Dynamical energy loss formalism: from describing suppression patterns to implications for future experiments
Magdalena Djordjevic, Dusan Zigic, Bojana Blagojevic, Jussi Auvinen, Igor Salom, Marko Djordjevic
NNuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2018)
Dynamical energy loss formalism: from describingsuppression patterns to implications for future experiments
Magdalena Djordjevic a , Dusan Zigic a , Bojana Blagojevic a , Jussi Auvinen a , IgorSalom a and Marko Djordjevic b a Institute of Physics Belgrade, University of Belgrade, Serbia b Faculty of Biology, University of Belgrade, Serbia
Abstract
Understanding properties of Quark-Gluon Plasma requires an unbiased comparison of experimental data with theoreticalpredictions. To that end, we developed the dynamical energy loss formalism which, in distinction to most other methods,takes into account a realistic medium composed of dynamical scattering centers. The formalism also allows makingnumerical predictions for a wide number of observables with the same parameter set fixed to standard literature values.In this proceedings, we overview our recently developed DREENA-C and DREENA-B frameworks, where DREENA isa computational implementation of the dynamical energy loss formalism, and where C stands for constant temperatureQCD medium, while B stands for the medium modeled by 1 +
1D Bjorken expansion. At constant temperature ourpredictions overestimate v , in contrast to other models, but consistent with simple analytical estimates. With Bjorkenexpansion, we have a good agreement of the predictions with both R AA and v measurements. We find that introducingmedium evolution has a larger e ff ect on v predictions, but for precision predictions it has to be taken into account in R AA predictions as well. Based on numerical calculations and simple analytical derivations, we also propose a newobservable, which we call path length sensitive suppression ratio, for which we argue that the path length dependencecan be assessed in a straightforward manner. We also argue that Pb + Pb vs. Xe + Xe measurements make a goodsystem to assess the path length dependence. As an outlook, we expect that introduction of more complex mediumevolution (beyond Bjorken expansion) in the dynamical energy loss formalism can provide a basis for a state of the artQGP tomography tool e.g. to jointly constrain the medium properties from the point of both high pt and low pt data. Keywords:
1. Introduction
Energy loss of high-pt particles traversing QCD medium is considered to be an excellent probe of QGPproperties [1, 2, 3]. The theoretical predictions can be generated and compared with a wide range of ex-perimental data, coming from di ff erent experiments, collision systems, collision energies, centralities, ob-servables. This comprehensive comparison of theoretical predictions and high p ⊥ data, can then be usedtogether with low p ⊥ theory and data to study the properties of created QCD medium [4, 5, 6, 7], that is, for a r X i v : . [ nu c l - t h ] S e p / Nuclear Physics A 00 (2020) 1–4 precision QGP tomography. However, to implement this idea, it is crucial to have a reliable high p ⊥ partonenergy loss model. With this goal in mind, during the past several years, we developed the dynamical energyloss formalism [8]. Contrary to the widely used approximation of static scattering centers, this model takesinto account that QGP consists of dynamical (moving) partons, and that the created medium has finite size.The calculations are based on the finite temperature field theory, and generalized HTL approach. The for-malism takes into account both radiative and collisional energy losses, is applicable to both light and heavyflavor, and has been recently generalized to the case of finite magnetic mass and running coupling [10].Most recently, we also relaxed the soft-gluon approximation within the model [9]. Finally, the formalismis integrated in an up-to-date numerical procedure [10], which contains parton production, fragmentationfunctions, path-length and multi-gluon fluctuations.The model up-to-now explained a wide range of R AA data [10, 11, 12, 13], with the same numericalprocedure, the same parameter set, and with no fitting parameters, including explaining puzzling data andgenerating predictions for future experiments. This then strongly suggests that the model provides a realisticdescription of high p ⊥ parton-medium interactions. However, the model did not take into account themedium evolution, so we used it to provide predictions only for those observables that are considered to beweakly sensitive to QGP evolution.Therefore, our goal, which will be addressed in this proceedings, is to develop a framework which willallow systematic comparison of experimental data and theoretical predictions, obtained by the same formal-ism and the same parameter set. In particular, we want to develop a framework, which can systematicallygenerate predictions for di ff erent observables (both R AA and v ), di ff erent collision systems ( Pb + Pb and Xe + Xe ), di ff erent probes (light and heavy), di ff erent collision energies and di ff erent centralities [14, 15, 16].Within this, our major goal is to introduce medium evolution in the dynamical energy loss formalism [15],where we start with 1 +
1D Bjorken expansion [17], and where our developments in this direction, will alsobe outlined in this proceedings. Finally, we also want to address an important question of how to di ff er-entiate between di ff erent energy loss models; in particular, what is appropriate observable, and what areappropriate systems, to assess energy loss path-length dependence [16]. Note that only the main results arepresented here; for a more detailed version, see [14, 15, 16], and references therein.
2. Results and discussion
As a first step towards the goals specified above, we developed DREENA-C framework [14], which isa fully optimized computational suppression procedure based on our dynamical energy loss formalism inconstant temperature finite size QCD medium. With this framework we, for the first time, generated joint R AA and v predictions within our dynamical energy loss formalism. We generated predictions for both lightand heavy flavor probes, and di ff erent centrality regions in Pb + Pb collisions at the LHC (see [14] for moredetails). We obtained that, despite the fact that DREENA-C does not contain medium evolution (to which v is largely sensitive), it leads to qualitatively good agreement with this data, though quantitatively, thepredictions are visibly above the experimental data.The theoretical models up-to-now, faced di ffi culties in jointly explaining R AA and v data, i.e. lead tounderprediction of v , unless new phenomena are introduced, which is known as v puzzle [18]. Having thisin mind, the overestimation of v , obtained by DREENA-C, seems surprising. However, by using a simplescaling arguments, where fractional energy loss is proportional to T a and L b , and where, within our model a , b are close to 1, we can straightforwardly obtain that, in constant temperature medium, R AA ≈ − ξ T L and v ≈ ξ T ∆ L , while in evolving medium they have the following expressions R AA ≈ − ξ T L and v ≈ ξ T ∆ L − ξ ∆ TL (see [14] for more details, ξ is a proportionality factor that depends on initial jet p ⊥ )). So, it is our expectationthat, within our model, the medium evolution will not significantly a ff ect R AA , while it will notably lowerthe v predictions.To check the reliability of these simple estimates, we developed DREENA-B framework [15], which isour most recent development within dynamical energy loss formalism. Here B stands for 1 +
1D Bjorkenexpansion [17], i.e. the medium evolution is introduced in dynamical energy loss formalism in a simpleanalytic way. We provided first joint R AA and v predictions with dynamical energy loss formalism inexpanding QCD medium, which are presented in Fig. 1 (for charged hadrons), and we observe very good Nuclear Physics A 00 (2020) 1–4 joint agreement with R AA and v data. We equivalently obtained the same good agreement for D mesons,and predicted non-zero v for high p ⊥ B mesons.
Fig. 1.
Joint R AA and v predictions for charged hadrons in . TeV Pb + Pb collisions. Upper panels:
Predictions for R AA vs. p ⊥ are compared with ALICE [19] (red circles) and CMS [20] (blue squares) charged hadron experimental data in 5 .
02 TeV Pb + Pb collisions. Lower panels:
Predictions for v vs. p ⊥ are compared with ALICE [21] (red circles) and CMS [22] (blue squares)experimental data in 5 .
02 TeV Pb + Pb collisions. Full and dashed curves correspond, respectively, to the predictions obtained withDREENA-B and DREENA-C frameworks. Columns 1-6 correspond, respectively, to 0 − − − −
50% centralityregions. The figure is adapted from [14, 15] and the parameter set is specified there.
In Fig. 2, we further present predictions for Xe + Xe data [16], where we note that these predictionswere generated before the data became available. In this figure (see also Fig. 1), we compare DREENA-C and DREENA-B frameworks, to assess the importance of including medium evolution on R AA and v observables. We see that inclusion of medium evolution has e ff ect on both R AA and v data. That is, itsystematically somewhat increase R AA , while significantly decreasing v ; this observation is in agreementwith our estimate provided above. Consequently, we see that this e ff ect has large influence on v predictions,confirming previous arguments that v observable is quite sensitive to medium evolution. On the otherhand, this e ff ect is rather small on R AA , consistent with the notion that R AA is not very sensitive to mediumevolution. However, our observation from Figs. 1 and 2 is that medium evolution e ff ect on R AA , though notlarge, should still not be neglected in precise R AA calculations, especially for high pt and higher centralities. Fig. 2.
Joint R AA and v predictions for charged hadronsin . TeV Xe + Xe collisions. Predictions for and R AA vs.p ⊥ and v vs. p ⊥ are shown on upper and lower panels, re-spectively. Columns 1-3, respectively, correspond to 5 − −
30% and 40 −
50% centrality regions. Full and dashedcurves correspond, respectively, to the predictions obtainedwith DREENA-B and DREENA-C frameworks. In each panel,the upper (lower) boundary of each gray band corresponds to µ M /µ E = . µ M /µ E = . Path-length sensitive suppression ratio ( R XePbL )for light and heavy probes.
Predictions for R XePbL vs. p ⊥ is shown for charged hadrons (full), D mesons (dashed) andB mesons (dot-dashed). First and second column, respec-tively, correspond to 30 −
40% and 50 −
60% centrality regions. µ M /µ E = .
4. The figure is adapted from [16] and the param-eter set is specified there. / Nuclear Physics A 00 (2020) 1–4
Finally, as the last topic of this proceedings, we address a question on how to di ff erentiate between di ff er-ent energy loss models. With regard to this, note that path length dependence provides an excellent signaturedi ff erentiating between di ff erent energy loss models, and consequently also between the underlying energyloss mechanisms. For example, some energy loss models have linear, some have quadratic path-length de-pendence, and the dynamical energy loss path-length dependence is between linear and quadratic, which isdue to both collisional and radiative energy loss mechanisms included in the model. To address this ques-tion, we first have to answer what is an appropriate system for such a study. We argue that comparison ofsuppressions in Pb + Pb and Xe + Xe is an excellent way to study the path length dependence: From thesuppression calculation perspective, almost all properties of these two systems are the same. That is, weshow [16] that these two systems have very similar initial momentum distributions, average temperature foreach centrality region and path length distributions (up to rescaling factor A / ). That is, the main propertydi ff erentiating the two systems is its size, i.e. rescaling factor A / , which therefore makes comparison ofsuppressions in Pb + Pb and Xe + Xe collisions an excellent way to study the path length dependence.The second question is what is appropriate observable? With regards to that, the ratio of the two R AA seems a natural choice, as has been proposed before. However, in this way the path length dependencecannot be naturally extracted, as shown in [16]. For example, this ratio approaches one for high p ⊥ and highcentralities, suggesting no path length dependence, while the dynamical energy loss used to generate thisfigure has strong path length dependence. Also, the ratio has strong centrality dependence. That is, fromthis ratio, no useful information can be deduced. The reason for this is that this ratio includes a complicatedrelationship (see [16] for more details) which depends on the initial jet energy and centrality; so extractingthe path-length dependence from this observable would not be possible.However, based on the derivation presented in [16], we propose to use the ratio of 1- R AA instead. Fromthis estimate, we see that this ratio R XePbL ≡ − R XeXe − R PbPb ≈ (cid:16) A Xe A Pb (cid:17) b / has a simple dependence on only the size ofthe medium ( A / ratio) and the path length dependence (exponent b ). In Fig. 3 we plot this ratio, where wesee that the path length dependence can be extracted from this ratio in a simple way, and moreover there isonly a weak centrality dependence. Therefore, 1- R AA ratio seems as a natural observable, which we proposeto call path-length sensitive suppression ratio. Acknowledgements:
This work is supported by the European Research Council, grant ERC-2016-COG: 725741, and by the Ministry of Science and Technological Development of the Republic of Serbia,under project numbers ON171004, ON173052 and ON171031.
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