Benchmark of medium-induced radiative energy loss model for heavy-ion collisions
Iurii Karpenko, Joerg Aichelin, Pol Bernard Gossiaux, Martin Rohrmoser
BBenchmark of medium-induced radiative energy lossmodel for heavy-ion collisions
Iurii Karpenko, a , ∗ Joerg Aichelin, b Pol Bernard Gossiaux b and Martin Rohrmoser c a Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague,Břehová 7, 11519 Prague 1, Czech Republic b SUBATECH, Université de Nantes, IMT Atlantique, IN2P3/CNRS,4 rue Alfred Kastler, 44307 Nantes cedex 3, France c H. Niewodniczański Institute of Nuclear Physics PAN, 31-342 Cracow, Poland
E-mail: [email protected]
We report on a benchmark calculation of the in-medium radiative energy loss of low-virtualityjet partons within the EPOS3-Jet framework. The radiative energy loss is based on an extensionof the Gunion-Bertsch matrix element for a massive projectile and a massive radiated gluon. Ontop of that, the coherence (LPM effect) is implemented by assigning a formation phase to the trialradiated gluons in a fashion similar to [3] by Zapp, Stachel and Wiedemann. In a calculationwith a simplified radiation kernel, we reproduce the radiation spectrum reported in [3]. Theradiation spectrum produces the LPM behaviour dI / d ω ∝ ω − / up to an energy ω = ω c , whenthe formation length of radiated gluons becomes comparable to the size of the medium. Beyond ω c , the radiation spectrum shows a characteristic suppression due to a smaller probability for agluon to be formed in-medium.Next, we embed the radiative energy loss of low-virtuality jet partons into a more realistic “partongun” calculation, where a stream of hard partons at high initial energy E ini =
100 GeV and initialvirtuality Q = E passes through a box of QGP medium with a constant temperature. At theend of the box evolution, the partons are hadronized using Pythia 8, and the jets are reconstructedwith the FASTJET package. We find that the full jet energy loss in such scenario approaches aballpark value reported by the ALICE collaboration. However, the calculation uses a somewhatlarger value of the coupling constant α s to compensate for the missing collisional energy loss ofthe low-virtuality jet partons. HardProbes20201-5 June 2020Austin, Texas ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ nu c l - t h ] S e p enchmark of medium-induced radiative energy loss model for heavy-ion collisions Iurii Karpenko
Introduction:
In the last decade, both experimental extraction and theoretical modeling ofjets in heavy-ion collisions became more and more refined. At present, one has understood that thedescription of the fine substructure properties of the jets, such as the jet shape, requires a ratherprecise description of both, the underlying space-time evolution of the medium and the back reactionof the jet on the medium, sometimes called “medium recoil”. Our aim is to create a comprehensivemodel of jet and medium evolution, and in these proceedings we report on the development ofone of its core components: the process of medium-induced gluon radiation by low-virtuality jetpartons.
The model:
The medium-induced radiation is based on the emission of gluons by massivequarks, which move through and interact with light medium quarks and medium gluons [1]. Thelatter extends the known calculation by Gunion and Bertsch [2] to the case of a massive projectileand a massive radiated gluon.A direct computation of the matrix elements corresponding to the gluon bremsstrahlung isdifficult. A simplifying assumption used in [1] is that, in the region of small x , the matrix elementsfrom QCD can be approximated by a so-called scalar QCD. The scalar QCD (SQCD) is a caseof spin-0 quarks interacting with a non-Abelian gauge field (gluons). At high enough energy, theSQCD leads to a factorized formula for the total cross section of the radiation process: d σ Qq → Qqg dxd k T d l T = d σ el d l T P g ( x , k T , l T ) θ ( ∆ ) , (1)where k T is the transverse momentum of the radiated gluon, l T is the transverse momentum acquiredby the medium parton, d σ el d l T → α s ( (cid:174) l T + µ ) and ∆ = (cid:16) x ( − x ) s − x M − (cid:174) k T + x (cid:174) k T · (cid:174) l T (cid:17) − x ( − x ) (cid:174) l T ( x s − (cid:174) k T ) . (2)The Θ function encodes the kinematic limits. The part corresponding to the gluon radiation is: P g ( x , (cid:174) k T , (cid:174) l T ; M ) = C A α s π − xx (cid:32) (cid:174) k T (cid:174) k T + x M − (cid:174) k T − (cid:174) l T ( (cid:174) k T − (cid:174) l T ) + x M (cid:33) , (3)where M is the mass of the projectile Q . An important feature of the expressions above is that they canbe easily extended for the case of a massive radiated gluon by substituting x M → x M + ( − x ) m g ,where m g is the gluon mass. As one can see, the mass of the projectile quark and the gluon entersthe expressions explicitly. However, in the present proceedings we do not study the hierarchy of theenergy loss by projectiles with different masses.On top of the radiation kernel described by the formulas above, we have implemented thecoherent gluon radiation via multiple scatterings of the projectile with the medium partons. Moredetails and tests of the procedure will be reported in an upcoming publication, whereas here we listthe main details:• The formation and evolution of the parton shower from the initial hard parton proceeds intime-steps. Such feature makes it very convenient to couple the parton shower to a realistichydrodynamic evolution of the medium, which is typically performed numerically.2 enchmark of medium-induced radiative energy loss model for heavy-ion collisions Iurii Karpenko• At each time-step, we decide whether an elastic scattering or an incoherent inelastic scatteringtakes place, according to probabilities Γ el ∆ t and Γ inel ∆ t , respectively. The result of suchincoherent inelastic scattering is a trial radiated (or unformed) gluon.• Each of the trial radiated gluons starts its evolution with an initial phase ϕ = N s =
1. The projectile may have more than one trial radiated gluon associated withit, and the gluons are treated independently and in parallel.• Each of the trial radiated gluons also experiences elastic scatterings with the medium partons,according to the same elastic rate Γ coll . Each scattering changes the transverse momentum k T of the trial radiated gluon, and increments its the collision counter N s by one. The phaseof a trial radiated gluon increases by ∆ ϕ = ω / k T · ∆ t .• Once a trial radiated gluon accumulates formation phase ϕ = . / N s , or isdiscarded with a probability 1 − / N s .• If the trial radiated gluon is accepted, its initial energy-momentum are subtracted from theenergy-momentum of the projectile.Such an algorithm allows to mimic the process of coherent radiation in a probabilistic fashion [3].To test the algorithm, we first set it up to reproduce an exact result for the energy spectrum of radiatedgluons in the BDMPS-Z limit. To do so, we reduce the radiation kernel to dN /( d ω dk T ) = / ω , k T = Γ el = Γ inel = . k T =
0, in accordance with [3] and assuming that the transversemomentum is picked up mostly by the multiple elastic scatterings with the medium partons.
Results and discussion:
With the setup above and the ϕ = . E =
100 GeV into a box ofmedium, where the temperature is adjusted so that the ˆ q = . /fm. The resulting intensityspectra of the radiated gluons, as a function of the gluon energy ω , are plotted in Fig. 1. A transitionfrom the coherent regime (dubbed as “LPM” in the plot) to the regime where at most 1 gluon isbeing emitted (dubbed as “N=1” in the plot), happens around gluon’s energy: ω c ≈ ˆ qL ϕ f (cid:126) . With the present settings and a box size L = ω c ≈ . L = ω c ≈ . L = ω c value, which was calculated above. Also, by setting the formation phasecondition ϕ =
0, we can restore the incoherent radiation regime (which is a green curve on the plot),where the radiation spectrum follows the known 1 / ω dependence.Next, we turn to a more realistic scenario, where the jet evolution starts from an energeticparton with E =
100 GeV and initial virtuality scale Q ini = E . As such, the process of jet formation- subsequent parton splittings via a virtuality-ordered parton shower - takes place before the partonsat the lowest virtuality scale, Q = . enchmark of medium-induced radiative energy loss model for heavy-ion collisions Iurii Karpenko ω [GeV]10 − − − d I / d ω initial k T = 0; no phase space restrictionsLPM N=1 BHL=1 fmL=2 fmno LPM ω − (N=1) ω − / (LPM) ω − (BH) Figure 1:
Energy spectrum of gluons, radiated by a low-virtuality projectile with initial energy E ini =
100 GeV in a medium with lengths L = , Γ inel = . this scenario, the medium is modelled as a gas of N f = m q ( T ) =
330 MeVand N c = m g ( T ) =
564 MeV, at a temperature of T =
350 MeV. The size ofthe medium is taken as L = µ =
623 MeV (which is proportional to the Debye mass). We takea somewhat larger value of the coupling constant with respect to other approaches, α s = . ϕ = k T algorithm with a cone size R = . ∆ t = E / Q . First we note that the profiles of the jet energy in both,the vacuum and the“standard” medium-modified case, increase monotonically with the energy of the reconstructed jet.In the scenario of the short jet formation (the green curve), there is a broad peak around E ≈
94 GeV.Such profile of the radiative energy loss of a jet is qualitatively consistent with an eariler studiesin AMY formalism with a similar setup [6]. We note that the difference between the mean energy4 enchmark of medium-induced radiative energy loss model for heavy-ion collisions
Iurii Karpenko
50 60 70 80 90 100 E [GeV]0 . . . . . . . d N j e t / d E h E jet i =96.7 GeV h E jet i =94.7 GeV h E jet i =91.4 GeVvacuumradiative EL, ∆ t = E/Q radiative EL, ∆ t = E/Q Figure 2:
Profile (distribution) of radiative energy loss by a projectile with initial energy E ini =
100 GeV ina QGP medium with length L = T =
350 MeV. of the reconstructed “vacuum” jet and the reconstructed medium-modified jet with ∆ t = E / Q isin the same ballpark as the p T shift of the jet spectrum, measured in Pb-Pb collisions in the jet p T range [60,100] GeV by ALICE [7]. Acknowledgements:
We acknowledge support by the project Centre of Advanced AppliedSciences with number CZ.02.1.01/0.0/0.0/16-019/0000778, which is co-financed by the EuropeanUnion, and from the European Union’s Horizon 2020 research and innovation program STRONG-2020 under grant agreement No 824093.
References [1] J. Aichelin, P. B. Gossiaux and T. Gousset, Phys. Rev. D (2014) no.7, 074018[2] J. F. Gunion and G. Bertsch, Phys. Rev. D (1982), 746[3] K. C. Zapp, J. Stachel and U. A. Wiedemann, JHEP (2011), 118[4] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel,C. O. Rasmussen and P. Z. Skands, Comput. Phys. Commun. (2015), 159-177[5] M. Cacciari, G. P. Salam and G. Soyez, Eur. Phys. J. C (2012), 1896[6] G. Y. Qin, J. Ruppert, C. Gale, S. Jeon, G. D. Moore and M. G. Mustafa, Phys. Rev. Lett. (2008), 072301[7] J. Adam et al. [ALICE], JHEP09