aa r X i v : . [ nu c l - t h ] S e p Initial State Summary of Hard Probes 2020
Björn Schenke a , ∗ a Physics Department, Brookhaven National Laboratory, Bldg. 510A, Upton, NY 11973, USA
E-mail: [email protected]
The description of the initial state of heavy ion collisions, which covers the description of theincoming nuclei, the initial hard and soft interactions, the resulting spatial geometry of theproduced matter, as well as the dynamic approach to a medium well described by hydrodynamics,has important consequences for the study of hard and electromagnetic probes. I will reviewnew developments presented at Hard Probes 2020 that have an impact on these aspects of ourunderstanding of the initial state of heavy ion and smaller system collisions.
HardProbes20201-6 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/ nitial State Summary of Hard Probes 2020
Björn Schenke
1. Initial geometry
It has been established that the azimuthal momentum anisotropy of produced hadrons in heavyion collisions originates from the (hydrodynamic) response of the produced medium to the initialgeometry in the plane transverse to the beamline [1]. Understanding the precise geometry and itsfluctuations over a wide range of collision systems and energies is thus crucial for describing thebulk observables in heavy ion collisions.A powerful new observable that correlates the elliptic anisotropy v and the mean transversemomentum was suggested in [2], and measurements by the ATLAS Collaboration [3] were pre-sented. The correlator is sensitive to the details of the initial state model and dominated by theinitial geometry [2, 4] in all systems, as long as dN ch / d η >
10 . For smaller multiplicities initialmomentum anisotropies will begin to dominate the final correlator, resulting in a characteristicsign change as a function of multiplicity [5]. Experiments have begun to investigate this, but arechallenged by the presence of “non-flow” contributions at small multiplicities.Other observables that can distinguish different models, for example the difference betweenenergy deposition ∼ √ T A T B and ∼ T A T B (where T A / B are the position dependent target and projectilethickness functions), include the ratio of the four and two particle cumulants v n { }/ v n { } [6]. Theprescription ∼ √ T A T B is preferred by the Trento model [7], which does not include the possibilityof ∼ T A T B scaling, which is predicted by the color glass condensate (CGC) effective field theory(EFT) / glasma [8] and AdS/CFT [9].We particularly need to better understand the rapidity dependence of the initial state. Even at thehighest LHC energies, measurements of flow harmonics show a rather strong rapidity dependence[10, 11], especially in more peripheral events. More complex observables can provide betterconstraints for 3+1 dimensional models, for example the longitudinal flow decorrelation, which wasstudied in Xe+Xe and Pb+Pb systems by the ATLAS Collaboration [12]. This measurement revealedthat hydrodynamic models that can describe the ratios of harmonic flow coefficients between Xe+Xeand Pb+Pb collisions, fail to describe most of the rapidity dependence characterized by v n rapiditydecorrelations. New initial state models for the three dimensional structure of heavy ion collisionsare being developed [13, 14], and especially at low collision energies dynamical energy depositionis required, resulting in complex three dimensional fluctuating initial energy and net baryon densitydistributions [13]. Detailed data as that described above will be very useful for constraining suchmodels.Finally, input that helps constrain the transverse geometry in small system collisions, such asp/d+A collisions, can be obtained from measurements of photoproduction of vector mesons, aswas done in [15] using data from diffractive J / ψ production in e+p collisions at HERA. New dataon J / ψ photoproduction in d+Au collisions was presented by the STAR Collaboration [16]. Thecomputation of the coherent and incoherent cross section in the CGC framework is sensitive to theaverage shape and fluctutions of the deuteron, and the data seems to be able to constrain both [17],and will hopefully also provide more insight into short range nucleon correlations [18].
2. Nuclear effects
To properly describe the initial state of heavy ion collisions and understand for examplethe background to the medium modification of jets, nuclear modifications of parton distribution2 nitial State Summary of Hard Probes 2020
Björn Schenkefunctions (PDFs) need to be well understood. A range of observables can be used to constrainnuclear PDFs, including quarkonium, electroweak boson, light meson, as well as dijet production. J / ψ production in p+p collisions can be well described within a combined CGC+non-relativistic QCD (NRQCD) (+Fixed Order+Next-to-Leading Log (FONLL) [19]) framework [20].The nuclear modification observed in p+Pb collisions [21, 22] is also well described within the CGCEFT [23, 24], and also using constrained nuclear PDFs [24, 25] and coherent energy loss [24, 26].What has not yet been fully described theoretically is the correlation between J / ψ production atbackward and forward rapidities and midrapidity charged hadron production in p+Pb collisions[27]. It will be interesting to see what physics aspects are needed to describe the observed trends.The nuclear dependence of J / ψ production as a function of rapidity was studied by PHENIXat RHIC [28]. As expected, in p+Au collisions one finds stronger shadowing in the forwarddirection and stronger nuclear absorption in the backward direction compared to p+Al collisions.For collisions with a Au target (p+Au and He+Au), only nuclear PDFs are not sufficient to describethe measured R AB ratios. These types of measurements can be very useful to understand thedependence on both nuclear projectile and target.Electroweak boson production is also sensitive to nuclear effects, as demonstrated by ALICEfor Z [29] and W ± production (preliminary data presented at this conference), and new forwardmeasurements can be used as additional input to global nuclear PDF fits. Electroweak boson datahas also been suggested to be used to calibrate the Glauber model [30]: Assuming that EPPS16correctly describes nuclear effects on the production of W and Z bosons, using a reduced nucleon-nucleon inelastic cross section of 41 . + . − . mb compared to the usual 70 ± √ s = R PbPb for W and Z bosons measured at LHC [31, 32], implyingnuclear shadowing of the nucleon-nucleon cross section itself.The nuclear modification of light mesons has now been measured out to p T of up to 200 GeV in8.16 TeV p+Pb collisions by ALICE and presented at this conference. The results are consistent withtheory calculations within the CGC EFT [33] and coherent energy loss [34]. Further insight can begained from small system scan collisions at RHIC, where the π R p / d / He + Au has been measured byPHENIX ([35] and preliminary data). Similar to p+Pb collisions at LHC, the centrality dependenceobserved is consistent with fluctuating proton sizes [36].Finally, dijet measurements in p+p and p+A collisions provide additional information onnuclear effects. For example, predictions for forward dijet angular correlations were presentedwithin the CGC framework [37]. Because of Sudakov effects, which depend on the kinematicsand can mask saturation effects, the ideal range in dijet transverse momenta to observe saturationeffects, was identified to be 5 to 8 GeV (at forward rapidities) in √ s = . x , thegluon PDF at large x in Pb is strongly suppressed with respect to the PDF in unbound nucleons.
3. Theory progress at small x
Steady progress is being made in extending calculations within the CGC EFT to next-to-leading order (NLO). First phenomenological applications using the full NLO impact factor andthe NLO Balitsky-Kovchegov (BK) equation [39–42] to determine the x dependence of deepinelastic scattering (DIS) observables have become available [43]. While the calculation does only3 nitial State Summary of Hard Probes 2020 Björn Schenkeinclude terms that are enhanced by large transverse logarithms, three different formulations of theseevolution equations (which resum some or all of the transverse logarithms) yield little difference.Like at leading order (LO), there seems to be a significant nonperturbative contribution to thestructure function for light quarks. Extension of the NLO calculation of the impact factor for heavyquarks, which would improve this situation, is still outstanding.The BK equation can be viewed as the large N c limit of the JIMWLK equation [44, 45], whichhas also been extended to NLO [46, 47]. At LO, it is known that finite N c corrections are smalland the BK equation approximates the dipole evolution well [48, 49]. At NLO, appearing six-pointfunctions factorize into dipole operators at large N c . Using the Gaussian approximation for thesehigher point correlators, a closed finite- N c BK equation at NLO was obtained [50]. Again, it wasshown that finite N c corrections are smaller than the naively expected 1 / N c ∼ O( ) .A complete NLO calculation of inclusive dijet+photon production in e+p/A collisions withinthe CGC EFT has recently been outlined in [51–53]. This involves in particular the calculation ofthe NLO impact factors. The calculation is powerful, as it includes many NLO processes at small x , such as inclusive dijet, inclusive photon+jet, and inclusive photon production, as well as fullyinclusive DIS. It further carries information on LO q ¯ q g and q ¯ q g + γ production. Combining theseresults for the NLO impact factor with next-to-leading-log (NLL) resummed evolution kernels,an accuracy of order α s ln ( / x ) can be achieved. Based on this, explicit calculations for promptphoton+jet production can be done at NLO. First LO results for this process, studying the azimuthalphoton-jet correlations, which carry information on saturation, have recently been published in [54].Further progress reported included extensions beyond the eikonal approximation: 1) in thecalculation of quark-nucleus scattering in a light-front Hamiltonian approach [55], and 2) byincluding large x gluons in the target, which also aims at developing a unified picture for particleproduction at small and large x [56]. A generalized connection between transverse momentumdependent PDFs (TMDs) and the CGC EFT, using a new approach to TMDs at small x employingtransverse gauge link operators [57] was presented, as well as the first computation of entanglementand “ignorance” entropies within the CGC EFT, the latter reflecting our inability to perform acomplete set of measurements (sensitive to off-diagonal elements of the density matrix) [58].
4. Approach to equilibrium
Another area where a lot of progress has been made in the last couple of years is the study of theearly time non-equlibrium evolution that is expected to result in a system that is well approximatedby hydrodynamics [59, 60]. The question of when hydrodynamics is applicable can be studied inboth strong and weak coupling limits [61]. In the strong coupling limit, described within AdS/CFT,causality requires that hydrodynamization occurs on time scales of order ∼ / T , where T is thetemperature, as this is the distance from the horizon to the boundary, where the field theory lives. Inthe weak coupling limit, described by the Boltzmann equation and a relaxation time approximation(RTA) for the collision term, hydrodynamization is found to occur within 2 τ , where τ is the initialtime. The two limits behave somewhat differently, as in the RTA solutions approach the attractorbefore any finite order hydrodynamic expansion agrees with the attractor, while in AdS/CFT 2ndorder hydrodynamics is usually a good approximation by the time the solutions approach theattractor. 4 nitial State Summary of Hard Probes 2020 Björn SchenkeAlso chemical equilibration has been studied using the Boltzmann equation for quarks andgluons including 2 ↔ ↔ dN ch / d η & Music hydrodynamics [68, 69], and UrQMD hadronic afterbuner [70].
5. Conclusions
Our understanding of the initial state in heavy ion collisions and the early time dynamics iscontinuously improving. A lot of progress is being made in the first principles understanding ofthe nuclear wave function and nuclear and saturation effects, specifically the CGC EFT is beingextended to NLO and calculations for a variety of processes at NLO are emerging. Furthermore,the initial geometry and its fluctuations are being better constrained, including the longitudinaldirection, and the approach to a system that is described by hydrodynamics is being understoodincreasingly well. Among many other subfields of high energy nuclear physics, the study of hardand electromagnetic probes in heavy ion collisions will benefit immensly from these developments.
Acknowledgments
B.P.S. is supported under DOE Contract No. DE-SC0012704.
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