Bulk observables at 5.02 TeV using quasiparticle anisotropic hydrodynamics
BBulk observables at 5.02 TeV using quasiparticle anisotropic hydrodynamics
Mubarak Alqahtani
Department of Basic Sciences, College of Education, Imam Abdulrahman Bin Faisal University, Dammam 34212, Saudi Arabia
Michael Strickland
Department of Physics, Kent State University, Kent, OH 44242 United States
Abstract
We present comparisons between 3+1D quasiparticle anisotropic hydrodynamics (aHydroQP) predictions for a large setof bulk observables and experimental data collected in 5.02 TeV Pb-Pb collisions. We make aHydroQP predictions foridentified hadron spectra, identified hadron average transverse momentum, charged particle multiplicity as a functionof pseudorapidity, the kaon-to-pion (
K/π ) and proton-to-pion ( p/π ) ratios, and integrated elliptic flow. We compare todata collected by the ALICE collaboration in 5.02 TeV Pb-Pb collisions. We find that these bulk observables are quitewell described by aHydroQP with an assumed initial central temperature of T = 630 MeV at τ = 0 .
25 fm/c and aconstant specific shear viscosity of η/s = 0 .
159 and a peak specific bulk viscosity of ζ/s = 0 . K/π ) and proton-to-pion ( p/π ) ratios reported recently by theALICE collaboration are extremely well described by aHydroQP in the most central collisions.
Keywords:
Quark-gluon plasma, Relativistic heavy-ion collisions, Anisotropic hydrodynamics, Quasiparticle equationof state, Boltzmann equation
1. Introduction
At high-temperatures one expects hadronic matter toundergo a phase transition to a quark-gluon plasma (QGP)in which the appropriate degrees of freedom are quarksand gluons rather than hadrons. The phase transitionfrom hadronic matter to QGP is associated with boththe restoration of chiral symmetry and deconfinement ofthe quarks and gluons. Direct numerical calculations ofthe QGP phase transition temperature using lattice QCDhave found that the transition is a smooth crossover witha crossover temperature of T c ∼
155 MeV [1, 2]. To pro-duce the QGP in the lab, experimentalists at the Rela-tivistic Heavy Ion Collider (RHIC) and the Large HadronCollider (LHC) collide ultrarelativistic nuclei in order tocreate a short-lived QGP with a lifetime on the order of 12fm/c in central 5.02.TeV Pb-Pb collisions. Analysis of thedata produced in the last decades has shown that manyaspects of the collective behavior observed in high-energyheavy-ion collisions are well-described by relativistic vis-cous hydrodynamics with an equation of state that takesinto account the transition between hadronic and partonicdegrees of freedom [3–9].In viscous hydrodynamics approaches one typically startsfrom the assumption that the non-equilibrium correctionsto the dynamics, e.g. shear and bulk viscous tensors,are small relative to the equilibrium contributions to theenergy-momentum tensor. One of the challenges such ap-proaches face is that at early times, τ <
Preprint submitted to Physics Letters B August 19, 2020 a r X i v : . [ nu c l - t h ] A ug amics framework proposed in Refs. [14, 15] has been ex-tended to full 3+1-dimensional (3+1D) hydrodynamics in-cluding a realistic equation of state taken from latticeQCD calculations. In addition, both shear and bulk vis-couse correction plus an infinite set of implicit higher-ordertransport coefficients are included, as there is no trunca-tion in inverse Reynolds number [30–47] (for a recent re-view, see Ref. [48]). In Refs. [46, 47, 49–52] the resulting3+1D quasiparticle anisotropic hydrodynamics code (aHy-droQP) was used to make model to data comparisons for2.76 TeV Pb-Pb collisions and 200 GeV Au-Au collisions.These prior studies found quite good agreement betweenaHydroQP and many heavy-ion observables such as theidentified hadron spectra, mean transverse momentum ofidentified hadrons, multiplicities, the elliptic flow, and theHBT radii. For all of these observables, the aHydroQPmodel was able to describe the data quite reasonably overa broad range of centrality bins.In this work, we continue our comparisons with heavy-ion experimental data, this time for 5.02 TeV collisions.We present predictions for identified hadron spectra andtheir ratios, the charged particle multiplicity, identifiedhadron average transverse momentum, and integrated el-liptic flow. We compare our aHydroQP predictions withdata collected by the ALICE experiment and find thatthe agreement with data is quite good. In particular, wefind that the momentum dependence of the kaon-to-pion( K/π ) and proton-to-pion ( p/π ) ratios reported recentlyby the ALICE collaboration are extremely well describedby aHydroQP in 0-5% centrality collisions out to trans-verse momentum of 2.5 GeV. The resulting initial tem-perature extracted for the QGP in 5.02 TeV collisions is T = 630 MeV at τ = 0 .
25 fm/c and the specific shearviscosity found to give best agreement with the data is η/s = 0 . ζ/s = 0 . R AA and el-liptic flow v of bottomonium states in 5.02 TeV Pb-Pbcollisions [53, 54].The structure of our paper is as follows. In Sec. 2,we review the basics of the 3+1D quasiparticle anisotropichydrodynamics model. In Sec. 3, we present the predic-tions of the aHydroQP model for 5.02 TeV collisions andcompare them to experimental data for many heavy-ionobservables. Sec. 4 contains our conclusions and an out-look for the future.
2. Model
The evolution of the medium is performed using thefirst and second moments of Boltzmann equation for a sys- tem with temperature-dependent quasiparticle masses [40] p µ ∂ µ f ( x, p ) + 12 ∂ i m ∂ i ( p ) f ( x, p ) = − C [ f ( x, p )] . (1)The first and second moments of Eq. (1) give ∂ µ T µν = 0 , (2) ∂ α I ανλ − J ( ν ∂ λ ) m = − (cid:90) dP p ν p λ C [ f ] , (3)where J µ = (cid:90) dP p µ f , (4) T µν = (cid:90) dP p µ p ν f , (5)and I µνλ = (cid:90) dP p µ p ν p λ f , (6)with (cid:82) dP = N dof (cid:82) d p (2 π ) E being the Lorentz invariantintegration measure.In the aHydroQP approach, the mass is a function oftemperature which can be obtained from lattice QCD cal-culations of the entropy density in order to enforce a realis-tic equation of state [40]. The collisional kernel C [ f ( x, p )]in aHydroQP is taken in the relaxation-time approxima-tion (RTA). C [ f ] = − p · uτ eq ( T ) [ f − f eq ( T )] , (7)where u µ is the four-velocity of the fluid local rest frameand τ eq ( T ) is the temperature- (and hence time-) depen-dent relaxation time [40].We obtain the necessary dynamical equations by tak-ing projections of the Boltzmann equation. For this pur-pose, one needs to first specify the form of the underlyingone-particle distribution function. In aHydroQP, the dis-tribution function is taken to be anisotropic in momentumspace, with only diagonal momemtum-space anisotropyparameters, and having the form f ( x, p ) = f eq (cid:32) λ (cid:115)(cid:88) i p i α i + m (cid:33) . (8)This distribution function reduces back to an equilibriumdistribution function with temperature T when α i = 1and λ = T. For details of the derivation of the dynamicalequations for aHydroQP we refer readers to Refs. [36, 40,43, 48].Using the aHydroQP dynamical equations we allow thesystem to evolve until reaching the freeze-out temperature T FO = 130 MeV where a hypersurface is constructed ata constant energy-density. On this hypersurface we con-vert the underlying hydrodynamic evolution results for theflow velocity, the anisotropy parameters, and the scale λ into explicit ‘primioridial’ hadronic distribution functions2 + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE ( / π p T ) d N / dp T [ G e V - ] ( a ) - % π + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE ( b ) - % π + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE ( / π p T ) d N / dp T [ G e V - ] ( c ) - % π + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE ( d ) - % π + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE p T [ GeV ] ( / π p T ) d N / dp T [ G e V - ] ( e ) - % π + + π - - aHydro K + + K - - aHydrop + p - aHydro π + + π - - ALICE K + + K - - ALICEp + p - ALICE p T [ GeV ] ( f ) - % Figure 1: Combined transverse momentum spectra of pions, kaons and protons for 5.02 TeV Pb-Pb collisions in different centrality classes.The solid lines are the predictions of 3+1D aHydroQP and the points are experimental results from the ALICE Collaboration [55]. using a generalized Cooper-Frye prescription [48]. For thispurpose, we use a customized version of THERMINATOR2 [56] to perform the production and necessary decay(s)of the primordial hadrons. Both the aHydroQP and modi-fied THERMINATOR 2a codes are publicly available [57].Note that the freeze-out temperature used herein and allother parameters besides T and η/s were assumed to bethe same as in our prior 2.76 TeV study [46, 47]. Simi-larly, in order to have a meaningful comparison to resultsobtained previously at 200 GeV and 2.76 TeV, we usesmooth Glauber type initial conditions with the centralenergy density scaling with the nuclear overlap profile.
3. Results
In this section, we present comparisons of aHydroQPpredictions with 5.02 TeV Pb-Pb collision data collectedby the ALICE collaboration. We consider only two freeparameters, the initial central temperature T and the spe-cific shear viscosity η/s . We fix these two parameters byfitting the spectra of pions, kaons, and protons in both Note that aHydroQP also includes bulk viscous effects,however, within the relaxation time approximation, the bulkviscosity as a function of temperature is fixed once one speci-fies the shear viscosity [40, 46, 47]. - % - aHydro p T [ GeV ] ( K + + K - ) / ( π + + π - ) - % - ALICE p T [ GeV ] ( p + + p - ) / ( π + + π - ) - % - aHydro p T [ GeV ] ( K + + K - ) / ( π + + π - ) - % - ALICE p T [ GeV ] ( p + + p - ) / ( π + + π - ) - % - aHydro p T [ GeV ] ( K + + K - ) / ( π + + π - ) - % - ALICE p T [ GeV ] ( p + + p - ) / ( π + + π - ) Figure 2: The
K/π (left) and p/π (right) ratios as a function of p T measured in Pb-Pb collisions at 5.02 TeV in different centrality classes.Solid lines are predictions of aHydroQP model where symbols with error bars are experimental data from Ref. [55]. the 0-5% and 30-40% centrality classes. The parametersobtained from the spectra fit were: T = 630 MeV and η/s = 0 . T = 600 MeV, by 5% [47].The best fit value for η/s is the same as was found at 2.76TeV [47].We begin by presenting aHydroQP predictions for thetransverse momentum distribution of identified hadronsin 5.02 TeV Pb-Pb collisions. We will compare our aHy-droQP predictions with experimental data from the AL-ICE collaboration [55, 60]. In Fig. 1, we show the com-bined spectra of pions, kaons, and protons as a function oftransverse momentum in six different centrality classes. Inmore central collisions, aHydroQP shows very good agree-ment with the data as shown in Fig. 1a. On the other hand, for more peripheral collisions the agreement is goodonly for p T (cid:46) K/π (left column) and p/π (right column)ratios are shown as a function of p T in three different cen-trality classes and once again compared to experimentaldata. The agreement between aHydroQP and the data at p T (cid:46) K/π ratio, the agreement be-tween aHydroQP and the data extends up to p T ∼ . p/π is extends up to p T ∼ . K/π and p/π rations as afunction of centrality are shown in Fig. 3, in the left andright panels, respectively. In both panels, we see that aHy-droQP is able to describe the ratios reported by the ALICEcollaboration well over a broad range of centralities.4
LICE aHydro
Centrality (%) ( K + + K - ) / ( π + + π - ) ALICE aHydro
Centrality (%) ( p + + p - ) / ( π + + π - ) Figure 3: Transverse-momentum integrated
K/π (left) and p/π (right) ratios as a function of centrality measured in Pb-Pb collisions at 5.02TeV. Solid lines are predictions of aHydroQP model where symbols with error bars are experimental data from Ref. [55]. - - - η d N / d η ( a ) - - - η ( b ) Figure 4: The charged-particle pseudorapidity density in Pb-Pb collisions at 5.02 TeV obtained by aHydroQP model (solid lines) as afunction of pseudorapidity η . Different centrality classes are shown in both panels (a) and (b) starting from more central 0-5% (blue) to moreperipheral 80-90% (green). Data are from ALICE Collaboration Ref. [58]. In Fig. 4, we present the aHydroQP prediction for thecharged-particle pseudorapidity density in Pb-Pb collisionsat 5.02 TeV along with data provided by the ALICE col-laboration [58] . In all centrality bins shown, aHydroQPdescribes the data quite well over a broad range of pseu-dorapidity. At high rapidities we notice some differencesfrom the data where there are indicates of a more slowdecrease. This was not the case at 2.76 TeV where, inthe most central class, the agreement between aHydroQPand experimental data extended out to | η | ∼
5. Overall,however, we see good agreement at central rapidities in allcentrality classes considered in Fig. 4.Next we turn to the left panel of Fig. 5 in which presentaHydroQP predictions for the mean transverse momentum (cid:104) p T (cid:105) of pions, kaons and protons. The aHydroQP resultsare compared to experimental data from the ALICE col-laboration [55]. For both pions and kaons, we see goodagreement between aHydroQP and the experimental dataat all centralities, however, aHydroQP seems to underes-timate the mean p T for protons. We have no immediateexplanation for why there is such a discrepancy, but we donote that a similar discrepancy exists in state-of-the-art second-order viscous hydrodynamics calculations [61].Finally, in Fig. 5 (right panel), we present the aHy-droQP predictions for the integrated flow as a functionof centrality. Since we used smooth initial conditions,the event plane is known and we computed v using the (cid:104) cos(2 φ ) (cid:105) for all hadrons. The aHydroQP predictions arecompared to ALICE data for v { } and v { } reportedin Ref. [59]. As can be seen from this comparison, theaHydroQP predictions agree well with the experimentallymeasured v { } in the most central bins ( < v { } at higher centralities.
4. Conclusions and outlook
In this work, we continued our comparisons of aHy-droQP with experimental data. In the past, we presentedcomparisons with data at 2.76 TeV Pb-Pb collisions [46,47] and 200 GeV Au-Au collisions [49, 52]. Herein we madetheory to data comparisons between aHydroQP and datacollected by the ALICE collaboration using 5.02 TeV Pb-Pb collisions. We presented aHydroQP predictions for alarge set of bulk observables and found quite reasonable5
10 20 30 40 500.40.60.81.01.21.41.6
Centrality (%) 〈 p T 〉 [ G e V ] π + + π - K + + K - p + p aHydro v { } - ALICEv { } - ALICE
Centrality (%) v c hg Figure 5: In panel (a), identified particle mean transverse momentum vs. centrality is shown in 5.02 TeV Pb+Pb collisions where data arefrom ALICE Collaboration Ref. [55], while in panel (b), the centrality dependence of the elliptic flow v of charged particles in 5.02 TeVPb-Pb collisions is shown where data are from Ref. [59]. agreement with experimental data using a central temper-ature of T = 630 MeV at τ = 0 .
25 fm/c and a specificshear viscosity of η/s = 0 . T and η/s were assumed to be the same.We made aHydroQP predictions for identified hadronspectra, identified hadron average transverse momentum,charged particle multiplicity as a function of rapidity, thekaon-to-pion ( K/π ) and proton-to-pion ( p/π ) ratios, andintegrated elliptic flow. In all of these comparisons, aHy-droQP was quite successful in describing the experimen-tal data in 5.02 TeV Pb-Pb collisions. In particular, wefind that the momentum dependence of the kaon-to-pion(
K/π ) and proton-to-pion ( p/π ) ratios reported recentlyby the ALICE collaboration are extremely well describedby aHydroQP in the most central collisions. In a followuppaper, due to the increased statistics required, we intend topresent aHydroQP predictions for Hanbury Brown-Twissradii and compare aHydroQP predictions for the identi-fied hadron elliptic flow for pions, kaons, and protons withexperimental data [62].We note, in closing, that the the initial state model(Glauber model) and assumed collision kernel (RTA) usedherein are rather simple. As a result of the smooth initialcondition assumed, we do not correctly reproduce the v chg2 in the most central collisions. The aHydroQP code allowsfor fluctuating initial conditions and we plan to report onthe results of such simulations in a forthcoming paper. Oneof the challenges with using, e.g. IPGlasma-type, fluctu-ating initial conditions is that these types of initial con-ditions can possess large numbers of cells in which thereare negative total pressures in the local rest frame, whichis incompatible with the kinetic-theory based assumptionsunderpinning aHydroQP. With respect to the collision ker-nel, a framework for including realistic collisional kernelsin the aHydro framework was introduced in Refs. [63, 64].It will be interesting to see if aHydroQP results are sensi- tive to the choice of the collisional kernel.Finally, we mention that another assumption madeherein was that the anisotropy tensor is diagonal in thelocal-rest frame. Although this is justified by the smallnessof the off-diagonal contributions, it is desirable to have acomplete treatment which includes the off-diagonal contri-butions in a non-perturbative manner. Such a scheme wasintroduced in Ref. [65] and is currently being implemented. Acknowledgments
M. Alqahtani is supported by the Deanship of Scien-tific Research at the Imam Abdulrahman Bin Faisal Uni-versity under grant number 2020-080-CED. M. Stricklandwas supported by the U.S. Department of Energy, Office ofScience, Office of Nuclear Physics under Award No. DE-SC0013470. This research in part utilized Imam Abdul-rahman Bin Faisal (IAU)’s Bridge HPC facility, supportedby IAU Scientific and High Performance Computing Cen-ter [66].
References [1] A. Bazavov, An overview of (selected) recent results in finite-temperature lattice QCD, J. Phys. Conf. Ser. 446 (2013) 012011. arXiv:1303.6294 , doi:10.1088/1742-6596/446/1/012011 .[2] S. Borsanyi, Frontiers of finite temperature lattice QCD, EPJWeb Conf. 137 (2017) 01006. arXiv:1612.06755 , doi:10.1051/epjconf/201713701006 .[3] P. Huovinen, P. Kolb, U. W. Heinz, P. Ruuskanen, S. Voloshin,Radial and elliptic flow at RHIC: Further predictions, Phys.Lett. B 503 (2001) 58–64. arXiv:hep-ph/0101136 , doi:10.1016/S0370-2693(01)00219-2 .[4] P. Romatschke, U. Romatschke, Viscosity Information fromRelativistic Nuclear Collisions: How Perfect is the Fluid Ob-served at RHIC?, Phys. Rev. Lett. 99 (2007) 172301. arXiv:0706.1522 , doi:10.1103/PhysRevLett.99.172301 .[5] S. Ryu, J. F. Paquet, C. Shen, G. Denicol, B. Schenke, S. Jeon,C. Gale, Importance of the Bulk Viscosity of QCD in Ul-trarelativistic Heavy-Ion Collisions, Phys. Rev. Lett. 115 (13)(2015) 132301. arXiv:1502.01675 , doi:10.1103/PhysRevLett.115.132301 .
6] H. Niemi, G. S. Denicol, P. Huovinen, E. Molnar, D. H.Rischke, Influence of the shear viscosity of the quark-gluonplasma on elliptic flow in ultrarelativistic heavy-ion collisions,Phys. Rev. Lett. 106 (2011) 212302. arXiv:1101.2442 , doi:10.1103/PhysRevLett.106.212302 .[7] R. Averbeck, J. W. Harris, B. Schenke, Heavy-Ion Physics at theLHC, 2015, pp. 355–420. doi:10.1007/978-3-319-15001-7\_9 .[8] S. Jeon, U. Heinz, Introduction to Hydrodynamics, 2016, pp.131–187. doi:10.1142/9789814663717\_0003 .[9] P. Romatschke, U. Romatschke, Relativistic Fluid DynamicsIn and Out of Equilibrium, Cambridge Monographs on Math-ematical Physics, Cambridge University Press, 2019. arXiv:1712.05815 , doi:10.1017/9781108651998 .[10] M. Strickland, Anisotropic Hydrodynamics: Three lectures,Acta Phys. Polon. B 45 (12) (2014) 2355–2394. arXiv:1410.5786 , doi:10.5506/APhysPolB.45.2355 .[11] M. Alqahtani, M. Nopoush, M. Strickland, Quasiparticleanisotropic hydrodynamics for central collisions, Phys. Rev.C 95 (3) (2017) 034906. arXiv:1605.02101 , doi:10.1103/PhysRevC.95.034906 .[12] M. Martinez, M. Strickland, Constraining relativistic viscoushydrodynamical evolution, Phys. Rev. C 79 (2009) 044903. arXiv:0902.3834 , doi:10.1103/PhysRevC.79.044903 .[13] W. Florkowski, R. Ryblewski, M. Strickland, L. Tinti, Non-boost-invariant dissipative hydrodynamics, Phys. Rev. C 94 (6)(2016) 064903. arXiv:1609.06293 , doi:10.1103/PhysRevC.94.064903 .[14] W. Florkowski, R. Ryblewski, Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions, Phys. Rev. C 83 (2011) 034907. arXiv:1007.0130 , doi:10.1103/PhysRevC.83.034907 .[15] M. Martinez, M. Strickland, Dissipative Dynamics of HighlyAnisotropic Systems, Nucl. Phys. A 848 (2010) 183–197. arXiv:1007.0889 , doi:10.1016/j.nuclphysa.2010.08.011 .[16] W. Florkowski, R. Ryblewski, M. Strickland, Anisotropic Hy-drodynamics for Rapidly Expanding Systems, Nucl. Phys. A 916(2013) 249–259. arXiv:1304.0665 , doi:10.1016/j.nuclphysa.2013.08.004 .[17] W. Florkowski, R. Ryblewski, M. Strickland, Testing viscousand anisotropic hydrodynamics in an exactly solvable case,Phys. Rev. C 88 (2013) 024903. arXiv:1305.7234 , doi:10.1103/PhysRevC.88.024903 .[18] W. Florkowski, E. Maksymiuk, R. Ryblewski, M. Strickland,Exact solution of the (0+1)-dimensional Boltzmann equationfor a massive gas, Phys. Rev. C 89 (5) (2014) 054908. arXiv:1402.7348 , doi:10.1103/PhysRevC.89.054908 .[19] G. S. Denicol, U. W. Heinz, M. Martinez, J. Noronha, M. Strick-land, Studying the validity of relativistic hydrodynamics witha new exact solution of the Boltzmann equation, Phys. Rev.D 90 (12) (2014) 125026. arXiv:1408.7048 , doi:10.1103/PhysRevD.90.125026 .[20] G. S. Denicol, U. W. Heinz, M. Martinez, J. Noronha, M. Strick-land, New Exact Solution of the Relativistic Boltzmann Equa-tion and its Hydrodynamic Limit, Phys. Rev. Lett. 113 (20)(2014) 202301. arXiv:1408.5646 , doi:10.1103/PhysRevLett.113.202301 .[21] M. Nopoush, R. Ryblewski, M. Strickland, Anisotropic hydro-dynamics for conformal Gubser flow, Phys. Rev. D 91 (4) (2015)045007. arXiv:1410.6790 , doi:10.1103/PhysRevD.91.045007 .[22] G. Baym, THERMAL EQUILIBRATION IN ULTRARELA-TIVISTIC HEAVY ION COLLISIONS, Phys. Lett. B 138(1984) 18–22. doi:10.1016/0370-2693(84)91863-X .[23] G. Baym, ENTROPY PRODUCTION AND THE EVO-LUTION OF ULTRARELATIVISTIC HEAVY ION COLLI-SIONS, Nucl. Phys. A 418 (1984) 525C–537C. doi:10.1016/0375-9474(84)90573-6 .[24] H. Heiselberg, X.-N. Wang, Expansion, thermalization and en-tropy production in high-energy nuclear collisions, Phys. Rev.C 53 (1996) 1892–1902. arXiv:hep-ph/9504244 , doi:10.1103/PhysRevC.53.1892 .[25] S. Wong, Thermal and chemical equilibration in relativistic heavy ion collisions, Phys. Rev. C 54 (1996) 2588–2599. arXiv:hep-ph/9609287 , doi:10.1103/PhysRevC.54.2588 .[26] M. Strickland, The non-equilibrium attractor for kinetic theoryin relaxation time approximation, JHEP 12 (2018) 128. arXiv:1809.01200 , doi:10.1007/JHEP12(2018)128 .[27] M. Strickland, U. Tantary, Exact solution for the non-equilibrium attractor in number-conserving relaxation time ap-proximation, JHEP 10 (2019) 069. arXiv:1903.03145 , doi:10.1007/JHEP10(2019)069 .[28] H. Alalawi, M. Strickland, An improved anisotropic hydrody-namics ansatz (6 2020). arXiv:2006.13834 .[29] D. Almaalol, A. Kurkela, M. Strickland, Non-equilibrium at-tractor in high-temperature QCD plasmas (4 2020). arXiv:2004.05195 .[30] R. Ryblewski, W. Florkowski, Highly anisotropic hydrodynam-ics – discussion of the model assumptions and forms of theinitial conditions, Acta Phys. Polon. B 42 (2011) 115–138. arXiv:1011.6213 , doi:10.5506/APhysPolB.42.115 .[31] W. Florkowski, R. Ryblewski, Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynam-ics, Phys. Rev. C 85 (2012) 044902. arXiv:1111.5997 , doi:10.1103/PhysRevC.85.044902 .[32] M. Martinez, R. Ryblewski, M. Strickland, Boost-Invariant(2+1)-dimensional Anisotropic Hydrodynamics, Phys. Rev. C85 (2012) 064913. arXiv:1204.1473 , doi:10.1103/PhysRevC.85.064913 .[33] R. Ryblewski, W. Florkowski, Highly-anisotropic hydrodynam-ics in 3+1 space-time dimensions, Phys. Rev. C 85 (2012)064901. arXiv:1204.2624 , doi:10.1103/PhysRevC.85.064901 .[34] D. Bazow, U. W. Heinz, M. Strickland, Second-order (2+1)-dimensional anisotropic hydrodynamics, Phys. Rev. C 90 (5)(2014) 054910. arXiv:1311.6720 , doi:10.1103/PhysRevC.90.054910 .[35] L. Tinti, W. Florkowski, Projection method and new for-mulation of leading-order anisotropic hydrodynamics, Phys.Rev. C 89 (3) (2014) 034907. arXiv:1312.6614 , doi:10.1103/PhysRevC.89.034907 .[36] M. Nopoush, R. Ryblewski, M. Strickland, Bulk viscous evo-lution within anisotropic hydrodynamics, Phys. Rev. C 90 (1)(2014) 014908. arXiv:1405.1355 , doi:10.1103/PhysRevC.90.014908 .[37] L. Tinti, Anisotropic matching principle for the hydrodynamicexpansion, Phys. Rev. C 94 (4) (2016) 044902. arXiv:1506.07164 , doi:10.1103/PhysRevC.94.044902 .[38] D. Bazow, U. W. Heinz, M. Martinez, Nonconformal viscousanisotropic hydrodynamics, Phys. Rev. C 91 (6) (2015) 064903. arXiv:1503.07443 , doi:10.1103/PhysRevC.91.064903 .[39] M. Strickland, M. Nopoush, R. Ryblewski, Anisotropic hydro-dynamics for conformal Gubser flow, Nucl. Phys. A 956 (2016)268–271. arXiv:1512.07334 , doi:10.1016/j.nuclphysa.2016.02.014 .[40] M. Alqahtani, M. Nopoush, M. Strickland, Quasiparticle equa-tion of state for anisotropic hydrodynamics, Phys. Rev. C 92 (5)(2015) 054910. arXiv:1509.02913 , doi:10.1103/PhysRevC.92.054910 .[41] E. Molnar, H. Niemi, D. Rischke, Derivation of anisotropic dis-sipative fluid dynamics from the Boltzmann equation, Phys.Rev. D 93 (11) (2016) 114025. arXiv:1602.00573 , doi:10.1103/PhysRevD.93.114025 .[42] E. Molnr, H. Niemi, D. H. Rischke, Closing the equations ofmotion of anisotropic fluid dynamics by a judicious choice of amoment of the Boltzmann equation, Phys. Rev. D 94 (12) (2016)125003. arXiv:1606.09019 , doi:10.1103/PhysRevD.94.125003 .[43] M. Alqahtani, M. Nopoush, M. Strickland, Quasiparticleanisotropic hydrodynamics for central collisions, Phys. Rev.C 95 (3) (2017) 034906. arXiv:1605.02101 , doi:10.1103/PhysRevC.95.034906 .[44] M. Bluhm, T. Schfer, Dissipative fluid dynamics for the di-lute Fermi gas at unitarity: Anisotropic fluid dynamics, Phys.Rev. A 92 (4) (2015) 043602. arXiv:1505.00846 , doi:10.1103/PhysRevA.92.043602 .
45] M. Bluhm, T. Schaefer, Model-independent determination ofthe shear viscosity of a trapped unitary Fermi gas: Appli-cation to high temperature data, Phys. Rev. Lett. 116 (11)(2016) 115301. arXiv:1512.00862 , doi:10.1103/PhysRevLett.116.115301 .[46] M. Alqahtani, M. Nopoush, R. Ryblewski, M. Strickland,(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarel-ativistic Heavy-Ion Collisions, Phys. Rev. Lett. 119 (4) (2017)042301. arXiv:1703.05808 , doi:10.1103/PhysRevLett.119.042301 .[47] M. Alqahtani, M. Nopoush, R. Ryblewski, M. Strickland,Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb colli-sions, Phys. Rev. C 96 (4) (2017) 044910. arXiv:1705.10191 , doi:10.1103/PhysRevC.96.044910 .[48] M. Alqahtani, M. Nopoush, M. Strickland, Relativisticanisotropic hydrodynamics, Prog. Part. Nucl. Phys. 101 (2018)204–248. arXiv:1712.03282 , doi:10.1016/j.ppnp.2018.05.004 .[49] D. Almaalol, M. Alqahtani, M. Strickland, Anisotropic hydro-dynamic modeling of 200 GeV Au-Au collisions, Phys. Rev.C 99 (4) (2019) 044902. arXiv:1807.04337 , doi:10.1103/PhysRevC.99.044902 .[50] M. Alqahtani, D. Almaalol, M. Nopoush, R. Ryblewski,M. Strickland, Anisotropic hydrodynamic modeling of heavy-ioncollisions at LHC and RHIC, Nucl. Phys. A 982 (2019) 423–426. arXiv:1807.05508 , doi:10.1016/j.nuclphysa.2018.10.066 .[51] M. Alqahtani, D. Almaalol, M. Strickland, Anisotropichydrodynamics for Au-Au collisions at 200 GeV, MDPIProc. 10 (1) (2019) 38. arXiv:1811.01856 , doi:10.3390/proceedings2019010038 .[52] M. Alqahtani, M. Strickland, Pion interferometry at 200 GeVusing anisotropic hydrodynamics (7 2020). arXiv:2007.04209 .[53] P. P. Bhaduri, M. Alqahtani, N. Borghini, A. Jaiswal, M. Strick-land, Fireball tomography from bottomonia elliptic flow in rel-ativistic heavy-ion collisions (7 2020). arXiv:2007.03939 .[54] A. Islam, M. Strickland, Bottomonium suppression and ellipticflow from real-time quantum evolution (7 2020). arXiv:2007.10211 .[55] S. Acharya, et al., Production of charged pions, kaons, and(anti-)protons in Pb-Pb and inelastic pp collisions at √ s NN = 5.02 TeV, Phys. Rev. C 101 (4) (2020) 044907. arXiv:1910.07678 , doi:10.1103/PhysRevC.101.044907 .[56] M. Chojnacki, A. Kisiel, W. Florkowski, W. Broniowski, THER-MINATOR 2: THERMal heavy IoN generATOR 2, Com-put. Phys. Commun. 183 (2012) 746–773. arXiv:1102.0273 , doi:10.1016/j.cpc.2011.11.018 .[57] M. Strickland, http://personal.kent.edu/~mstrick6/code/ (2017).[58] J. Adam, et al., Centrality dependence of the pseudorapiditydensity distribution for charged particles in Pb-Pb collisions at √ s NN = 5 .
02 TeV, Phys. Lett. B 772 (2017) 567–577. arXiv:1612.08966 , doi:10.1016/j.physletb.2017.07.017 .[59] J. Adam, et al., Anisotropic flow of charged particles in Pb-Pb collisions at √ s NN = 5 .
02 TeV, Phys. Rev. Lett. 116 (13)(2016) 132302. arXiv:1602.01119 , doi:10.1103/PhysRevLett.116.132302 .[60] N. Jacazio, Production of identified charged hadrons in Pb–Pb collisions at √ s NN = 5.02 TeV, Nucl. Phys. A 967 (2017)421–424. arXiv:1704.06030 , doi:10.1016/j.nuclphysa.2017.05.023 .[61] B. Schenke, C. Shen, P. Tribedy, Running the gamut of highenergy nuclear collisions (5 2020). arXiv:2005.14682 .[62] S. Acharya, et al., Anisotropic flow of identified particles inPb-Pb collisions at √ s NN = 5 .
02 TeV, JHEP 09 (2018) 006. arXiv:1805.04390 , doi:10.1007/JHEP09(2018)006 .[63] D. Almaalol, M. Strickland, Anisotropic hydrodynamics witha scalar collisional kernel, Phys. Rev. C 97 (4) (2018) 044911. arXiv:1801.10173 , doi:10.1103/PhysRevC.97.044911 .[64] D. Almaalol, M. Alqahtani, M. Strickland, Anisotropic hydro-dynamics with number-conserving kernels, Phys. Rev. C 99 (1)(2019) 014903. arXiv:1808.07038 , doi:10.1103/PhysRevC.99. 014903 .[65] M. Nopoush, M. Strickland, Including off-diagonal anisotropiesin anisotropic hydrodynamics, Phys. Rev. C 100 (1) (2019)014904. arXiv:1902.03303 , doi:10.1103/PhysRevC.100.014904 .[66] S. S. Al-Amri, et al., https://doi.org/10.5281/zenodo.1117442 (2018).(2018).