 Okay, well, welcome everybody. Let's go ahead and get the event started today. We'll have a brief introduction here at the beginning and then we'll get to the actual seminar. Let me begin by welcoming everybody to the SMU Physics Department Speaker Series yet again for fall 2020. Now, today's event is a seminar and we're gonna keep digging deeper into this month's theme of computing the cosmos. In a moment, Dr. Tim Hobbs, a postdoctoral researcher in our department and our host for the event today, we'll introduce our speaker, Vincent Chung. But before we get started, I wanted to sort of make some reminders to our audience on Zoom. So Zoom is an imperfect system for having events like this. It's impossible to see everybody. All the cues, the physical cues are largely lost, even with cameras on. So in order to speak, if you wanna ask a question during the event, you just have to type speak in the chat window and hit enter. And at the next opportunity, we'll interrupt Vincent and we'll let him know that there's a question and then we'll have some time for the Q&A during the talk. And of course, there's gonna be time for questions and answers at the end of the seminar as well. In general, you'll only be able to speak when called upon by a moderator and that's just to keep the hot mic problem from occurring as we all experience in all these meetings. Now, I wanna let everybody know this event is being recorded and would normally be simulcast on YouTube, but apparently the ability to simulcast to YouTube has been broken by Zoom and or SMU in the last two weeks. So we're gonna have to give that up for today and we won't be able to support anybody on the YouTube live stream today. All right, with those things in mind, I'm going to stop sharing and I'm gonna hand things over to Tim Hopps. So, Tim, go for it. Thanks so much, Steve. Yeah, for that introduction instead of reminders. So, yeah, we're really delighted to have Vincent Chung joining us to give us an interesting seminar today. Yeah, so Vincent's an advanced graduate student in the nuclear physics group at the University of California Davis where he works with Ramona Vogt. So his work has primarily focused on explorations of corconian polarization. For instance, in the context of the color evaporation model and the number of other frameworks. So with his advisor in collaboration with Harry, he's made a number of pioneering calculations including the first polarization calculation using the particular model that he'll be describing for us today that color evaporation or improved color evaporation model. At the moment, our understanding is that he's also looking into the next deleting order of calculations in this context. So we're really excited to have Vincent and I'll just turn the floor over to him and thank him for joining us today for this exciting talk. All right, thank you, Tim. And for the introduction and thank you, Steve, for the invitation. It's my pleasure to be here giving a seminar. And so this is the title slide. So I'm going to talk about corconian production and polarization in the color evaporation model. And I come from UC Davis Department of Physics and Astronomy. So this is my overview slide. I will mainly talk about corconian polarization. So I'll give a brief introduction of what corconium is and what are the production models we have so far. And my main study is on polarization. So I would also talk about what polarization is, how is it being defined and how is it being measured? And I'll go over my work in the color evaporation model and a more recently improved color evaporation model. So what is corconium? Corconium is a bound state of QQ bar. Mainly in terms of QQ bar, we only refer corconium as bound state of charm and bottom. So for a charm, anti-charm bound state, we will refer it as termonium and for a bottom, anti-bottom bound state, it would be a bottom monium. So they are being bound by the interquart potential. Could be written in this form where the linear terms refer to the confinement and one of our terms refer to the Coulomb-like short distance behavior. So you can form bound states given this potential and you could have a spectrum of states. So on the left here is the bound state for a CC bar bound state. It is the charmonium family and on the right is the BB bar bound state, the bottom monium family. So it gives a spectrum of states because we're having a bound state of two spin one-half particles and they could also have orbital angular momentum. So it would have a spectrum of spin states as notated in this spectroscopic notation. So all of them, all of the physical states are color singlets. They're colorally white objects and there's an important threshold per family. It is the HH bar threshold for charmonium. It will be the DD bar threshold and for charmonium as the DD bar threshold and for bottom monium as the BB bar threshold. And what this threshold is important is that all the states below this threshold would decay electromagnetically into a pair of a lepton and anti-lepton. So how are they being detected? For S states, they decay to L plus L minus. So they could be observed as peaks in a lepton mass spectrum. So this is a lepton, a dimulon mass spectrum measured at the CMS at 7 TeV. We can see all the peaks here, all of them are the vector mesons including the lighter vector mesons and here are the charmoniums and the bottom monium and there's also an assumed plot for the bottom monium where we can see the three S states opsulons. The chi states could be reconstructed by matching an S state with a low momentum photon. So they're not being shown here because they also need to be matched with a low momentum photon and for the eight of states, they decay hydronically so we won't be able to see it in this spectrum either. So perconium could be produced in a lot of collision system. The one that I study most is the hydronic collision system where it's two hadron colliding with each other. One example is proton on proton. You could also have proton on a nucleus or even a nucleus on a nucleus and these could be achieved in, these collision system could be achieved in rake, tevatron and LHC but there are also other collision system that can produce perconium. For example, you could have two gamma and you can also have photo production and E plus, E minus. These are examples of collision systems where perconium could be produced. So here's a brief timeline of how the theory and the measurement goes. So in 1974, the first perconium, the trimonium, j psi, it was being discovered and followed by the discovery of Upsilon and the color evaporation model which average all the spins and colors was being developed about the same time and followed by the color singlet model which only considered the color singlet contribution and followed by the non-relativistic NR2CD. So in a brief summary of where we're standing is that we're not able to accurately describe every observable associated with perconium production using just one production model and one set of model parameters. So what are the observables that we're trying to describe? They would include the use and distribution of the S state perconium, the eta states and the chi states. And more precise tests of model would include the production of one state relative to the other. For example, the ratio of two S to one S ratio for trimonium. And another test of model could be the production of one spin state relative to the other within the same spin state. And that's the polarization. For example, we could be talking about how much of J psi being produced in JZ equals to plus or minus one versus being produced at JZ equals to zero. And the status as right now is that the production models are still unsettled even though J psi and Opsilons are discovered in 1974 and 1977 respectively and the production mechanism hasn't been solved yet. So there are different models being developed to describe the observables and we can take a look at them one by one. So the first production model was the color evaporation model. And the production cross-section of the carconium is modeled as shown here where the carconium are treated just like a pair of Q and Q bar. So if we're modeling for J psi production cross-section that is essentially the same as producing a pair of C and C bar below the HH bar threshold. So we add the leading order. This is to calculate the cross-section of producing a CC bar with the invariant mass from the production threshold to the hadron threshold. And there's one factor which is supposed to be universal for the carconium state. And it's independent of the projectile target and energy. So you can treat it as how much, as a fraction of the CC bar pair being produced in this window here at the end becomes a J psi, for example. And all diagrams for producing a QG bar are being included independent of their color. And it has only just one fitting fit parameters per carconium states. So for J psi, it would take a number. For psi two S, it would take another number. And this number, this FQ is being fixed by comparing the NLO calculation of the cross-section as a function of root S or the rapidity at this, or the rapidity distribution at central rapidity. So this factor could be obtained by matching with the data. The color singlet model, it's kind of trying to make more sense because the final state that we observe is the color singlet state. So the color singlet model only constraints the production of the QQ bar to just the color singlet state only. And it assumes to produce QQ bar, it does not change its color and spin between the production and the hadronization. So the color singlet model just focused on what is the production cross-section for a QQ bar producing a single state and assume that what eventually becomes the carconium that we see. And the last model is the NRQ CD. It is an effective field theory where the production is described as an expansion of alpha-S and you have the quart velocity, the C relative quart velocity. So hence the name, non-relativistic NRQ CD. And at each order, the production is further factorized into a perturbative part known as the short distance coefficients and a non-predurbative part known as the long distance matrix elements. So for example, if we're considering the production cross-section for JPSI, it would come from a sum of color and spin state. And for each color and spin state, it's being factorized into the perturbatively calculable part and a non-predurbative part in those expansions shown. So the color states are the single states and the octa states. And all the color and spin state are being considered in this NRQ CD model. And a non-predurbative part, the LDMEs, that describe the conversion of the CZ bar, color and spin state into the final state JPSI. And this also assumed that the patronization does not change its momentum. So these LDMEs or the mixing of the LDMEs are conjectured to be universal and these parameters are being determined by fitting into the data. So there is a more recently developed improved version of the color evaporation model. The basic color evaporation model has no improvement made to it since the 90s. And the improved color evaporation model made two changes to it. One of the changes is that the lower threshold of the mass of the CZ bar pair, it's now changed from the production threshold, which was the mass, two times the mass of charm into the physical mass of the Tremont Charmone state. And the second change is that there's a distinction now made between the CZ bar pair momentum and the momentum of the Charmone. So these two changes allow this model, this improved version of the model to describe the relative production for 2S to 1S and also make the PT distribution a bit softer and to explain the high PT data. So this model, this improved model has been employed to calculate the production and polarization for all S states and the relative production of the chi states. So let's look at some selected plots from each model. So this is a result in color singlet model. It's rather a new plot, but it also includes the old plot. The old calculation in gray is the next to leading order calculation in the color singlet model. And this was kind of famously known but it doesn't describe the Tevetron data. It has a huge gap between the next to leading order calculation and the Tevetron data measured. So there's a recent improvement in this color singlet model, which shows that if we add the real emission contribution at the next to next leading order, and this is the red curve, if we add that real emission contribution, then this color singlet model can describe the distribution. It can also describe that it can fill in the gap between the data and the NLO result at Tevetron. And it can also fill in the gap at other hadronic collision system. But it should also be noted that the real emission is not the entire calculation. There is also virtual emission that could change the result at the end. And in our QCD, in our QCD so far, the most employed to the most kind of collision system. So it has been applied to hadronic collisions, to gamma's photo production and E plus E minus. And there's a global fit by Boudtention and Neal that consider their mixing of the LDMEs and fit it to the global data, which is available. So they're able to use the same set of LDMEs to describe as much data as possible. And they have a great success in describing the data in hadro production, in photo production, and E plus E minus. Except for this plot right here, on the right right here, in the two gamma, the new fit that they did has the worst comparison to data compared to the old fit, which only consider the mixing of the LDMEs to a single measurement. So overall, they have a good success in describing the global data using the same mixing of their LDMEs. And they have a very low PT cut as well. So the lowest they could go is 1GV. And for hadronic collision, they go as low as 3GV. So this is what NRQCD looks like if we were to take it component-wise. So on the left is the decomposition of just next to leading order and leading order comparing the color singlet and the color octet contribution. If we look at the sine curve here, just looking at the color singlet contribution, even at next to the leading order, it would underestimate the data. And once they add in the color octet contribution, then NRQCD can describe the data really well. And so on the right shown is the component-wise, how they look like in this global fit, how each component contributes to the total yield that they predict. So this is one of the selected plots for relative production in NRQCD, where the ratio is the 2S to 1S ratio for the Charmonium family. And what they calculated is what this group calculated results shows that it agrees with the data at most PT. And the relative production of chi C and chi B are also dominated by the color singlet model contribution. So this is what they have calculated. But there are also other groups that use NRQCD and they have a different method. Each groups vary slightly, but they, in general, the relative production is well described in NRQCD also. But there is one problem in NRQCD. It's that for A to C production, so far all of the NRQCD result would overestimate the LHCB A to C yields. So each column refers to different groups and each role is the LHCB A to C yields at 70 EV and then the second row is at 80 EV. So the first column is the global fit result. The yellow is the total, which is the color singlet plus the color octet contribution. And there are the closest to the experimental data, but they're still overestimating it. And so far, all of the groups are showing that the result could be described by the color singlet model alone. So if they are using the same mixing to describe then using heavy quark spin symmetry, you can also translate that result into A to C yields. But apparently this translation does not describe the A to C result. There are other NRQCD calculation which can describe the A to C result. But again, if they were to use the same mixing of the LDMEs to describe the jpeg Psi, they would not describe the jpeg Psi polarization. And that's what we're going into. So on the other hand, in the color evaporation model, it has one fitting factor for each quarkonium state. So for a quarkonium state jpeg Psi, there would be an Fj Psi for Psi 2S. That would be a Psi F2S. It has great consistency with experimental result over a large range of root S. So on the left, it's the jpeg Psi cross section all the way from 40GB to the TV scale. And using just one fitting factor, it has a great consistency and it can describe the experimental data really well. And on the right, it's a similar plot for the sum of the bottomonium states. Again, three fitting factor can describe the cross section as a function of root S. And it can also describe rapidity distribution and PT distribution very well. And overall, it is a less rigorous model. It is averaging over all color states and only just using one fitting parameter for each state. But it gives accurate predictions. And there were no advance in this basic model since the 90s. And in 2016, Yan Qingma and Ramona vote, they improved this model and made two changes. Again, it's one is in the lower threshold of the mass of the CC bar and the momentum of the CC bar versus the momentum of the termonium. So making these two changes allow this model to now describe the ratio of the cross section, the 2S to 1S ratio, and also makes it describe the PT distribution better. So here is the PT distribution in this model. On the left column is that 200 TV. On the right column is that 70 TV. In the top row, it is a jpeg side result. And in the bottom row is the side prime result. If you take the ratio to 2, then you can get the relative reduction in that model. So at 200 TV and a 70 TV, this ratio is being described with the two changes made to the model. Without these two changes, this ratio is very close to flat in a traditional color evaporation model. And part of my work is to use this model to calculate the chi C and chi B production. I had some success in chi C ratio, but not that much in chi B. The ratio will become flat at high enough PT. But the bottom monium mass is a bit larger. So in terms of scaling, it doesn't become flat until you hit 20 GB. But for the term monium, it's relatively smaller mass. So it becomes flat at a lower PT value. So these are for KT factorized resulted. They are not directly comparable. Should be noted that. So in summary of the model of the development, we started with a simple model by just averaging over color and spin states. And historically, both color and spin are being averaged in the color evaporation model. And we started to make more sense by limiting our consideration to just color singlet production, and hence named color singlet model. Because it couldn't describe the data, which suggested that there should be more being added to describe the experimental data. So we bring in the contribution from color octave states through the non-perturbative parameters. And that's NRQCD. There are some recent improvement made on the color evaporation model. But there are also other work in improving other model as well. So that's historically where we come from. So color evaporation model and NRQCD remain the most commonly used model today. And they can predict yields and relative production of different carcunium states. But we need more precise tests of models. Or we need other tests of model, because they can already predict the yields and relative production. So we would be asking question, what about the relative production of different spin projection state of the same carcunium states? And that would be polarization. So it's just a quick comparison between the color evaporation model family and the NRQCD. The color evaporation model is less rigorous. It has fewer fit parameters. And so far, it has only been applied extensively to hazard production. And on the other hand, NRQCD is more rigorous. It's split into color and spin state. And hence, it has more fit parameters. And it has been applied to all collision system, as we have seen in the global fit. So what is polarization in precise? In general, polarization is just being defined as the tendency of the carcunium to be in a certain angular momentum state, given its total angular momentum. So for example, if we have an impolarized j equals to 1 production, it means jz equals to negative 1, 0, and plus 1 are being produced equally likely. So we get 1 third for each. And this could be observed when we make an angular spectrum as a function of theta. If you have a purely longitudinal production, then it will be in this dotted curve. It would have a peak at half pi. If we have a purely transverse production, then we would have this dashed line here and has peaks at 0 and pi. And if we have an impolarized production, then it would look like a flat line. So how is that theta being defined? There are three commonly used choice for the z-axis. And regardless of the z-axis to theta is being defined as the angle of the positively charged lepton, and the angle theta is always being defined as the angle it makes for the positively charged lepton to the z-axis. So how is the z-axis being defined? There are three commonly used choice. The first one is the helicity axis. It is the querconium traveling direction when boosted back into the querconium rest frame. The second choice is the Collins-Sopper. Sorry, the second commonly choice is the Gottfried Jackson frame, where the z-axis is pointing exactly as one of the beam direction. And the secondly commonly used choice is the Collins-Sopper frame, although I introduce them in the third order. It is the angle bisector of the Gottfried Jackson z-axis and the direction of the other beam. So it bisects this angle right here. So helicity frame and Collins-Sopper frame, these are the two most commonly used frame to measure polarization. And regardless of the z-axis choice, the theta angle is always defined the same way. That's the angle between the z-axis of the choice and a direction of travel for the positively charged lepton in the querconium rest frame. So the angular distribution could be expanded in this way. And the most commonly referred as polar, all the pre-factor the lambda-pheta, lambda-phi, lambda-pheta-phi, they're all referred as polarization parameters. But the one that makes the most intuitive sense is the lambda-pheta, because lambda-pheta described how much is being produced in a jz equals to 0 and how much it is being produced in jz equals to plus or minus 1. But they're all being referred as polarization parameters. And they could be obtained by making angular spectrum. And for example, if you want to extract lambda-pheta, you can make an angular distribution as a function of cosine-pheta. And you can measure the curvature and obtain the lambda-pheta that way. And other polarization parameter could be measured in the similar fashion. So why do we need a model? For a single elementary process, the polarized total cross-section could be written in terms of the amplitudes a, j, z. So for a single elementary process, it comes from a 0 squared, a plus 1 squared, and a minus 1 squared. And you can combine them to give the polarization parameters. These are lambda-pheta, lambda-phi, and lambda-pheta-phi. However, for just a single elementary process, there's no combination that would give all of them to be the same and be 0. So an unpolarized production can only be described by a mixture of sub-processes, or you have to do some randomization modeling. So this is a great plot showing that you could have lambda-pheta to be 0, lambda-phi to be 0. But then you would miss lambda-pheta-phi to be 0. So if you're just considering just one single elementary process, then you will never have all of them being 0. So it has to come from a mixture of sub-processes, and hence we need a model. So it's important to understand polarization, not just from the theory standpoint that they are strong tests of production models. But to detect their acceptance also depends on the polarization hypothesis. And understanding the polarization would help us to narrow down the systematic uncertainties. So here in the below of three plots is the acceptance at that atlas, where if you assume the polarization to be all 0 as flat, then the acceptance as a function of PT and rapidity would have a different look compared to if you assume the polarization to be completely transverse and it will again be different if you assume the polarization to be completely longitudinal. And these acceptance variations would eventually be reported as systematic uncertainties. And this is a plot from an LHCB that if they assume the production is fully transverse, it would be the rep data points. And if they assume the polarization to be fully longitudinal, then they would have the blue data points. So understanding polarization, it's good for theory and experimental interests. So what is the polarization puzzle that we're trying to solve? This is a kind of all-in-one plot to show that NRQCD cannot describe the polarization and the end of production simultaneously using the same PT cut and the same mixing of their LDMEs. So for each role here is a calculation being done in NRQCD using different PT cuts. And each column refers to an experimental observable. And they are E plus E minus cross-section, EP cross-section, and a hydronic PT distribution, and the japside polarization in hydronic collisions. So the first group, which was the global fit group, uses the smallest PT cut, includes a lot of data, not just these three sets of data, into the fit. And they can describe the data really well, as seen before. But using the same LDMEs, using the same mixing of the LDMEs, they would not have agreement with the polarization data. And the second group, which uses a larger PT cut when fitting their LDMEs, and only takes the hadger production into their fit, they would have a better description of the polarization. But using the same mixing of the LDMEs, they would overpredict the data at other places. And the third group here uses a larger PT cut, which also have taken the polarization data into the fit. They would have a good agreement with the data. But if the same mixing of the LDMEs are being applied to describe other observables, then they would overpredict even more. So this is known as a polarization puzzle in an RQCD, where you can't just use one set of LDMEs, use a small PT cut, and to describe all of the data and its polarization. So this is a problem that we're facing right now. And not to leave this out is that there are approach within the framework of NRQCD, as the colored condensate, to when being applied on top of NRQCD, this could be a solution to solve the polarization puzzle. And what they did is the gluon distribution is calculated using CGC. And the QQ bar conversion to the final state javessi is being described by NRQCD formulation. So this is one of the proposed solution to solve the puzzle. And they have a good agreement to data for PT less than 15 GEV. So back to NRQCD, just NRQCD alone. Upsilon polarization for 1S2S3S doesn't seem to be a big problem in NRQCD, probably due to the Upsilon mass. So it's essentially the same group. If they have included the feed-down production from the KiB states, then the polarization for 1S2N and 3S state will be a lot more closer to the data measured by the CMS. So Upsilon polarization due to its mass is less of a problem in NRQCD. So mostly polarization problem, it's referring to javessi polarization. So what my work is is that, well, color evaporation model, it's the oldest model. But no one has used that to predict polarized calculation. So it's worth revisiting back to this model to calculate polarized results. And my advisor and I made a few calculations using the color evaporation model. And then we also moved on to the improved color evaporation model. So what we started with is we started with unpolarized color evaporation model at the leading order. And we first, as a proof of concept, we separate the different SZ states from the total production. And after that, we tried to extract the orbital angular momentum so we can actually match our CZ bar to the real germanium state. And after that, we tried to explore the PD dependence using KD factorization. And what we are doing right now is that we're trying to go to the next order in alpha S to describe the PD dependence of Jpsi polarization in our model. So I'll first describe how our calculation goes at alpha S square. So at the leading order to produce a QQ bar, then the QQ bar would not have any PT. It would only travel along the beam line. So there is no difference in the three commonly used axes. So we first started by projecting the spin of the heavy quark onto the beam axis. So the diagrams being used at this order is there's one diagram for light QQ bar to heavy QQ bar and three diagrams for glon fusion to QQ bar. So the polarized amplitudes are obtained by first separating these amplitudes according to the SZ of the final state. And then before we square the amplitudes, we extract the orbital angular momentum by looking at the dependence on cosine theta. And then we square the amplitudes and so we get the polarized amplitudes. There are some, once we have the polarized amplitudes calculated, then we form the amplitudes for the definite J values, 0, 1, 2, to match the physical states for Jpsi, CaC1P and CaC1 and CaC2. So the formula that we calculate with the hydronic cross-section is the traditional color evaporation model for our first calculation. And then we also move from color evaporation model to the improved color evaporation model. So we convoluted our partonic cross-section with the C-tex 6 parton distribution function. And the alpha-S is calculated at one-loop level. And we took the factorization and renormalization scale to be the same. And we varied the mass of the charm quark and the bottom quark to obtain our uncertainty band. And in this model, we assume the polarization is unchanged by the transition from the parton level to the hydron level. So the traditional color evaporation model assumes the linear momentum is unchanged in the hydronization transition. So what we did is we go a little bit further in assuming that the angular momentum is also unchanged in the same transition. So after we can calculate the polarized cross-section for each spin state, Jpsi, CaC2S, CaC1 and CaC2, for the termonium, we combine the polarization by modeling a feed-down process. So basically, what we did is we modeled the prompt production of Jpsi, assuming that 62% of the direct Jpsi, assuming 62% comes from directly produced Jpsi. And we do some spin algebra in figuring out how would that influence the polarization of the promptly produced states. And for the S states, it's one-to-one conversion. But for the P states, it's slightly different. So when we are presenting the polarization, it's usually presented in terms of polarization parameters, as seen before. So one of the polarization parameter that describe how much the production is favoring jz equals to 0 versus how much the production is favoring jz equals to plus or minus 1 is the lambda theta parameters. So if we take a look at this formula right here, if we only have a purely longitudinal polarization, if we have a purely longitudinal production, and that is only jz equals to 0 is being produced, then we would have lambda theta equals to negative 1. And if we have a purely transverse production, then lambda theta would be plus 1. So this is a polarization parameter. It's a number that goes from negative 1 to 1. And that would describe which components is favored more. And for the P states, you can do it in a similar fashion. But you also have to keep in mind that jz equals to plus 1 for chi C1 is not going to be the same as the j psi jz equals to plus 1. So the factors here, the coefficients here, are carefully crafted or chosen so that they would describe the polarization of the final state j psi, assuming the production purely comes from the feed down. So in our calculation, we only have jz equals to plus 1 and minus 1 and 0. And so we don't have jz equals to plus or minus 2. And using symmetry, the jz equals to plus 1 and jz equals to negative 1 amplitudes have to be the same. So the polarization parameters can just be described as the ratio of the jz equals to 0 to the total production. So this is one selector plot using collinear factorization approach. And this is for a promptly produced Upsilon 1S in proton copper with the root SNN at 38.8 GeV. So we found that the polarization of promptly produced Upsilon 1S is longitudinally polarized at small xf. And it's transversely polarized at large xf values. And this prediction is consistent with the near zero polarization for Upsilon 1S reported by the new Z collaboration. So after we did our calculation using collinear factorization approach, we started to explore the PT dependence. But without getting into the next order, so we thought the KT factorization approach would be a quick way to figure it out. How would it look like if we were to put in PT dependence? So in the KT factorization approach, we used the following. We made some changes to the calculation so that it fits into the KT factorization approach. So for this calculation, we only used the gluon fusion diagrams in our calculations. So the amplitudes are being calculated in a similar fashion. We first sorted by according to the SZ of the final state. And then we determined the orbital angular momentum by extracting the component. And then we convoluted it with the transfer as momentum-dependent part-time distribution functions. So this is what the cross-section looks like in the KT factorized ICM. So we consider two off-shell gluon going into the final state QQ bar. And these off-shell gluons are governed by these KT-dependent PDFs. And the PDFs that we use is the Jung and Haltmann PDFs in 2013, a PDF set. The factorization scale is set as the transverse mass of the produced CC bar. And we also vary the mass and the renormalization scale to obtain our uncertainty band. So this is what the result looks like. On the left is the jpeg side PT distribution. On the right is the side 2S PT distribution. So we did try to vary the mass of the charm, the factorization scale, and the renormalization scale. And by fitting to the data, we obtained the factor for jpeg side production. So we also assume, since what we have calculated is a directly produced jpeg side, and we're comparing it with inclusive jpeg side, so we assume the constant ratio of the direct to inclusive production. And we also compare our result for side 2S, assuming that the direct production of side 2S is the same as the prompt production of side 2S. So we found that this model is able to describe the yield, the PD distribution, and the rapidity distribution. But it has a strong dependence on the factorization scale at high PT. This comes from the fact that the PT of the final state quercolium purely comes from the kTs, the sum of the kTs, from the off-shark one. So it would have a strong dependence on the factorization scale. And this would grow as a function of PT as well. In terms of describing chi C1 and chi C2, we also try to do that and compare it with the atlas data. So we find that, and by taking the ratio, we can also take, we can also compare our calculation to the ratio measured atlas. So we found a good consistency with the data by considering our calculation for the chi states. So now we have all of the fqs fitted. We have fq for j psi, psi 2S and chi C1 and chi C2. Then we can form or promptly produce j psi, assuming the same feed-down production as considered before. So we have a good agreement with previous color evaporation model result and the data as well. So the new one is in blue. In blue is the improved color evaporation model using a kD factorization. And in magenta is the traditional color evaporation model in collinear factorization. And in green is the improved color evaporation model in the collinearly factorized approach. So all three of them are agreeing each other. And when the feed-down from BMS on is also added using FONL, we also found that a good agreement with the inclusive j psi production measured at least over a large range of beam energy. So it can describe the inclusive j psi all the way from 5 TeV to 13 TeV. And our main goal is to get polarization. So the polarization in this calculation in the collinear software frame, it is slightly negative, slightly towards longitudinal at low pT. And it becomes nearly unpolarized at moderate pT. And at large pT, it becomes slightly longitudinal again. In the helicity frame, it's the opposite behavior. At low pT, it is slightly transverse. And at moderate, it becomes nearly unpolarized. And at really large pT, it becomes slightly transverse. So the agreement with data, it's kind of frame dependent. It depends on which frame that you're trying to compare with data. So a similar story for Upsilon production when we switch our charm mass into bottom mass, then we can consider Upsilon production. This is the pT distribution at 7 TeV when compared to CMS data. It also has this round dependence on the factorization scale at large pT. And when we set the factorization scale at just mT, then both the pT distribution and the rapidity distribution are being described. So right here is the Upsilon 1, 2, 3S, rapidity distribution at 7 TeV and compared to data. So the polarization in bottomonium, it's similar when calculated in the Collins-Sopper frame. It is slightly longitudinal. And it becomes unpolarized at larger pT. And when calculated in the Helicity frame, it is slightly transverse at low pT. And it becomes unpolarized at large pT. And when we're considering really large pT, then such as the region measured by the CMS detector, then the polarization becomes really close to unpolarized. And this has a good agreement with the data as well. So we're trying to go to the next order in this calculation. So to do that, we're trying to consider all the diagrams that would give a CC bar and that would give a CC bar with non-zero pT. And there are 16 diagrams of them. And the CC bar produced, partonically, will become the prothramonium before the hadronization. And the mass of the CC bar would then fix the relative momentum of the heavy quark, which is the k. So we parametrized the momentum of the C and the momentum of the C bar for the momentum of the j psi and the relative momentum of the heavy quark. So these polarized cross-section are then computed using the appropriate polarization factor for the charmonium. And all the final state momenta are integrated while restricting this p psi dot k equals 0. And the PDFs that we use in this calculation is the CT14. It's a newer set than the C-texics. And in order to describe the distribution at low pT, some kT smearing is applied to the initial state parton. So this is a formula that we use at the next order. So we're using an improved color evaporation model where the mass of the j psi is being restrained from the real mass, the pDg mass of the quarkonium, to the hadronic threshold. So when we go back to the collinearally factorized approach, this should not have a strong dependence on the factorization scale. So we use a different sets of variation in constructing the error bands. But these are the same set of variation used in other color evaporation model approach. So these are the preliminary results that we have for this calculation. And again, we give it a small kT kick for the initial state parton at the order of about 1 GeV squared to the initial state. But this was not needed in the kT factorization approach as the unintegrated PDFs are already kT dependent. So on the left shown is the pD distribution at 70 EV when compared to the LHCB data. And the same calculation, but for the polarization parameter and compared to the LHCB data. So these are preliminary results with uncertainty bands constructed by varying the charm quark mass only. We have tried to vary the factorization and renormalization scale. They do not give a huge dependence on the scale, but it's not shown right now. And we have some agreement with the polarization data if we just look at the result by the charm quark mass variation. So there are also other polarization parameters. And we're also trying to calculate them to give a more complete picture of what the polarization is. So what lambda phi and lambda tilde is is that it can give you a frame invariant polarization parameter. So if you calculate the lambda theta, which is the part that I've shown before, and also the lambda phi using this formula, then you can have a combination of lambda theta and lambda phi to give you a lambda, which is frame invariant. So this is one of the ways to come up with a frame invariant polarization parameter, which is known as lambda tilde. So how is that invariant? So if we take a look at an example, which is a completely transverse lambda theta equals to plus 1 in this chosen z-axis. So this lambda phi described the azimuthal anisotropy. So if we have a completely transverse with lambda phi equals to 0, then if we rotate the same distribution, we would have a different lambda theta. But the lambda phi would also co-vary with this rotation. But if you use this formula to calculate lambda tilde, they will still give you the same lambda tilde to be plus 1. And a similar story, if we choose this axis, the same axis, and we have a completely longitudinal production to start with, with lambda phi equals to 0. And even if we rotate the distribution to have lambda theta equals to plus 1, which is the other extreme, but the fact that lambda phi co-vary in this rotation would allow lambda tilde to be the same as before. So calculating lambda tilde would, in principle, remove all frame-induced kinematics dependencies. And it would give you a more direct comparison of theory to data. So what we did is we computed lambda phi. And using lambda theta and lambda phi that we calculated, we calculated the lambda tilde. So what we have found is that the invariant polarization parameter, it's close to 0, and at large, pt is slightly negative. But this would give us a better comparison to data. Better in a way that we, such that no frames are good. So the column-software frame would have a set of lambda phi would have a band in column-software frame and a different band in the helicity frame. But when we're calculating lambda tilde, then it is just one lambda doesn't depend on the frame. So this is the last slide. In this talk, I tried to review different models developed to describe the querconium yield in higher-energy collisions. And I also reviewed recent attempts to solve the polarization puzzle in the color evaporation model family. So I'm suggesting that the color evaporation model, any improved color evaporation model, it's worth exploring in terms of polarized production. So there are also other questions to be answered in the future that NRQCD is rigorous, but it still can't describe the A to C production and a jpeg-side polarization simultaneously using the same LDMEs and also respecting heavy querc spin symmetry. On the other hand, color evaporation model is less rigorous. It can describe the yield and perhaps the polarization in the hydro production. But we haven't applied it to other collision systems. And how about A to C for improved color evaporation models? We still haven't calculated that yet. But beyond that, we still want to learn more about querconium production. How do the C to C bar pairs eventually end up in jpeg-side? Can we describe the mechanism beyond just FQs in the color evaporation model and the LDMEs? So there are a lot more to be learned in the future. So that's it for my presentation. Thank you very much, Vincent. Let's try to give Vincent some virtual applause in the participants' window. And I'll try to give him some real applause here. Excellent, Vincent. Thanks for this really systematic overview. It was quite a nice talk. So are there any questions? Yeah, again, if you have a question, to unmute your mic, we need to know that you want to speak. So type speak in the chat window. And while we're waiting for that, Tim, if you don't mind, I have a question. Is that OK? Please, oh, no, of course. Yeah, so Vincent, can we go back to this lambda tilde that you were describing here? One of my original questions was, of course, to understand what would be required to remove this frame dependence that you were seeing. What do experiments need to do in order to put data points on this plot you show on slide 54? So there are experiments that also do lambda tilde measurement. But the most straightforward way is to just convert their measured lambda theta and lambda phi in this way. And this is not the only way to construct a frame invariant parameter. But this is one of the most commonly used now invariant form to give a lambda tilde, because it still runs from negative 1 to 1, which is very similar to lambda theta. All right, so it is a relatively simple transform for the experiments to do. This doesn't require a lot of retooling for experiments when they quote their results. Yeah, but if you directly transform, take just in one frame, for example, the experiment measured in the Collins-Opper frame, the lambda theta and lambda phi, if you just do this conversion and versus the same conversion in the Helicity frame, some systematic uncertainty will make them look like not invariant. OK. All right, Pavel, you have a question. Yes, Havins, and this is Pavel Natovsky. Well, thank you so much, first of all, for this very interesting review of the measurements. You have shown a variety of measurements at different levels of accuracy. And I also was very happy to see that you use some of the results from our C-Tech collaboration, like my part on distribution functions. What's not clear to me is that what are your objectives in terms of, let's say, validating various models. So it seems that the accuracy of these predictions varies quite a bit. Like, for example, if you were to say, what is your next big target? So that would really dim down certain things and would really clarify some of the comparisons that you have made, as well as maybe you need something from us, like new PDFs or some predictions. I noticed, for example, that you use leading order PDFs, but those are not very precise. And then again, so maybe that's sufficient for you in your case. So what are your questions? Yeah, the objective is to have a polarized calculation and a color evaporation model to make it as competitive or trying to be competitive with NRQCD, because NRQCD is not going to describe polarization, jpecite cross-section, NA to C cross-section, all at the same time using the same mixing. So our objective is to provide a color evaporation model version of the calculation. And we're just starting right now. And we're just starting with hydro production. Did I answer your question, or am I missing? Yeah, but then again, looking forward, OK. So is working with this leading order predictions still acceptable for the next two years, or what would be? So I guess what is the vision towards the future in this case? So we're trying to calculate the S-date to start with. And we will try to calculate the P-state contribution as well. Yeah, that's pretty much where we're heading to. OK. OK, thank you. Yep. OK, I think Richard had a question. So I've unmuted you, Richard. Yeah, I have a rather experimental question. All the data that you compared to central coming from experiments with unpolarized beams, if you would have a beam or target that is polarized, how different would that picture be? Yeah, that is a good question. So I've been asked multiple times that to give what if your initial state is polarized, how would that change? In this calculation, we assume the initial state is unpolarized in a fashion that we sum over all the polarization for the initial state gluon. And if the initial state is polarized, then it would have an influence of the final state as well. So I can't say for sure. But there's a big difference in terms of setting up the calculation. Thank you. Yeah. OK, it doesn't look like we have any more questions. And we're about 10 minutes over our time. Does anybody have one last urgent question that they would like to ask? And Tim, I'll trust you to unmute them if they need it. OK, it sounds like none. So let's thank Vincent one more time. So thank you very much for providing this excellent seminar for us. Yeah, thanks for the chance as well. Yeah, no. And I hope you stay safe and stay well out in California. I know it's rough out there right now. And to everybody else as well, I hope you stay well and stay safe as well. Have a good evening, everybody. Thanks again, Vincent. Take care. Me too. Thanks, everyone.