Global Constraints from RHIC and LHC on Transport Properties of QCD Fluids in CUJET/CIBJET Framework
GGlobal Constraints from RHIC and LHC on Transport Properties ofQCD Fluids in CUJET/CIBJET Framework
Shuzhe Shi
Jinfeng Liao
Miklos Gyulassy , , Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane,Bloomington, IN 47408, USA. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Pupin Lab MS-5202, Department of Physics, Columbia University, New York, NY 10027, USA. Institute of Particle Physics and Key Laboratory of Quark & Lepton Physics (MOE), Central China Normal University, Wuhan,430079, China.
April 16, 2019
Abstract:
We report results of a comprehensive global χ analysis of nuclear collision data from RHIC (0.2 ATeV),LHC1 (2.76 ATeV), and recent LHC2 (5.02 ATeV) energies using the updated CUJET framework. The frameworkconsistently combines viscous hydrodynamic fields predicted by VISHNU2+1 (validated with soft p T < α c , and the ratio c m of color magnetic to electric screeningscales) and calculate the global χ ( α c , c m ) compared with available jet fragment observables ( R AA , v ). A global χ < α c ≈ . ± . c m ≈ . ± .
03. Using CIBJET, the event-by-event (ebe)generalization of the CUJET framework, we show that ebe fluctuations in the initial conditions do not significantlyalter our conclusions (except for v ). An important theoretical advantage of the CUJET and CIBJET frameworksis not only its global χ consistency with jet fragment observables at RHIC and LHC and with non-perturbativelattice QCD data, but also its internal consistency of the constrained jet transport coefficient, ˆ q ( E, T ) /T , with thenear-perfect fluid viscosity to entropy ratio ( η/s ∼ T / ˆ q ∼ . − .
2) property of QCD fluids near T c needed to accountfor the low p T < Keywords: jet quenching, quark-gluon plasma, relativistic heavy-ion collisions, heavy flavor physics
PACS:
1) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected] a r X i v : . [ h e p - ph ] A p r Introduction
High energy quark and gluon jets, initially generated in rare perturbative QCD processes, lose energy and diffusetransversely along their paths due to interactions with microscopic constituents in the hot quark-gluon plasma createdby heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Such hard( p T >
10 GeV) processes provide an independent probe of the evolution history of the soft QCD matter ( p T < e.g. DGLV [1–9], HT [10–13], AMY [14–16],or AdS [17, 18]), (ii) a detailed model of bulk initial conditions ( e.g.
Glauber [19], TRENTO [20], or CGC [21]), and(iii) a long wavelength collective transport theory of the bulk QCD matter, such as relativistic viscous hydrodynamics( e.g.
VISHNU [22], vUSPHydro [23–25], or MUSIC [26, 27]), the observed attenuation pattern of hard jet observablesand their correlations with soft bulk collective flow observables can help differentiate competing dynamical modelsof high energy A + A collisions. In Refs. [28, 29] we developed the CUJET3.0 framework that combines the DGLVtheory of jet energy loss coupled with nearly “perfect QCD fluids” described by the viscous hydrodynamics theory(and simulated via VISHNU [30]) to constrain the color degrees of freedom.
CIBJET ebeGL ( η / s = ) vs ebeTR ( η / s = ) R AA v { } v { } v - soft v - soft ( - % centrality ) ALICE, ATLAS, CMS
Solid: ebe geomDash: avg geom p T ( GeV ) Fig. 1. (color online) Nuclear modification factor R AA as well as the second and third harmonic coefficients v and v of final hadron azimuthal distribution as functions of p T for 20–30% Pb + Pb collisions at 5.02 ATeV. Solidcurves are obtained from event-by-event calculations, while the dashed curves depict averaged smooth geometry.CIBJET results in both soft and hard regions, with either Monte-Carlo Glauber (red) or Trento (blue) initialconditions, are in excellent agreement with experimental data from ALICE, ATLAS, and CMS [31–35]. SimilarCIBJET results for 30–40% centrality, in excellent agreement with experimental data, were shown in [36]. The simplest class of hard observables in a specific centrality class, C , is the p T and relative azimuthal angledependence of the nuclear modification factor R fAA for final state hadrons (with flavor species denoted by f ), whichis decomposed into Fourier harmonics as: R fAA (cid:0) p T , φ ; C ; √ s (cid:1) = dN fAA ( C ) p T dp T dφ T AA ( C ) dσ fpp p T dp T dφ = R fAA (cid:0) p T ; C ; √ s (cid:1) (cid:34) (cid:88) n (cid:104) v fn (cid:0) p T ; C ; √ s ; (cid:1) cos( n ( φ − Ψ n )) (cid:105) C (cid:35) (1)where T AA ( C ) is the average number of binary nucleon-nucleon scattering per unit area in centrality class C . Typically,2 is expressed as a percentage interval of the inelastic cross section, e.g.
10 – 20% of the charged multiplicity per unitrapidity distribution. The p T and φ depict the transverse momentum and the azimuthal angle of observed leadinghadrons, respectively, relative to the bulk collective flow azimuthal harmonics. The experimental measurements ofhard particle harmonics v fn are performed with respect to event-wise soft harmonics, and event-by-event fluctuationsof the bulk initial condition may play an important role [37]. Within the CUJET3 framework, the influence of event-by-event fluctuations has been investigated with a generalized CIBJET (= ebeIC + VISHNU + DGLV) framework,with the results reported in Ref. [36]. The CIBJET results of R AA , v , and v observables across a very wide rangeof p T for 30–40% centrality Pb + Pb collisions at 5.02 ATeV were shown in [36], and they are in excellent agreementwith experimental data. In Fig. 1, we further present the CIBJET results of R AA , v and v for a different centralityof 20–30%, which likewise show excellent agreement with experimental data and demonstrate the correct centralitydependence of the CIBJET results. One conclusion found with CIBJET is that the p T and centrality dependenceof the elliptic v f ( p T , C ) azimuthal harmonics shows quantitative consistency at a ∼
10% level between calculationswith averaged smooth bulk geometry and those with fluctuating initial conditions. This conclusion is true for thevaried centrality class and is in agreement with a similar consistency-check from the ebeIC + LBT + HT hard +soft framework in Ref. [13, 38], while different from the ebeIC + vUSPhydro + BBMG framework in Ref. [37], whichfound a much larger sensitivity (factor ∼
2) of the hard elliptic harmonic to event-by-event fluctuations. The findingfrom CIBJET justifies the use of averaged smooth geometry in the CUJET3 framework, as we shall adopt in thepresent paper.The prime motivation of this work is to conduct a comprehensive new global χ analysis of nuclear collision datafrom RHIC (0.2ATeV), LHC1 (2.76ATeV), and recent LHC2 (5.02ATeV) energies for high p T light and heavy flavorhadrons. This analysis is performed with the updated CUJET3.1 framework to evaluate jet energy loss distributionsin various models of the color structure of QCD fluids produced in heavy ion collisions. The CUJET3.1 is based on ourprevious CUJET3.0 framework [28, 29] and successfully addressed a few issues in CUJET3.0. A brief introduction toCUJET3.0 and a detailed discussion regarding the improvements in CUJET3.1 are included in the two appendices.We will show that CUJET3.1 provides a non-perturbative solution to the long standing hard ( R AA and v ) versussoft “perfect fluidity” puzzle. We further examine the crucial issue of consistency between soft and hard transportproperties of the QCD fluid in this framework. Predictions for future tests at LHC with 5.44 ATeV Xe + Xe and5.02 ATeV Pb + Pb will also be presented.The organization of this paper is as follows. We perform the model parameter optimization in Sec. , based onthe quantitative χ analysis with a comprehensive set of experimental data for light hadrons. In Sec. , we show thesuccessful CUJET3.1 description of available experimental data for light hadrons as well as the successful independenttest with heavy flavor hadrons. The temperature dependence of the jet transport coefficient and the correspondingshear viscosity for the quark-gluon plasma, extracted from CUJET3.1, are presented in Sec. . CUJET3.1 predictionsfor on going experimental analysis are shown in Sec. . Finally, we summarize the paper in Sec. . A brief introductionof the CUJET3 framework, as well as the improvements made in CUJET3.1, are included in the two appendices. χ Analysis with CUJET3
As discussed in Appendix A, the CUJET3 framework is a quantification model solving jet energy loss in ahydrodynamics background, implementing DGLV jet energy loss from both inelastic and elastic scattering, andtaking into account interactions with both chromo-electric and magnetic charges of the medium. There are two keyparameters in the model. One is α c (see also Eq.12 in App.A): α s ( Q ) = α c α c π log( Q /T c ) , which is the value of QCD running coupling at the non-perturbative scale Q = T c . It sensitively controls andpositively influences the overall opaqueness of the hot medium. The other is c m , defined via µ M = c m g ( T ) µ , (seealso Eq.12, 14 and 15 in App.A), which is the coefficient for magnetic screening mass in the medium and influencesthe contribution of the magnetic component to the jet energy loss. The increase of c m leads to the enhancement ofmonopole mass, hence overall opaqueness. Magnetic mass scales with magnetic scale g T , but its coefficient receivesnon-perturbative contributions and can-not be perturbatively calculated even at high temperature. Constrained bythe lattice QCD calculation [39], the reasonable value of c m varies in the range of 0 . (cid:46) c m (cid:46) . χ analysis and utilize centraland semi-central high transverse momentum light hadron’s R AA and v for all available data. We compare the relative3ariance between theoretical expectation and experimental data, which is defined as the ratio of squared differencebetween experimental data points and corresponding CUJET3 expectation, to the quadratic sum of experimentalstatistic and systematic uncertainties for that data point: χ / d . o . f . = (cid:88) i ( y exp ,i − y theo ,i ) (cid:80) s ( σ s,i ) (cid:44) (cid:88) i , (2)where (cid:80) i runs over all experimental data point in the momentum range 8 ≤ p T ≤
50 GeV/ c , and (cid:80) s denotessumming over all sources of uncertainties, e.g. systematic and statistic uncertainties. We compute χ / d . o . f . for eachof the following 12 data sets: •
200 GeV Au-Au Collisions, 0–10% Centrality Bin, R AA ( π ): PHENIX [40, 41]; •
200 GeV Au-Au Collisions, 0–10% Centrality Bin, v ( π ): PHENIX [41]; •
200 GeV Au-Au Collisions, 20–30% Centrality Bin, R AA ( π ): PHENIX [40, 41]; •
200 GeV Au-Au Collisions, 20–30% Centrality Bin, v ( π ): PHENIX [41]; • R AA ( h ± ): ALICE [42]; • v ( h ± ): ATLAS [43], CMS [44]; • R AA ( h ± ): ALICE [42]; • v ( h ± ): ALICE [45], ATLAS [43], CMS [44]; • R AA ( h ± ): ATLAS-preliminary [32], CMS [33]; • v ( h ± ): CMS [34]; • R AA ( h ± ): CMS [33]; • v ( h ± ): CMS [34];and finally obtain the overall χ / d . o . f . as the average over these data sets. α c c m α c c m α c c m χ / d.o.f.1.11.31.51.71.92.12.3 R AA only v only R AA & v Fig. 2. (color online) χ / d . o . f . comparing χ LT -scheme CUJET3 results with RHIC and LHC data. Left: χ / d . o . f . for R AA only. Middle: χ / d . o . f . for v only. Right: χ / d . o . f . including both R AA and v First of all, we perform the analysis in the “slow” quark-libration scheme ( χ LT -scheme) for a wide range ofparameter space: 0 . ≤ α c ≤ .
3, 0 . ≤ c m ≤ .
32. As shown in Fig. 2, χ / d . o . f . with only R AA data (left panel) oronly v data (middle panel) yields different tension and favors different regions of parameter space. Taking all datatogether (right panel), we identify a data-selected optimal parameter set as ( α c = 0 . c m = 0 . χ / d . o . f . closeto unity, while the “uncertainty region” spanned by ( α c = 0 . c m = 0 .
22) and ( α c = 1 . c m = 0 .
28) with a χ / d . o . f . about two times the minimal value. Both the optimal parameter set and the “uncertainty region” remain essentiallyunchanged if χ / d . o . f . is computed giving the same weight for each data point instead of each data set.In order to test the need of the of chromo-magnetic-monopole (cmm) degrees of freedom and to explore thepotential influence of theoretical uncertainties of different quark liberation schemes, we perform the same χ analysiswith two other schemes: (a) the “fast” quark-libration scheme ( χ uT -scheme); (b) the weakly coupling QGP (wQGP)scheme, equivalent to CUJET2.0 mode, and assuming no cmm, i.e. taking f E = 1, f M = 0, and chromo-electric-components fraction χ T = 1, while the running coupling takes the Zakharov formula as in Eq. (13).By using these three schemes with their corresponding most optimal parameter set: • (i) sQGMP χ LT -scheme: α c = 0 . c m = 0 .
25, 4
10 12 14 16 18 200.20.40.60.8 p T ( GeV ) R AA - % χ TL : 1.60 χ Tu : 1.09wQGP: 1.83 p T ( GeV ) R AA - % χ TL : 0.37 χ Tu : 0.21wQGP: 0.33 p T ( GeV ) v - % χ TL : 0.66 χ Tu : 0.76wQGP: 0.83 p T ( GeV ) v - % χ TL : 0.37 χ Tu : 0.43wQGP: 1.17 p T ( GeV ) R AA - % χ TL : 0.02 χ Tu : 0.03wQGP: 0.03 p T ( GeV ) R AA - % χ TL : 0.27 χ Tu : 0.35wQGP: 0.22 p T ( GeV ) v - % χ TL : 1.81 χ Tu : 1.04wQGP: 8.09 p T ( GeV ) v - % χ TL : 2.84 χ Tu : 2.63wQGP: 28.20 p T ( GeV ) R AA - % χ TL : 1.16 χ Tu : 2.13wQGP: 1.28 p T ( GeV ) R AA - % χ TL : 0.18 χ Tu : 0.74wQGP: 0.28 p T ( GeV ) v - % χ TL : 0.36 χ Tu : 0.84wQGP: 10.55 p T ( GeV ) v - % χ TL : 1.99 χ Tu : 2.03wQGP: 25.28 Fig. 3. (color online) CUJET theoretical expectation of light hadron R AA and v using three different schemes:sQGMP χ LT -scheme (black solid), sQGMP χ uT -scheme (red dashed), wQGP/CUJET2 scheme (blue dashed dotted).Corresponding χ / d . o . f . are shown, with respect to following experimental data: PHENIX 2008 (orange solidcircle) [40], PHENIX 2012 (magenta solid square) [41]; ALICE (magenta open diamond) [42, 45], ATLAS (greenopen circle) [32, 43], CMS (orange open square) [33, 34, 44]. • (ii) sQGMP χ uT -scheme: α c = 0 . c m = 0 . • (iii) wQGP/CUJET2 scheme: α max = 0 .
4, (optimized by R AA )we show in Fig. 3 their comparison with above the experimental data sets, including the quantitative value of χ / d . o . f . for each data set. While both sQGMP schemes ( χ LT and χ uT ) give similar jet quenching variables, the QGP schemegives similar R AA but less azimuthal anisotropy. In particular, one can see clearly from the quantitative value of their χ / d . o . f . that the theoretical expectations of both sQGMP schemes are in good consistency with the experimentaldata, and that of the QGP scheme, without cmm degree of freedom, differs significantly from the highly precise LHC v measurements. The χ analysis strongly supports the need of cmm degrees of freedom, but remains robust on thespecific quark liberation scheme.While we maintain the unification of the CUJET3 model by using the same (globally optimized) parameter set,it’s worth mentioning that quantitative χ analysis for a different data set, e.g. a different observable or differentbeam energy, flavors a different parameter regime, as shown in Tab. 1. When comparing to the R AA results, theazimuthal anisotropy measurement with more shrink uncertainties yields higher χ / d . o . f and hence has strongerconstrain power. On the other hand, in CUJET3 models, the RHIC results flavor stronger coupling (larger α c or c m ) than the LHC results. Meanwhile, the latter are more precise and provide better distinction of different models.Particularly in the case of 5.02 TeV data, the sQGMP schemes are explicitly more phenomenologically flavored thanthe wQGP scheme. 5QGMP χ LT sQGMP χ uT wQGP α c c m χ / d . o . f c m χ / d . o . f α max χ / d . o . f R AA v Table 1. Optimal parameter and corresponding χ / d . o . f . for different data sets in different schemes. Note that thesQGMP χ uT scheme is optimized by taking α c ≡ . With the high statistics of 5.02 TeV Pb-Pb data, we further expect that highly precise jet quenching observablesfor heavy flavored hadrons, e.g. D meson, could serve as an independent probe to discriminate sQGMP versuswQGP models. As shown in Fig. 4, we find the sQGMP and wQGP models predict similar R AA , while theirsignificantly different predictions of v require experimental data with higher accuracy and higher p T to provide adecisive distinction. p T ( GeV ) R AA D - % s Q G M P w Q G P p T ( GeV ) v D - % s QG M P w QG P Fig. 4. (color online) CUJET theoretical expectation of D meson R AA and v using: sQGMP χ LT -scheme (blacksolid line), and wQGP/CUJET2 scheme (blue dashed-dotted line). Comparison with preliminary-CMS data (orangesolid squares) [46, 47] is also shown. Corresponding R AA and v data for light hadrons [32–34] are depicted withgray symbols. Comparison with Experimental Data
With the systematic χ analysis, we obtained the optimal region of CUJET3 parameters constrained by only lighthadron R AA and v , for central and semi-central collisions. To provide a critical independent test of the model, wecompute CUJET3 results for both light and heavy flavor hadrons, with all centrality ranges up to semi-peripheralcollisions, and perform apple-to-apple comparisons with all available experimental data.Starting from this section, in CUJET3 simulations we employed the χ LT -scheme assuming slow quark-libration,while keeping the theoretical uncertainties by taking the parameter region spanned by ( α c = 0 . c m = 0 .
22) and( α c = 1 . c m = 0 . R AA and lower/upper bounds of v , respectively. First of all, in Figures 5-10, we compare CUJET3.1 results for light hadron R AA and v , with all available data:PHENIX [40, 41] and STAR [48] measurements for 200 GeV Au-Au collisions; ALICE [42, 45], ATLAS [43, 49] andCMS [44, 50] results for 2.76 TeV Pb-Pb collisions; and ATLAS [32] and CMS [33, 34] data for 5.02 TeV Pb-Pbcollisions. One can clearly see the excellent agreement for all centrality ranges at all mentioned collision energies.In particular, it is worth to emphasize that after the aforementioned correction, the current CUJET3.1 simulationframework is able to correctly reproduce the p T and centrality dependence of both R AA and v .200 GeV 2.76 TeV 5.02 TeV0%–5% 40%–50% 0%–5% 40%–50% 0%–5% 40%–50% T ini , center (MeV) 358 294 465 366 506 397 (cid:15) , ini τ hydro (fm/c) 9.4 5.2 11.4 6.3 11.8 6.7 Table 2. Comparison of the initial central temperature T ini , center , initial ellipticity (cid:15) , ini , and life-time τ hydro indifferent collision conditions. The initial ellipticity is defined with respect to entropy density s at hydro startingtime τ = 0 . (cid:15) , ini ≡ − [ (cid:82) s ρ cos(2 φ ) dxdy ] / [ (cid:82) s ρ dxdy ] . We note that such a comprehensive data set covers a rich diversity of geometrical and thermal profiles of the QCDPlasma. In different centrality bins at various colliding energies, the bulk backgrounds are significantly distinctive inlifetime, size, ellipticity and temperature, and consequently, the path length of the jets, either direction averaging ordepending, varies in a wide range. In Tab. 2, we show the quantitative comparison of the initial central temperature T ini , center , initial ellipticity (cid:15) , ini , and life time τ hydro .The temperature, as well as the life-time of such systems vary bya factor of ∼
2, while the geometries change from nearly symmetric to those with an ellipticity ∼ .
4. The success inexplaining R AA and v from central to semi-peripheral data, at beam energies from 0.2 TeV to 5.02 TeV, indicatesthe success of the temperature and path dependence of the CUJET3 energy loss model.7 π PHENIX2004PHENIX2007STAR R AA - % - % - % - % p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 5. (color online) Light hadron R AA for 200 GeV Au-Au collisions in comparison with PHENIX [40, 41] andSTAR [48] results. Magenta (blue) circles labeled PHENIX2004 (PHENIX2007) correspond to data published inRef. [40] (Ref. [41]) analysis of the RHIC 2004 (2007) data set.
200 GeV π PHENIX - p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 6. (color online) Light hadron v for 200 GeV Au-Au collisions in comparison with PHENIX data [41]. .76 TeV h ± ALICEATLASCMS R AA - % - % - % - % R AA - % - % - % - % p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 7. (color online) Light hadron R AA for 2.76 TeV Pb-Pb collisions in comparison with ALICE [42], ATLAS [49]and CMS [50] results. v - % - % - % - % p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % h ± ALICEATLASCMS
Fig. 8. (color online) Light hadron v for 2.76 TeV Pb-Pb collisions in comparison with ALICE [45], ATLAS [43]and CMS [44] results. .00.20.40.60.81.0 R AA - % - % - % - % p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % h ± ATLASCMS
Fig. 9. (color online) Light hadron R AA for 5.02 TeV Pb-Pb collisions in comparison with ATLAS [32] and CMS [33]results. h ± CMS - v - % - % - % - p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % Fig. 10. (color online) Light hadron v for 5.02 TeV Pb-Pb collisions in comparison with CMS data [34]. .2 Heavy Flavor Measurements Having successfully described high- p T R AA and v data for light hadrons, we now perform further independenttests of the energy-loss mechanism using heavy flavor data [51]. In Figures 11-19, we compare CUJET3 results forthe energy-loss observables of prompt D & B mesons as well as electrons or muons from heavy flavor decay, withall available data: PHENIX [52], STAR [53] measurements for 200 GeV Au-Au collisions; ALICE [54–58], CMS [59]data for 2.76 TeV Pb-Pb collisions; and finally CMS results [46, 47, 60] for 5.02 TeV Pb-Pb collisions. A very goodagreement between model and data is found, which validate a successful and unified description of CUJET3 for bothlight and heavy flavor jet energy loss observables. → e STARPHENIX R AA - % - % - % p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % Fig. 11. (color online) Heavy flavor decayed electron R AA for 200 GeV Au-Au collisions in comparison withPHENIX [52] and STAR [53] results. →μ ALICE p T ( GeV ) R AA - % p T ( GeV ) - % Fig. 12. (color online) Heavy flavor decayed muon R AA for 2.76 TeV Pb-Pb collisions in comparison with ALICEdata [58]. .76 TeV HF → e ALICE p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 13. (color online) Heavy flavor decayed electron R AA for 2.76 TeV Pb-Pb collisions in comparison with ALICEdata [56]. → e ALICE - p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % Fig. 14. (color online) Heavy flavor decayed electron v for 2.76 TeV Pb-Pb collisions in comparison with ALICEdata [57]. D ALICECMS R AA - % - % - % p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % Fig. 15. (color online) Prompt D meson R AA for 2.76 TeV Pb-Pb collisions in comparison with ALICE [54] andpreliminary CMS [59] results. .76 TeV D ALICE - p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % Fig. 16. (color online) D meson v for 2.76 TeV Pb-Pb collisions in comparison with ALICE data [55]. D CMS p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 17. (color online) Prompt D meson R AA for 5.02 TeV Pb-Pb collisions in comparison with preliminary CMSdata [47]. CMS p T ( GeV ) v - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 18. (color online) Prompt D meson v for 5.02 TeV Pb-Pb collisions in comparison with preliminary CMS data [46]. B + CMS p T ( GeV ) R AA - % Fig. 19. (color online) Prompt B meson R AA for 5.02 TeV Pb-Pb collisions in comparison with CMS data [60]. CUJET3 Predictions for Other Experimental Observables
In the above section we perform a successful test of the CUJET3 framework, which provides a united descriptionfor comprehensive sets of experimental data, from average suppression to azimuthal anisotropy, from light flavorto heavy flavor observables, with beam energies from 200 GeV to 5 .
02 TeV, and from central to semi-peripheralcollisions. With the new colliding system or new experimental observables, we expect more stringent tests to helpfurther constrain the CUJET3 energy loss model. In this section, we show the CUJET3 prediction for ongoingexperimental analysis, including jet quenching observables in
Xe +
Xe collisions at 5.44 TeV and more heavyflavor signals in 5.02 TeV Pb-Pb collisions. R AA in 5.44 TeV Xe-
Xe Collisions R AA - % - % - % - % ATLASALICECMSXe - Xe data
20 40 60 80 10002468 p T ( GeV ) v ( % )
20 40 60 80 100 p T ( GeV )
20 40 60 80 100 p T ( GeV )
20 40 60 80 100 p T ( GeV ) - Xe5.02TeV Pb - Pb Fig. 20. (color online) Light hadron R AA and v for 5 .
44 TeV Xe-Xe collisions (blue bands) and 5 .
02 TeV Pb-Pbcollisions (red dashed curves). Preliminary experimental data [61–63] are also shown.
Recently the LHC ran collisions with a new species of nuclei, colliding xenon with 129 nucleons (
Xe), at abeam energy of √ s NN = 5 .
44 TeV. In Xe-Xe collisions, the hot medium created is expected to be a bit cooler andshorter lived when compared with the one created in 5.02 TeV Pb-Pb collisions. Given the similar beam energy, it’sexpected that the difference between observables from these two colliding system provide valuable information onthe nature of the QGP, especially on how the hot medium interacts with high energy jets.In Fig. 20 we show the light hadron R AA and v for both systems. Higher R AA and lower v in 5 .
44 TeV Xe-Xecollisions (blue bands) are produced, compared with those in 5 .
02 TeV Pb-Pb collisions (red dashed curves). Thisindicates that the high- p T light hadrons produced in the former system are less suppressed than those produced inlatter, exhibiting the sensitivity of the jet-quenching observables to the system size and density: when comparingto those created in Pb-Pb collisions, jets created in Xe-Xe collisions travel a shorter path in the hot medium andinteract with less dense matter, hence losing less energy. With this new colliding system, we are able to furthertest the path length dependence of the CUJET3 jet energy loss model. Such predictions were made before theexperimental measurements reported at the Quark Matter 2018 conference. Our predictions are in good agreementwith the recently released preliminary data for charged hadron R AA from the ALICE [61], ATLAS [62], and CMS [63]collaborations (as shown in Fig. 20). See also Ref. [63] for a detailed data-model comparison.14 .02 TeV B → D 5.02 TeV D B + CMS p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % Fig. 21. (color online) R AA for D meson from B -decay (left), prompt D meson (middle), and B meson (right) inminimal-bias 5 .
02 TeV Pb-Pb collisions. B -decayed D Meson R AA in . TeV Pb-Pb Collisions
Another new experimental measurement is the B -decayed D meson R AA in 5 .
02 TeV Pb-Pb collisions. As shownin Fig. 21, the R AA of B -decay D meson (left panel) has similar p T -dependence as that of B mesons (right panel),and both of them are less suppressed than the prompt D meson (middle panel), especially in the region with lowermomentum ( p T <
20 GeV). We expect that the future precise measurement of B -decay D meson R AA will provideobservation of the “dead cone” effect, which suppresses the radiational energy loss of bottom jets. p T D mesons in 200 GeV Au-Au collisions Recently, the STAR Collaboration at RHIC installed the Heavy Flavor Tracker, which allows high precisionmeasurements of open heavy flavor hadrons. Early results of azimuthal anisotropy for lower p T D mesons has showninteresting properties of the low energy charm quarks [64]. With the CUJET3 predictions for D meson’s R AA and v shown in Fig. 22, precise measurements of high p T D meson jet quenching observable could enable the directcomparison with heavy flavor data, and further test the consistency of the HF sector of CUJET3 energy loss fordifferent beam energies. Finally, we show the CUJET3 predictions for heavy flavor decayed muons and electrons in Figs. 23 and 24. Beingthe decay product of both D and B mesons, the R AA in the lower p T regime is sensitive to relative ratios between D and B absolute cross sections. We expect more stringent future tests from the heavy flavor sector to help furtherconstrain CUJET3. 15 D STAR2010STAR2014 p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % D STAR p T ( GeV ) v - % p T ( GeV ) - % Fig. 22. D meson R AA and v in 200 GeV Au-Au collisions. STAR data [64–66] for lower p T range are also shown.Red (magenta) symbols labeled STAR2010 (STAR2014) correspond to data published in Ref. [65] (Ref. [66])analysis of the RHIC 2010/11 (2014) data set. →μ p T ( GeV ) R AA - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % p T ( GeV ) - % Fig. 23. R AA for heavy flavor decayed muon in 5.02 TeV Pb-Pb collisions. p T ( GeV ) R AA - % → e p T ( GeV ) v - % → e p T ( GeV ) - % Fig. 24. R AA (left) and v (right) for heavy flavor decayed muon in 5.02 TeV Pb-Pb collisions. Jet Transport Coefficient and Shear Viscosity
As discussed above, the jet quenching observables of light hadrons provide stringent constraints on values ofthe jet energy loss parameters. Furthermore, the comparison between three different schemes, (i) sQGMP- χ LT , (ii)sQGMP- χ uT , and (iii) wQGP, shows the need of chromo-magnetic-monopole degrees of freedom, robustly with respectto current theoretical uncertainties on the temperature dependence of the quark liberation rate. It is of great interestto further compare how the jet and bulk transport properties differ in these schemes, as this paves the way forclarifying the temperature dependence of jet quenching and shear viscous transport properties based on availablehigh p T data in high-energy A+A collisions.The jet transport coefficient ˆ q characterizes the averaged transverse momentum transfer squared per mean freepath [67]. For a quark jet (in the fundamental representation F) with initial energy E , we calculate its ˆ q in the sameway as the previous CUJET3.0 computation in [28, 29], viaˆ q F ( E, T ) = (cid:82) ET dq ⊥ π ( q ⊥ + f E µ ( z ))( q ⊥ + f M µ ( z )) ρ ( T ) × (cid:110) [ C qq f q + C qg f g ] · [ α s ( q ⊥ )] · [ f E q ⊥ + f E f M µ ( z )] +[ C qm (1 − f q − f g )] · [1] · [ f M q ⊥ + f E f M µ ( z )] (cid:111) , (3)and similarly for a gluon/cmm jet:ˆ q g ( E, T ) = (cid:82) ET dq ⊥ π ( q ⊥ + f E µ ( z ))( q ⊥ + f M µ ( z )) ρ ( T ) × (cid:110) [ C gq f q + C gg f g ] · [ α s ( q ⊥ )] · [ f E q ⊥ + f E f M µ ( z )] +[ C gm (1 − f q − f g )] · [1] · [ f M q ⊥ + f E f M µ ( z )] (cid:111) , (4)ˆ q m ( E, T ) = (cid:82) ET dq ⊥ π ( q ⊥ + f E µ ( z ))( q ⊥ + f M µ ( z )) ρ ( T ) × (cid:110) [ C mq f q + C mg f g ] · [1] · [ f E q ⊥ + f E f M µ ( z )] +[ C mm (1 − f q − f g )] · [ α − s ( q ⊥ )] · [ f M q ⊥ + f E f M µ ( z )] (cid:111) . (5)The quasi-parton density fractions of quark (q) or gluon (g), denoted as f q,g , are defined as f q = c q L ( T ) , f g = c g L ( T ) , (if χ LT ) f q = c q ˜ χ u ( T ) , f g = c g L ( T ) , (if χ uT ) (6)respectively for sQGMP χ LT and χ uT scheme. The magnetically charged quasi-particle density fraction is hence f m = 1 − χ T = 1 − f q − f g . The color factors are given by C qq = 49 , C gg = C mm = C gm = C mg = 94 ,C qg = C gq = C qm = C mq = 1 . (7)While switching to the wQGP scheme, by taking f q = c q , f g = c g , f E = 1 , f M = 0, turning off the cmm channel,and employing the running coupling α s ( Q ) defined in Eq.(13), the jet transport coefficient ˆ q for a quark/gluon jetdefined in Eq.(3/4) returns to that of the CUJET2.0 framework [68].Once the jet transport coefficient ˆ q has been computed, ˆ q ( T, E ) can be extrapolated down to thermal energyscales E ∼ T / η/s , based on kinetic theory in a17 .2 0.3 0.4 0.5 0.6051015202530 T ( GeV ) q F / T wQGP s QG M P SYM - LOSYM - NLO ( a ) E = ( GeV ) q F / T solid: χ TL dashed: χ Tu ( b ) E = SYM - NLO T ( GeV ) η / s wQGPsQGMP SYM ( GeV ) ρ q , g , m / ρ solid: χ TL dashed: χ Tu qgm Fig. 25. (Color online) (Left) Temperature dependence of the dimensionless jet transport coefficient ˆ q F /T fora light quark jet with initial energy E = (a) 30GeV, (b) 3GeV in CUJET framework with three schemes: (i)sQGMP- χ LT scheme (red solid curve), (ii) sQGMP- χ uT scheme (red dashed curve), and (iii) wQGP/CUJET2.0scheme (green dotted-dashed curve). N = 4 leading order/next to leading order Super Yang-Mills ˆ q SY M − LO /T = π / Γ( )Γ( ) √ λ and ˆ q SY M − NLO /T = π / Γ( )Γ( ) √ λ (1 − . √ λ ) respectively [17] with coupling λ = 4 π · · .
31, are plottedfor comparison. Green blobs in inset (b) shows the JET collaboration [67] model average of ˆ q F /T while boxesrepresent uncertainties. (Right) Shear viscosity to entropy density ratio η/s estimated with scheme (i) (red solidcurve), (ii) (red dashed curve), and (iii) (green dotted-dashed curve). The inset shows quasi-particle number densityfraction of q, g, m in liberation scheme χ LT (solid curve) and χ uT (dashed curve). weakly-coupled quasi-particle scenario [69–71]. An estimate of η/s can be derived as η/s = 1 s (cid:88) a ρ a (cid:104) p (cid:105) a λ ⊥ a = 4 T s (cid:88) a ρ a (cid:32)(cid:88) b ρ b (cid:90) (cid:104)S ab (cid:105) / dq ⊥ q ⊥ (cid:104)S ab (cid:105) dσ ab dq ⊥ (cid:33) − = 18 T s (cid:88) a ρ a / ˆ q a ( T, E = 3
T / . (8)The ρ a ( T ) ≡ f a ρ ( T ) is the quasi-parton density of type a = q, g, m . The mean thermal Mandelstam variable (cid:104)S ab (cid:105) ∼ T . Clearly the η/s of the system is dominated by the ingredient which has the largest ρ a / ˆ q a .In the left panel of Fig. 25, we show the temperature dependence of the dimensionless jet transport coefficientˆ q F /T for a light quark jet with initial energy E = 30GeV / 3GeV with all three schemes. Corresponding resultsfrom JET collaboration [67] model average and AdS/CFT limit [17] are also plotted for comparisons. As discussedin previous CUJET3.0 papers [28, 29], the near- T c enhancement of dimensionless jet transport coefficient can beobserved with robust dependence on quark liberation schemes.In the right panel of Fig. 25, we show the shear viscosity to entropy density ratio η/s estimated by kinetic theoryusing the ˆ q extrapolation Eq. (8) with schemes (i) (red solid curve), (ii) (red dashed curve), and (iii) (green dotted-dashed curve). The inset shows the quasi-particle number density fraction of q, g, and m in the liberation scheme χ LT (solid curve) and χ uT (dashed curve). In the near T c regime, in the χ uT scheme, the total η/s is dominated by q,while in the χ LT “slow” quark liberation scheme the total η/s is dominated by m. For each sQGMP scheme, there isa clear η/s minimum at T ∼
210 MeV, which is comparable with the SYM limit ( η/s ) min = 1 / π . In this study, we presented the CUJET3.1 framework and performed a global quantitative χ analysis by com-parsion with a large set of light hadron jet quenching observables for central and semi-central heavy-ion collisions18or beam energies √ s NN = 200 GeV(Au-Au), 2.76 TeV(Pb-Pb), and 5.02 TeV(Pb-Pb). This analysis allows theoptimization of the two key parameters in the CUJET3.1 framework, and the global χ is found to be minimized tonear unity for α c ≈ . ± .
1, and c m ≈ . ± .
03. With such parameters, the CUJET3 framework gives a unified,systematic and successful description of a comprehensive set of available data, from average suppression to azimuthalanisotropy, from light to heavy flavors, and from central to semi-peripheral collisions for all three colliding systems.Thus, CUJET3.1 provides a non-perturbative solution to the long standing hard ( R AA and v ) versus soft “perfectfluidity” puzzle. Such a quantitative analysis strongly supports the necessity of including the interaction between jetand chromo-magnetic-monopoles to provide a consistent description of both R AA and v across centrality and beamenergy.In this work, we also present CUJET3 predictions for a number of observables for additional tests. We expectthat the comparison between the light hadron R AA in 5.44 TeV Xe-Xe collisions and those observed in 5.02 TeVPb-Pb collisions, will further test the path length dependence of the CUJET3 jet energy loss model. The massdependence of the jet energy loss in CUJET3 can also be further tested by its predictions for B -decayed D meson R AA in 5.02 TeV Pb-Pb collisions, to be compared with future precise measurement of this observable.Finally, we emphasize the important theoretical advantage of the CUJET3.1 framework. It is not only χ con-sistent with soft and hard observables data at RHIC and LHC, but also with non-perturbative lattice QCD data.Remarkably, estimates from this framework lead to a shear viscosity to entropy density ratio ηs ∼ .
1, which are notonly consistent with the extracted values from experimental soft + hard A + A phenomenology, but also theoreti-cally internally consistent with the sQGMP kinetic theory link, ηs ∼ T ˆ q F ( E → T,T ) , between long distance collective fluidproperties and short distance jet quenching physics especially near T c . The authors are particularly grateful to Jiechen Xu for major contributions in establishing the CUJET3 frame-work. SS and JL are partly supported by the National Science Foundation under Grant No. PHY-1352368. MGacknowledges support from IOPP of CCNU, Wuhan China. The computations in this study were performed on IU’sBig Red II clusters, that are supported in part by Lilly Endowment, Inc., through its support for the Indiana UniversityPervasive Technology Institute, and in part by the Indiana METACyt Initiative. The Indiana METACyt Initiativeat IU was also supported in part by Lilly Endowment, Inc.
A CUJET3 Framework
The CUJET3 model is a jet energy loss simulation framework built on a non-perturbative microscopic model forhot medium as semi-quark-gluon-monopole plasma (sQGMP), which integrates two essential elements of confinement,i.e. the suppression of quarks/gluons and emergent magnetic monopoles. A detailed description of its frameworkcan be found in previously published CUJET studies [9, 28, 29, 67, 68]. The CUJET3 model employs the TG elasticenergy loss formula [72–74] for collisional processes, with the energy loss given by dE ( z ) dτ = − C R π [ α s ( µ ( z )) α s (6 E ( z )Γ( z ) T ( z ))] T ( z ) (cid:16) N f (cid:17) × log T ( z ) (cid:112) E ( z ) Γ( z ) − M (cid:16) E ( z )Γ( z ) − (cid:112) E ( z ) Γ( z ) − M + 6 T ( z ) (cid:17) µ ( z ) , (9)and the average number of collisions¯ N c = (cid:90) τ max dτ (cid:20) α ( µ ( z )) α (6 E ( z )Γ( z ) T ( z )) µ ( z ) (cid:21) (cid:20) Γ( z ) γ f ζ (3) π (4 + N f ) T ( z ) (cid:21) , (10)where the E ( z ) integral equation is solved recursively. For radiational processes, the CUJET3 model employsthe dynamical DGLV opacity expansion theory [1, 3, 6, 75] with the Liao–Shuryak chromo-magnetic-monopole19cenario [76–80]. The inclusive single gluon emission spectrum at n = 1 opacity series reads: x E dN n =1 g dx E = 18 C R π N f
16 + 9 N f (cid:90) dτ ρ ( z )Γ( z ) (cid:90) d k ⊥ α s (cid:16) k ⊥ x + (1 − x + ) (cid:17) × (cid:90) d q α s ( q ⊥ ) (cid:16) f E + f E f M µ ( z ) q ⊥ (cid:17) χ T + (cid:16) f M + f E f M µ ( z ) q ⊥ (cid:17) (1 − χ T )( q ⊥ + f E µ ( z ))( q ⊥ + f M µ ( z )) × − k ⊥ − q ⊥ )( k ⊥ − q ⊥ ) + χ ( z ) (cid:20) k ⊥ k ⊥ + χ ( z ) − ( k ⊥ − q ⊥ )( k ⊥ − q ⊥ ) + χ ( z ) (cid:21) × (cid:20) − cos (cid:16) ( k ⊥ − q ⊥ ) + χ ( z )2 x + E τ (cid:17)(cid:21) (cid:18) x E x + (cid:19) (cid:12)(cid:12)(cid:12)(cid:12) dx + dx E (cid:12)(cid:12)(cid:12)(cid:12) . (11) C R = 4 / z = (cid:16) x + τ cos φ, y + τ sin φ ; τ (cid:17) ; E is the energy of the hard parton in the lab frame; k ⊥ ( | k ⊥ | ≤ x E E · Γ( z ))and q ⊥ ( | q ⊥ | ≤ T ( z ) E · Γ( z )) are the local transverse momentum of the radiated gluon and the local transversemomentum transfer, respectively. The gluon fractional energy x E and fractional plus-momentum x + are connectedby x + ( x E ) = x E [1 + (cid:112) − ( k ⊥ /x E E ) ] /
2. We note that in the temperature range T ∼ T c , the coupling α s becomesnon-perturbative [76, 78, 81, 82]. Analysis of lattice data [78] suggests the following thermal running coupling form: α s ( Q ) = α c α c π log( Q T c ) , (12)with T c = 160 MeV. Note that at large Q , Eq. (12) converges to vacuum running α s ( Q ) = π Q / Λ ) , while at Q = T c , α s ( T c ) = α c .The particle number density ρ ( z ) is determined by the medium temperature T ( z ) via ρ ( T ) = ξ s s ( T ), where ξ s = 0 .
253 for N c = 3, N f = 2 . s ( T ) is the bulk entropy density. In the presence ofhydrodynamical four-velocity fields u µf ( z ), boosting back to the lab frame, a relativistic correction Γ( z ) = u µf n µ should be taken into account [18, 83], where the flow four-velocity u µf = γ f (1 , (cid:126)β f ) and null hard parton four-velocity n µ = (1 , (cid:126)β j ). The bulk evolution profiles ( T ( z ) , ρ ( z ) , u µf ( z )) are generated from the VISH2+1 code [22, 84, 85]with event-averaged Monte-Carlo Glauber initial condition, τ = 0 . η/s = 0 .
08, and Cooper-Frye freeze-out temperature 120 MeV [30, 86–90]. Event-averaged smooth profiles areembedded, and the path integrations (cid:82) dτ for jets initially produced at transverse coordinates ( x , φ ) are cut-off atdynamical T ( z ( x , φ, τ )) | τ max ≡ T cut = 160 MeV hyper-surfaces [68].In the CUJET2 framework, assuming weakly-coupling QGP, the running coupling takes the form (with Λ QCD =200 MeV) α s ( Q ) = α max if Q ≤ Q min , π Q / Λ QCD ) if
Q > Q min . (13)The Debye screening mass µ ( z ) is determined from solving the self-consistent equation µ ( z ) = (cid:112) πα s ( µ ( z )) T ( z ) (cid:113) N f / χ ( z ) = M x + m g ( z )(1 − x + ) regulates the soft collinear divergences in the color antennae and controlsthe Landau-Pomeranchuk-Migdal (LPM) phase, the gluon plasmon mass m g ( z ) = f E µ ( z ) / √ T c , the total quasi-particle numberdensity ρ is divided into EQPs with fraction χ T = ρ E /ρ and MQPs with fraction 1 − χ T = ρ M /ρ . The parameter f E and f M is defined via f E ≡ µ E /µ and f M ≡ µ M /µ , with µ E and µ M being the electric and magnetic screening mass,respectively, following f E ( T ( z ))) = (cid:112) χ T ( T ( z )) , f M ( T ( z )) = c m g ( T ( z )) , (15)with the local electric “coupling” g ( T ( z )) = (cid:112) πα s ( µ ( T ( z ))).20n current sQGMP modeling, the cec component fraction χ T remains a theoretical uncertainty related to thequestion of how fast the color degrees of freedom get liberated. To estimate χ T , one notices that: (1) when tem-perature is high, χ T should reach unity, i.e. χ T ( T (cid:29) T c ) →
1; (2) in the vicinity of the regime T ∼ (1 − T c , therenormalized expectation value of the Polyakov loop L (let us redefine L ≡ (cid:96) = (cid:104) tr P exp { ig (cid:82) /T dτ A }(cid:105) /N c ) deviatessignificantly from unity, implying the suppression ∼ L for quarks and ∼ L for gluons in the semi-QGP model [92–95].Consequently, in the liberation scheme ( χ LT -scheme), we define the cec component fraction as χ T ( T ) ≡ χ LT ( T ) = c q L ( T ) + c g L ( T ) (16)for the respective fraction of quarks and gluons, where we take the Stefan-Boltzmann (SB) fraction coefficients, c q =(10 . N f ) / (10 . N f +16) and c g = 16 / (10 . N f +16), and the temperature dependent Polyakov loop L ( T ) parameterizedas ( T in GeV) L ( T ) = (cid:20)
12 + 12 Tanh[7 . T − . (cid:21) , (17)adequately fitting both the HotQCD [96] and Wuppertal-Budapest [97] lattice results.On the other hand, another useful measure of the non-perturbative suppression of the color electric DOF isprovided by the quark number susceptibilities [98–101]. The diagonal susceptibility is proposed as part of the orderparameter for chiral symmetry breaking/restoration in [98], and plays a similar role as properly renormalized L for quark DOFs. In this scheme, we parametrize the lattice diagonal susceptibility of u quark number density,renormalizing the susceptibility by its value at T → ∞ , as ( T in GeV)˜ χ u ( T ) ≡ χ u ( T )0 .
91 = (cid:20) { . T − . } (cid:21) , (18)and define the cec component fraction in the deconfinement scheme ( χ uT -scheme) as: χ T ( T ) ≡ χ uT ( T ) = c q ˜ χ u ( T ) + c g L ( T ) . (19)These two different schemes, for the rate of “quark liberation”, with χ LT the “slow” and χ uT the “fast”, provide usefulestimates of theoretical systematic uncertainties associated with the quark component of the sQGMP model. - - - - N ev - E p d N / d p ( G e V - ) + p h ± CMS
10 10020 50 2000.91.01.1 p T ( GeV ) ex p . / t h e o . Fig. 26. (color online) Comparison between initial unquenched invariant momentum distribution of charged hadron,predicted using CTEQ5 [102] PDF and KKP fragmentation [103], and 5.02 TeV CMS data within | η | < p + p spectra of light quarks and gluons are generated by LO pQCD [102]calculations with CTEQ5 Parton Distribution Functions (PDF); while those of charm and bottom quarks are gener-ated from the FONLL calculation [104] with CTEQ6M Parton Distribution Functions. In the meantime, the spectraof light hadrons are computed with KKP Fragmentation Functions [103]; and those of open heavy flavor mesons arecomputed with Peterson Fragmentation Functions [105] (taking (cid:15) = 0 .
06 for D meson, and (cid:15) = 0 .
006 for B meson).The decay of heavy flavor mesons into leptons, including D → (cid:96) , B → (cid:96) , and B → D → (cid:96) channels, follows the sameparameterization as in [104]. Comparison between theory predictions and experimental measurements on the initialunquenched invariant p + p → h ± + X distribution in shown in the right panel of Fig. 26, for 5 .
02 TeV collisions, andin a previous CUJET3.0 study [29].
B Improvements in CUJET3.1
In this Appendix, we discuss the improvements of the CUJET3.1 framework with respect to the earlier CUJET3.0framework version. One important motivation for the CUJET3.1 upgrade reported in the present paper was touncover causes and correct the discrepancy of CUJET3.0 predictions for LHC 5 .
02 ATeV Pb + Pb collusions,reported by CMS in Ref. [33] with the nuclear modification factor R AA (see Fig. 27), as well as in Ref. [34] with theirobserved p T and especially the centrality dependence of the hard elliptic asymmetry v (see Fig. 28). (GeV) T p AA R WA98 (0-7%) p NA49 (0-5%) – p PHENIX (0-5%) p STAR (0-5%) – hALICE (0-5%)ATLAS (0-5%)CMS (0-5%)SPS 17.3 GeV (PbPb)RHIC 200 GeV (AuAu)LHC 2.76 TeV (PbPb) CMS (0-5%) (0-10%) G SCETHybrid Model (0-10%)Bianchi et al. (0-10%), 0-5%) p + – CUJET 3.0 (hs et al. (0-5%)eAndrv-USPhydro+BBMG (0-5%)LHC 5.02 TeV (PbPb)Models 5.02 TeV (PbPb)
SPS RHIC LHC (5.02 TeV PbPb) -1 b m (5.02 TeV pp) + 404 -1 CMS
CMS (0-5%) (0-10%) G SCETHybrid Model (0-10%)Bianchi et al. (0-10%), 0-5%) p + – CUJET 3.0 (hs et al. (0-5%)eAndrv-USPhydro+BBMG (0-5%)LHC 5.02 TeV (PbPb)Models 5.02 TeV (PbPb)
Fig. 27. (color online) Reproduced from Fig. 5 of CMS Ref. [33] (with permission): R AA results as a function of p T in (0 – 5)% centrality class. Vertical bars (shaded boxes) represent statistical (systematic) uncertainties. Bluecurve represents calculation made with CUJET3.0 [29]s. After a systematic examination, we found and corrected two issues in previous CUJET3.0 simulations for5.02 ATeV Pb + Pb collisions. (i) First, the initial parton spectra were not consistently read in: the flavor fac-tor of 3 was missed for light quark spectra. Resultabtly, a higher fraction of the final hadrons were fragmented fromgluon jets, which are more quenched relative to quark jets and caused the over-quenched R AA . (ii) Second, the prob-ability distribution of initial jet production was incorrectly oriented (with x - and y -axis switched), and consequentlywrong centrality dependence of v was predicted. By correcting these two issues, the CUJET3.1 simulation correctlyreproduces the p T and centrality dependence of both R AA and v . Details of the comparison are shown in Figs. 9and 10 in Sec. . References (GeV/c) T p
20 40 60 80 n v CMS {SP} v {SP} v CUJET3.0 v SHEE, lin. v SHEE, lin. v (GeV/c) T p
20 40 60 80 n v (GeV/c) T p
20 40 60 80 n v Centrality: 0-5% (GeV/c) T p
20 40 60 80 n v (GeV/c) T p
20 40 60 80 n v (GeV/c) T p
20 40 60 80 n v (GeV/c) T p
20 40 60 80 n v (5.02 TeV PbPb) -1 b m (GeV/c) T p
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