Thermalization time constrained by high- p ⊥ QGP tomography
Stefan Stojku, Jussi Auvinen, Marko Djordjevic, Pasi Huovinen, Magdalena Djordjevic
TThermalization time constrained by high- p ⊥ QGP tomography
Stefan Stojku, Jussi Auvinen, Marko Djordjevic, Pasi Huovinen, and Magdalena Djordjevic ∗ Institute of Physics Belgrade, University of Belgrade, Serbia Faculty of Biology, University of Belgrade, Serbia
We show that high- p ⊥ R AA and v are way more sensitive to the QGP thermalization time, τ ,than the distributions of low- p ⊥ particles, and that the high- p ⊥ observables prefer relatively latethermalization at τ ∼ c . To calculate high- p ⊥ R AA and v , we employ our newly developedDREENA-A formalism, which combines state-of-the-art dynamical energy loss model with 3+1-dimensional hydrodynamical simulations. The model applies to both light and heavy flavor, and wepredict a larger sensitivity of heavy observables to the thermalization time. Elliptic flow parameter v is also more sensitive to τ than R AA due to non-trivial differences in the evolution of in-plane andout-of-plane temperature profiles. This presents, to our knowledge, the first example of applyingQGP tomography to constrain bulk QGP observables with high- p ⊥ observables and related theory. Quark-Gluon-Plasma (QGP) [1, 2] is an extremeform of nuclear matter that consists of interactingquarks, antiquarks and gluons. Since the interactionsbetween quarks and gluons are governed by QuantumChromodynamics (QCD), it is sometimes called QCDmatter as well. This state of matter is formed in ul-trarelativistic heavy-ion collisions at the RelativisticHeavy-Ion Collider (RHIC) and the Large Hadron Col-lider (LHC). In these experiments, the bulk propertiesof QGP are traditionally explored by low- p ⊥ observ-ables [3–5], that describe the motion of 99 .
9% of par-ticles formed in heavy-ion collisions. Rare high energyprobes are, on the other hand, almost exclusively usedto understand the interactions of high- p ⊥ partons withthe surrounding QGP medium. While high- p ⊥ physicshad a decisive role in the QGP discovery [6], it hasbeen rarely used to understand bulk QGP properties.To our knowledge, so far in bulk QGP medium sim-ulations no parameter has been constrained by high- p ⊥ observables. On the other hand, some impor-tant bulk QGP properties are known to be difficultto constrain by low- p ⊥ observables and correspondingtheory/simulations [7–10]. We are therefore advocat-ing high- p ⊥ QGP tomography, where bulk QGP pa-rameters are jointly constrained by low- and high- p ⊥ physics. We have previously demonstrated how theshape of the QGP droplet formed in heavy-ion colli-sions is reflected in the high- p ⊥ observables [11], andnow we apply high- p ⊥ QGP tomography to constraina QGP parameter that is currently inferred with largeuncertainities.In particular, we here analyze how high- p ⊥ R AA and v depend on the QGP thermalization time τ .The dynamics before thermalization and applicabilityof hydrodynamics and, therefore, the associated energyloss phenomena, are not established yet [48]. To avoidspeculation, and to provide a baseline calculation forfurther studies, we assume free streaming of high- p ⊥ particles before thermalization, and neglect the pre- ∗ E-mail: [email protected] equilibrium evolution of the medium. After thermal-ization, the QCD medium is described as relativisticviscous fluid, and high- p ⊥ probes start to lose energythrough interactions with this medium. Consequently,thermalization time is an important parameter, whichaffects both the evolution of the system and interac-tions of the high- p ⊥ particles with the medium.Conventional approach to fix thermalization time isto carry out hydrodynamical simulations with variousvalues of τ , calculate the distributions of low- p ⊥ par-ticles, compare to data, and keep varying τ until thebest possible fit to the data is achieved. However,an analysis employing sophisticated Bayesian statisticshas shown that low- p ⊥ data provides only weak limitsto the thermalization time, τ = 0 . ± .
41 fm/ c with90% credibility [12], and further constraints would bevery useful. . . . . . . . p T [GeV] d N c h / p T d p T d η [ G e V − ] (0-5)% × × × × . τ = 0 . τ = 0 . τ = 0 . τ = 0 . τ = 1 . τ = 1 . FIG. 1: Transverse momentum spectrum of charged parti-cles in five centrality classes in Pb+Pb collisions at √ s NN =5 .
02 TeV, with thermalization time τ varied from 0 . . When calculating how the high- p ⊥ observables de-pend on τ , one has to ensure that the QGP mediumevolution is compatible with the observed distribu-tions of low- p ⊥ particles. We describe the mediumevolution using the 3+1-dimensional viscous hydrody- a r X i v : . [ nu c l - t h ] A ug FIG. 2: Charged hadron DREENA-A R AA (upper panels) and v (lower panels) predictions, generated for six different τ (indicated on the legend), are compared with ALICE [15, 30], CMS [31, 32] and ATLAS [33, 34] data. Four columns,from left to right, correspond to 10–20%, 20–30%, 30–40% and 40–50% centralities at √ s NN = 5 .
02 Pb+Pb collisions atthe LHC. namical model from Ref. [13]. For simplicity, we ig-nore pre-equilibrium evolution, i.e. v r ( x, y, τ ) = 0,choose a constant shear viscosity to entropy densityratio η/s = 0 .
12, and base the initial transverse energydensity profile e T on the binary collision density n BC from the optical Glauber model: e T ( τ , x, y, b ) = C e ( τ ) f BC ,f BC = n BC + c n BC + c n BC . (1)The parameters C e , c and c are tuned separately foreach τ value, to approximately describe the observedcharged particle multiplicities and v { } in Pb+Pbcollisions at √ s NN = 5 .
02 TeV. The thermalization(i.e. hydro initialization) time τ has been varied from0 . . √ s NN = 2 .
76 Pb+Pbcollisions in Ref. [13]. Likewise, the decoupling tem-perature T dec = 100 MeV and the equation of state s p -PCE-v1 [14] are the same as in that article.The transverse momentum distributions of chargedparticles are shown in Fig. 1, and p ⊥ -differential ellip-tic flow parameter v ( p ⊥ ) in the low momentum part( p ⊥ < τ —especially v ( p ⊥ ) is almost independent of τ .To evaluate the high- p ⊥ parton energy loss, we useour recently developed DREENA-A framework [49]based on our dynamical energy loss formalism, embed-ded within the hydrodynamical model outlined above.The dynamical energy loss formalism [16, 17] has sev- eral unique features not included in other approaches: i) QCD medium of finite size and temperature con-sisting of dynamical (i.e. moving) partons; this in dis-tinction to medium models with widely used static ap-proximation and/or vacuum like propagators [18–21]. ii)
Calculations based on generalized Hard-Thermal-Loop approach [22], with naturally regulated infrareddivergences [16, 17, 23]. iii)
Calculations of both ra-diative [16] and collisional [17] energy loss in the sametheoretical framework. iv)
Generalization towards run-ning coupling [24], finite magnetic mass [25], abol-ishment of widely used soft-gluon approximation [26].All of these effects are necessary for accurate predic-tions [27], but utilizing evolving temperature profilesobtained from numerical calculations is highly non-trivial within this complex energy loss framework. Thisframework has been implemented within DREENA-A,which can take any, arbitrary, temperature profile asinput (consequently ”A” stands for
Adaptive ). Sinceour framework is applicable for both light and heavyflavors, we evaluate high- p ⊥ R AA and v not only ofcharged hadrons, but of D and B mesons as well.We use the same parameter set to generate high- p ⊥ predictions as in our earlier studies using theDREENA-C [28] and DREENA-B [29] frameworks.The resulting DREENA-A predictions for chargedhadron R AA in four different centrality classes, and for τ in the range of 0.2–1.2 fm, are shown in the upperpanel of Fig. 2, and compared with experimental data.In the lower panel of Fig. 2, we show similar comparisonof predicted high- p ⊥ v to data. In distinction to the FIG. 3: Predicted D (full curves) and B meson (dashedcurves) R AA (upper panels) and v (lower panels) in Pb+Pbcollisions at √ s NN = 5 .
02 TeV. The predictions for Dmesons are compared with ALICE [35, 36] (red triangles)and CMS [37] (blue squares) D meson data, while predic-tions for B mesons are compared with CMS [38] (green cir-cles) non-prompt J/ Ψ data. On each panel, the predictionsare generated for six different τ (indicated on the legend).FIG. 4: DREENA-A predictions for charged hadron R AA (left) and v (right) in 20–30% centrality class of √ s NN =5 .
02 TeV Pb+Pb collisions at the LHC, generated for τ =0 . τ q (indicated on the legend). Thepredictions are compared with ALICE [15, 30], ATLAS [33,34] and CMS [31, 32] data. low- p ⊥ distributions, we see that high- p ⊥ predictionscan be resolved against experimental data, and that thelater thermalization is clearly preferred by both R AA and v . This resolution is particularly clear for v pre-dictions, which approach the high- p ⊥ tail of the data,as τ is increased. One can also observe that this res-olution (i.e. difference between the adjacent predictedcurves) increases for higher centralities, which we willanalyse below. FIG. 5: Average temperature along the jet path traversingthe system in out-of-plane (full curve) and in-plane (dashedcurve) directions. The average is over all sampled jet paths,and the path ends at T C ≈
160 MeV [39]. Centrality of thecollision and τ is indicated on the legend of each panel. Furthermore, we obtain that heavy quarks (charmand bottom) are even more sensitive to τ , as shownin Fig. 3. For bottom probes, the data are largely notavailable, making these true predictions, to be testedagainst upcoming high luminosity LHC Run 3 data.For charm probes, the available experimental data aremuch more sparse (and with larger error bars) than thecharged hadron data. However, where available, com-parison of our predictions with the data suggests thesame tendency as for charged hadrons, i.e. preferencetowards later thermalization. These results are impor-tant, as consistency between light and heavy flavor iscrucial (though highly non-trivial, as confirmed by thewell known heavy flavor puzzle [40]) for studying theQGP properties.In Ref. [41] it was proposed that jet quenching maystart later than the thermalization, and subsequentfluid dynamical evolution, of the bulk QCD medium.To test this scenario we follow that work, and intro-duce a separate quenching start time τ q ≥ τ . In Fig. 4we show the high- p ⊥ R AA and v in 20-30% centralityfor thermalization time τ = 0 . τ q values inthe range of 0.2–1.2 fm. The sensitivity to τ q is similarin other centralities, for larger τ and for heavy flavor. R AA shows similar sensitivity to τ q as to τ ; compareFigs. 4 and 2. The v is surprisingly insensitive to τ q ,and way below the data, consequently not supportingthe idea that quenching can start later than hydrody-namical evolution.To investigate the origin of the sensitivity of R AA and v to τ and τ q , we evaluate the temperature alongthe paths of jets traveling in-plane ( φ = 0) and out-of-plane ( φ = π/
2) directions, and average over allsampled jet paths. In Fig. 5 we show the resultingtemperature evolution in 10–20% and 30-40% centralcollisions for τ = 0 . τ is increased,the differences between in-plane and out-of-plane tem-perature profiles also increase. Since v is proportionalto the difference in suppression along in-plane and out-of-plane directions, larger difference along these direc-tions leads to larger v , and causes the observed depen-dency on τ . As well, for fixed τ , increasing τ q hardlychanges v since at early times the average tempera-ture in- and out-of-plane directions is almost identical,and no v is built up at that time in any case. Fur-thermore, the more peripheral the collision, the largerthe difference in average temperatures, which leads tohigher sensitivity of v to τ as seen in the lower panelsof Fig. 2.The change in τ affects the average temperaturealong the jet path in two ways. First, smaller τ meanslarger initial gradients, faster build-up of flow, andfaster dilution of the initial spatial anisotropy. Second,since the initial jet production is azimuthally symmet-ric, and jets travel along eikonal trajectories, at earlytimes both in- and out-of-plane jets probe the tempera-ture of the medium almost the same way. The averagetemperature of both is almost identical at τ = 0 . R AA with larger τ and τ q as seen in Figs. 2 and 4.Larger τ or τ q cuts away the large temperature partof the profile decreasing the average temperature, andthus increasing the angular average R AA [28, 29].As mentioned above, we do not include any pre-equilibrium evolution along the lines of, e.g., Refs. [42–45]. We do not expect pre-equilibrium evolution to de-stroy the sensitivity of high- p ⊥ observables to τ [46],but it may affect the favored value of τ . As ex-plained, reproduction of high- p ⊥ v requires that thespatial anisotropy is not smeared away too fast. Sincepre-equilibrium evolution is expected to reduce theanisotropy [43, 47], it is possible that when it is in-cluded the favored τ is even larger than seen here.In summary, we presented (to our knowledge) thefirst example of using high- p ⊥ theory and data to con-strain a parameter that is weakly sensitive to bulk QGPevolution. Specifically, we used high- p ⊥ R AA and v toinfer that experimental data prefer late thermalizationtime. Heavy flavor show large sensitivity to τ , so ourconclusion will be further tested by the upcoming highluminosity measurements. v shows a higher sensitivityto τ than R AA , and we showed that v is affected by τ because of differences in the in- and out-of-plane tem-perature profiles. 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