in particular this enables us to kind of unlock this data which was kind of measured from this inner tracker of these old experiments which was never used and was just kind of sitting there for um 30 years. Um and so just to kind of illustrate the improvement that this actually leads to. Um so this is a kind of map of the celestial sphere where these two dots are meant to represent the two kind of energy correlator um detectors. And so over here is the resolution which was achieved in this first uh Pluto experiment. Here is the resolution which was achieved in these kind of ALF and um LE measurements um in the '90s. And this is the resolution that we can now achieve using this um inner tracking detector. Um and so this really kind of transforms um what we're able to actually measure and this enables us to

25:58 um measure for first the first time at an actual subconfinement resolution. And so we'll be able to see kind of interesting um QCD confinement phenomena um using these measurements. Um okay. And so using that what we wanted to do is to use this amazing data set to actually measure these energy correlator distributions all the way from this kind of partonic regime um to this um hydronic regime. Um and so we recently had this paper with a large number of um excellent experimentalists um as well as theorists. And so we were very happy that we were able to kind of disprove um this and actually use this LEP data um and publish a kind of new paper using their um original data. Um and so before I show you the actual result for the distribution in QCD, I wanted to first show what this looks like in certain toy theories to kind of orient yourself um to how this or so to kind of give some intuition for how this observable

26:46 behaves. And as I said, the kind of nice thing about this observable is you can compute it in a variety of different theories and compare it to QCD. Um, and so the simplest theory which one can consider is just a completely free theory. And so to make it have something interesting, what you can consider is some large charge operator. So for example, just phi to the K or some heavy operator which you put in. Um, and so here there's really no interactions. This produces just a kind of whole bunch of particles um coming out like this.

27:09 And so you can compute this and it's just an exercise in phase space um saddle point integration because there's no um interactions. And so what you get is that the distribution is uniform which I've shown in this kind of data in this um dash purple line plus some corrections which go like one over k. Um and so it'll be important when in the future plots to kind of associate this kind of flat behavior with this kind of uniform um distribution of kind of non-interacting things. Um so the second example which is much more interesting um is in a conformal gauge theory at kind of weakish coupling. Um and so this is something someone cannot do it um non-perturvatively but there's kind of limits of the correlator which we can understand exactly um in the case of a conformal gauge theory and for this it will really be important um there's a gauge theory and this is of course because we have our eyes on QCD this is

27:55 why we're using this um gauge theory um and so what I want to just kind of do is to step through how the kind of kinematic limits in particular this colinear limit um and this backto-back limit kind of cleanly probe the properties of the kind of low and high spin um limits of operators in this theory Um so the first limit which can be understood exactly is this kind of small angle limit as I bring the two detectors on top of each other. Um and so this is governed by a particular operator product expansion. The details of this don't um matter too much but what it gives rise to is a kind of power law behavior governed by certain anomalous dimensions um in your theory.

28:31 Um and so if you're at weakish coupling this will in particular be dominated by the twist two um operators with spin 3. Um and so what this actually or the way of thinking about this is this operator product expansion gives some kind of leading operator or detector operator and what I'm essentially doing is isolating that particular state. So this time this um twist two spin three operator and I'm essentially kind of isolating that uh state or that state kind of dominates my measurement and leads to this very nice um power law uh behavior shown here. And so at weak coupling this an enormous dimension is very small. And so this behaves almost kind of like a single particle state. Um in the opposite limit in a gauge theory I have something much more um interesting which happens which is as I try to bring these two detectors um apart I have some kind of long range um conserved gauge flux um which has a very

29:19 interesting or kind of characteristic behavior um in uh gauge theories in particular when it has a logarithmic growth of the anomalous dimensions as a function of spin. Um and so if you work out what is actually probed in this and so I won't go through it in detail but at a value or you're essentially probing a value of the spin that kind of goes like one over one minus z. So as you go into this um backto-back limit you're probing the kind of very high spin behavior or these kind of Wilson loop or aldoscina um flux tube uh behavior. Um and so this leads to a much more complicated behavior which really strongly deviates from the kind of um single power law shown over here and in particular completely asmmptotes to a flat uh behavior. Um and so this will be very important um later on when in when understanding the effects of confinement which will be very different um in this these two uh particular particular

30:06 limits. Um okay so now that I've kind of gone through those two examples I can show you the actual data um for the real world. Um and so what's shown is in purple is the measurement using this kind of amazing um um high resolution um detectors which I showed before and then in blue um is our calculation. Um and so I'll step through the different pieces of this plot um in the in the coming slides but just to kind of emphasize it in a little bit of um or to give a kind of high level overview. So as I mentioned in the middle we're really probing the dynamics of the theory at some very high energy. So in particular this is set by the uh Z resonance. Um so this is really described by interacting quarks and gluons and we can comput it in perturbation theory. Um and then as I go either direction I have some kind of flow um to the IR where ultimately on either side I have some kind of free hadrons in my detector which you can

30:58 really see as to this flat um scaling behavior of non-interacting um hadrons. Um and so one kind of remarkable thing about the resolution of this measurement is you can really see that you essentially go for an order of magnitude below the confinement transition. And so you can really see that in the IR you have really like non-interacting um hadrons. Um and then so at intermediate scales you go through either the scaling behavior of these Wilson loops um which then confine or you go through this light ray operator product expansion which then again goes um into hadrons um and so again you'll see from the theory calculation that we completely lose control as you go to either of these regimes but the nice thing is that we really understand the phenomena that's under that's going um there and so we hope that we can use this to draw nice conclusions about the behavior um in real world QCD. Um and so now what I

31:46 want to do is just kind of step through the different pieces of this calculation in a little bit more detail. Um so as I mentioned so in the middle of the distribution you have no kind of nice um operator product expansion or no single state um that dominates and so the best we can do is perturbation theory. Um but we are actually quite good at perturbation theory and so in particular we can do it to quite high orders. So this we're in particular going up to third order in the strong um coupling constant. So we're including quite high states with many gluons. And so you can see that if you do that calculation, we actually get beautiful um agreement between this calculation performed on parts um and what we see um in the real world experiment. And so this really kind of shows that in this intermediate or in the bulk region we really have kind of these um partons um in the UV. Um so now what we can do is

32:32 to start moving more towards the large angle side where we generate this kind of um flux between the two detectors. Um and so in this limit, we're really dominated by this kind of leading Wilson loop contribution or this leading kind of flux tube contribution. And so one very nice thing about this is because it kind of projects us down to this single contribution, we can compute this to extraordinarily good accuracy. Um and so this is a very sensitive probe of this log j of the anomalous dimensions in QCD. And so in particular for the cusp anomalous dimension, which is really what governs this, we can actually compute this to five loop order in QCD.

33:05 So this is really kind of using or is an illustration of the absolute kind of state-of-the-art of what is computable in perturbation theory. And you can see that what we get out is this kind of beautiful agreement um at almost the percent level. So it's about kind of 2% or 1% um between what we compute in um or what we compute and the data. And so this is kind of a really nice illustration of these advances in perturbative techniques. Um, and so it doesn't matter the exact details of this, but this is just to show you that if you use kind of lower order calculations, um, so the actual original calculation is even lower than what's shown on here is that you really get large very large uncertainties and you really need these kind of very high order results to actually get this nice um, agreement. Um, and so one thing you can ask which is actually related to your question showing earlier um, is

33:47 once you have this level of agreement, can you detect um, kind of small imprints of confinement already in this regime? Um and so as you said so in real world QCD the particles are massless and don't or the part the hydrons are massive and do not make it out to asmtoic infinity. Um and so instead they have some kind of velocity which is going along. Um and so one way of thinking what this does is in this original expression which I showed you if you really had massive particles you excite kind of arbitrarily high spins.

34:15 Um if I put a cutoff on the velocity of these distributions or the velocity of these hydrons essentially what happens is I truncate the maximum value of um of spin um in this and this actually leads to a small deviation which is computable or this functional form is computable um in QCD um and so you can think of this as a kind of large spin expansion about the massless um case and it's a little bit hard to see here but this actually leads to about a 10% deviation um in real world QCD um and so to actually once we have things at the level of 1% % you actually really need to incorporate um this understanding. So it really shows that you have control over kind of real world QCD at the um few percent level and kind of really motivates an improved understanding um of these effects. Um okay so we can also now go to this colinear limit where we bring the two detectors um together and so as I said

35:04 in this limit it's governed by this um light ray operator product um expansion. Um and so in this case what you're probing is not this kind of high spin limit but it's instead the or kind of a limit at some generic spin. So in particular spin three. Um and so this is harder to compute in perturbation theory and less is known about kind of the generic spin values as opposed to the high spin um limit. And so unfortunately in this case we're only able to do although it's still quite good um but a three-loop um calculation. Um, and you can see that it still agrees very nicely with the kind of data, but you're getting kind of slightly larger to the kind of say 5% or so level instead of this amazing um behavior that we have in this um high spin limit. Um, and so that's quite nice. Um, but of course, so this kind of shows in some sense that we have control over these objects um in perturbation theory. Um but one thing

35:50 which one would like to do once one has control over perturbation theory is see what happens kind of to these observables non-perturbly or what is the actual effects of observable or of contributions that we do not understand. Um and so as I mentioned one of the nice features of this is we're now able to measure below the confinement scale and so this is just to re kind of highlight in these earlier data which are shown for example in the blue we kind of lose control whereas now we're really able to measure all the way to extremely small angles both in the backtoback and the colinear limit and so in these regimes we won't be able to compute what happens but we can kind of push our calculations and see um what actually happens um non-verbbally in QCD um and so in both of these limits what I'll do is I'll kind of compare what happens in a kind of conformal gauge theory on this side and then what happens in the real world

36:36 on this side. Um and so remember in these plots what I'm comparing is this small angle regime over here. And so in a conformal theory I just have this beautiful power law which kind of goes on um forever. Um in real world QCD what happens is remember that as I go to smaller and smaller angles I'm probing lower and lower scales. And so first what happens is my coupling begins to increase and then ultimately I just confine and I have some scale which kind of breaks that nice power loss scaling and then I transition to having just this scaling or of essentially free hadrons which are not interacting. Um and so you can really kind of see by eye this nice transition um occurring of confinement. Um and you can also see that in our calculations we just lose control of what's happening. Um but this is really kind of showing that the hope is that we can gain insight from these very precise measurements of this

37:22 confinement transition to actually learn something quantitative about the transition of in this case these kind of light race states into um hadrons in the detector. So we can also do this in this backtoback limit. So again here one should be comparing this kind of limit in the case of a conformal gauge theory and this is this equivalent in the real world um QCD and so the behavior confinement in this limit is very different because already in perturbation theory I'm able to kind of form this flux tube which even in the conformal case turns me over like this um and so it's important to emphasize that this turnover in the back limit is not set by the scale of confinement so it's not actually set um by the mass gap but it's just a property of the coupling of the theory um and So in particular what happens in this limit is I start to lose control of the calculation but it really does already turn over and then

38:10 you kind of have the kind of breaking of the string which is kind of continues into this uniform uh behavior going out here. And so again you now have a kind of very nice measurement of the kind of confinement in the large spin regime of this um energy correlator um observable. Okay. So there's two additional comments which I wanted to make about this backto-back limit. So the first is actually a very nice overlap with certain lattice results of uh Fiala who's part of this um collaboration. And so one neat thing is that in this backto-back limit in the real world so instead of evaluating this cusp anomous dimension which I mentioned at some fixed value of the coupling as I said as you're probing different values of the coupling you're actually kind of sweeping over the value of this of of this anomous dimension at which you're probing it. And so really what you're actually measuring is some kind of

38:53 integral over this which depends on the scale. Um and so in real world QCD this integral can go low enough that it becomes um non-perturbative. Um and so one kind of very nice um result or advance recently in the on the lattice side is it's become possible to compute these integrals of the cusp and almost dimension or certain properties of these Wilson loops um non-perturbatively on the lattice. Um and so it's a little bit hard to see in this calculation because it's covered nicely by the lattice results. But this kind of black thing here which is exactly under this and then kind of diverges here is actually the calculation of this um object in perturbation theory. And so you can see that we actually agree nicely and really extrapolate smoothly onto the values of the lattice. And so it diverges at about um 0.5 fmy. Um but so we're actually able to incorporate these lattice calculations into our calculation which

39:38 allows us to extend the regime of our calculations even further though ultimately it does fully kind of break down. Um and so I think it' be very interesting to kind of further sharpen this connection between the different pictures namely from the lattice perturbation theory and these kind of effective field theories for um the QCD flux too. Um so the other kind of very nice thing um which is more kind of suggestive and which is again where we really um lose control is what we believe to happen. Yeah. the conformal gauge theory

40:07 that's at large n or and the QCD is at finite end or yeah so in the so I'd say at finite coupling and the conformal gauge theory what really happens in this in this limit is a little bit I would say not fully clear um but you can think of it as you first take some weak coupling limit with n um infinite then you'll get this behavior really in this limit I would say as you go to infinite or as you go infinitely high spin you really have some mixing between some single and double trace things which is not really understood Um and so you can think of it as just like a large N conformal flux tube. Yeah.

40:40 But the plots on the right are for like SU3 or something like that. Yeah. So this is for like real Yeah. So this one is for um like SU3 um Yangs. Yeah. Yeah. Yeah. Um perfect. Um and so then so what is believed? So as again we understand what happens in the infinite IR where we have these hydrons. We understand in the UV where you have this nice flux tube. And so what one believes is that at some kind of radius which is set by like one over lambda QCD this string kind of just fragments into these hadrons which propagate off to infinity.

41:08 Um and so you can do this in simulations is you actually get a kind of very suggestive picture of what's happening if you look at the kind of flux of hadrons which are coming out and you essentially kind of see so these are the two kind of detectors and you see this almost kind of QCD string imprinted into the detector. Um and so this is kind of suggestive that you're really having that this is or this picture which I've drawn kind of here can really be sharpened and that you could actually kind of compute this um using effective um string theory and really provide some insights into what is um happening um here. And so now that you have this very high quality data, this is kind of very exciting to start actually beginning to make these um connections. Um okay, so again just coming back. So when you put all those pieces together, you get this very nice uh view of the dynamics of QCD. Um so again I think this is really

41:51 just at the stage now where we understand the kind of perturbative aspects of this and it's kind of very exciting for sharpening our understanding of these confinement phenomena both in this kind of string breaking regime over here as well as in this kind of colinear limit um over here. And so related to your kind of question also comparing not just with these um confining theories but also with kind of finite coupling results in conformal gauge theories which are now becoming available thanks to the conformal bootstrap will kind of really help us kind of elucidate um the differences um in these different theories particularly in the kind of string breaking regimes um over here.

42:25 Okay. And so in the last little bit of the talk, what I just wanted to highlight, so this is very very old data. And so one can ask what one can do with kind of modern and very high energy colliders um at the LHC. And so these are much messier colliders. And so it's harder to sharply draw um any any conclusions. Um but one thing which we've actually been kind of very happy with is we're able to understand and measure correlation functions of these operators just in this small angle limit but at extremely high energies. So of course in these very complicated collisions you cannot measure them at generic angles because these are really sensitive to the properties of the kind of colliding state because it's no longer produced by some local operator but because of this operator product expansion in the kind of colinear limit we're actually able to kind of make robust statements and very precisely

43:07 understand um these correlators um and so again I won't go through the whole detail but just again the fact that this is able to be possible is really due to huge advances in kind of modern effective field theory techniques which really allow us to kind combine this nice picture coming from the kind of conformal field theory side of this light operator product expansion through some anomalous dimensions ultimately with underlying scattering amplitudes and so we can really kind of combine the UV and the IR to make actually very precise predictions for what is going on um in these real world um hadron collisions um and in fact in this limit we're actually able to match um the precision of our calculations um of these earlier E plus E minus calculations now we can do it at much much higher um energies which is very exciting Um so the first thing we can do is again just measure this twopoint

43:53 correlation function. And so again this is a function of the angles between these two detectors. And so instead of having this nice plot which I showed before, we can only kind of zoom in on the colinear limit. Um but the very nice thing about this is you can just see by eye this kind of beautiful scaling behavior dictated by this operator product expansion before the confinement transition. And the nice thing is that at these extremely high energy, so now this is at individual jets of about 2 TEV. So this is essentially a thousand higher than what we were doing uh before. And so you can really see this beautiful scaling of these quarks and gluons uh states over multiple orders of magnitude. So you've really kind of zoomed in and are able to study the properties of essentially perturbative quarks and gluons uh before they confine. Um so this is kind of very satisfying to see that this really works

44:35 over this wider range of energies. Um and so just to further emphasize the distinction between the scales compared to these very very early um plots. So notice that in this original plot it goes from 0 to 180 whereas this plot essentially maxes out like 10 to the minus one in angle. So this entire distribution is inside essentially this single um data point here. Um and so this really emphasizes how amazing these kind of modern um detectors and very high energies are and has really kind of transformed the interaction between theory and experiment because we're now really able to access this beautiful kind of conformal regime um of QCD and then ultimately it's kind of confining um breakdown into hadrons at the end. Um and so one thing which is even more exciting is because you have such high energies, you can actually go much beyond and actually study the full kind of spectrum of these different operators

45:21 um which appear in the operator product expansion. Um and so one nice way of doing this is you can measure higher point correlation functions. Um and so if you measure or if you kind of consider the operator product expansion between some endpoint correlation function, essentially what you can work out is that it projects you onto some detector operator which has a spin n plus one. Um and so if you're familiar with looking at these kind of true Fouchy plots, essentially what happens is that as you measure higher and higher point correlation functions, so the onepoint function is just the stress tensor which is conferred and then you have the two three four etc which just probe different spins um in this um uh true fragie plot. Um and so this is very nice because it really provides a mapping between what an experimentalist can measure um and the spectrum of twist two operators in your theory. Um and so

46:05 you can now go out and do this experimentally. And so this is actually a plot. So here I'll always plot this ratio to the twopoint correlation function. And so it just essentially probes the kind of difference of the anomalous dimensions or the difference of the dimensions of these operators. Um and you can actually measure these up to 10point correlation functions. Um and this is because of the amazing high energies. Um and so you can really see that for each of these different so again this is the ratio of the end point to the two point and you can really see this kind of very nice um power law behavior that you would expect here. Um and again you see that these get steeper and steeper which is just the monotinicity of the of the reg trajectories. Um and so for us this is very nice because this really provides a kind of clean mapping from these very complicated experiments to something

46:45 that we really understand and we can really just measure the spectrum of these operators and then ultimately for each of these um kind of states we can study its um honization uh properties. Um and so for these again we can do quite nice theoretical calculations up to kind of three-loop order. But one thing which has been very satisfying is that by studying the precision scaling of these library operators, it actually now provides one of the most precise ways of measuring the value of the strong coupling constant in these hadron colliders. Um and so because we have this scaling under such good control and of course this is just proportional to the coupling of your theory. Um you can actually or this gives the kind of world's most precise value of the strong coupling constant from these jet sub techniques. But it's kind of a very kind of clean way because you're really just looking at the spectrum of operators in

47:26 your theory, computing it as a function of the strong coupling constant and just kind of reading it off by I. And so this is kind of really clarified how this is done um in these complicated haddrawn um experiments. Um okay, so just to kind of start wrapping up. So 50 years of study of these kind of um both on the experimental side and the theoretical side of trying to understand these correlations in energy flux have really kind of transformed this from these early kind of qualitative studies to really extremely precise um predictions of over the entire range in particular unveiling the kind of transition from the ponic degrees of freedom to the hydronic degrees of freedom um which is kind of at least to me a very exciting starting point now to begin asking the kind of more exciting questions. So in some sense we've mastered a large amount of the perturbative description and so this kind of gives us an exciting opportunity

48:13 to really begin asking questions about the more interesting regimes in particular um the confining uh transitions and trying to make connections with a lot of the nice theory developments um made by this collaboration. Um and so just to conclude so there's been a lot of recent progress in relating collider physics and field theory through these energy detectors. This really provides a very sharp connection between the underlying field theory and what you can measure um experimentally. And so because of this, there's been a lot of experimental work where you've really been able to measure the scaling and shape dependence of these energy correlators kind of very precisely. And we now have these beautiful maps of the dynamics of QCD um which some regions we don't understand but we understand kind of a whole bunch of limits. And so this really gives us kind of a very nice um view into confining dynamics. And I think this is

48:58 really an exciting opportunity to improve our understanding of the confinement phenomena um in real world QCD using advances um in field theory. Um so thank you.

Questions about this episode

Who speaks in "Ian Moult: Unveiling QCD Dynamics with Energy Correlators"?

Ian Moult (Host).

What is "Ian Moult: Unveiling QCD Dynamics with Energy Correlators" about?

Ian Moult discusses recent advancements in quantum chromodynamics (QCD) and how they bridge the gap between theoretical frameworks and experimental observations at collider experiments. By focusing on observable phenomena like confinement and QCD flux tubes, he emphasizes the potential for new experimental insights that could enhance our understanding of real-world QCD systems.

What is mentioned in this Simons Foundation episode?

16 people, works and ideas are mentioned, including QCD, Yanji Lee, George Sturman, asymptotic freedom, energy flux operator, Hoffman and Maldina. Each one on this page links to its own page with every episode that mentions it.

How long is "Ian Moult: Unveiling QCD Dynamics with Energy Correlators"?

The episode runs 49 min; the transcript is about 10,586 words in 71 timestamped sections.

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