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Effects of Subnucleonic Fluctuations on the Longitudinal Dynamics of Heavy-Ion Collisions
Authors:
Oscar Garcia-Montero,
Sören Schlichting,
Jie Zhu
Abstract:
It is well understood that subnuclear fluctuations in the initial state of heavy-ion collisions have an important impact on the creation of long-range correlations in the transverse plane. This is also true for the creation of particle correlations along the beam direction, which can be measured in particle detectors, e.g. through longitudinal decorrelation observables. In this work, we study the…
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It is well understood that subnuclear fluctuations in the initial state of heavy-ion collisions have an important impact on the creation of long-range correlations in the transverse plane. This is also true for the creation of particle correlations along the beam direction, which can be measured in particle detectors, e.g. through longitudinal decorrelation observables. In this work, we study the emergence of long-range rapidity structures in Pb+Pb collisions using a hybrid model connecting the 3D resolved {\Dipper} initial state model to a (3+1)D viscous hydrodynamics framework CLVisc. We include different sources of fluctuations at the (sub-)nucleon level and present the effects of their inclusion on the longitudinal structure of relevant observables, focusing in this proceedings paper on charged hadron multiplicities, baryon stopping, directed flow and flow decorrelation. We find remarkable agreement to the experimental data regarding directed flow and the rapidity resolved charge particle multiplicity.
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Submitted 22 October, 2025; v1 submitted 15 October, 2025;
originally announced October 2025.
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Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
Authors:
Yiyang Peng,
Victor E. Ambrus,
Clemens Werthmann,
Sören Schlichting,
Ulrich Heinz,
Huichao Song
Abstract:
We perform (2{+}1)-D simulations of viscous anisotropic hydrodynamics (VAH) under boost-invariant and conformal conditions. Comparing both VAH and traditional viscous hydrodynamics with kinetic theory in the relaxation-time approximation as the underlying microscopic theory, we show that VAH provides a superior description of the evolution across a wide range of opacity, effectively extending the…
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We perform (2{+}1)-D simulations of viscous anisotropic hydrodynamics (VAH) under boost-invariant and conformal conditions. Comparing both VAH and traditional viscous hydrodynamics with kinetic theory in the relaxation-time approximation as the underlying microscopic theory, we show that VAH provides a superior description of the evolution across a wide range of opacity, effectively extending the boundaries of the applicability of hydrodynamic modeling. Our results demonstrate VAH's potential for describing collective flow in small systems where traditional hydrodynamics faces challenges.
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Submitted 4 September, 2025;
originally announced September 2025.
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The (3+1)D structure of the dilute Glasma
Authors:
Andreas Ipp,
Markus Leuthner,
David I. Müller,
Sören Schlichting,
Kayran Schmidt,
Pragya Singh
Abstract:
We study the (3+1)D structure of the Glasma in the dilute approximation, which allows us to describe the longitudinal dynamics that arise from the three-dimensional nuclear structure. We employ a nuclear model with tunable longitudinal and transverse fluctuation scales that generalizes the McLerran-Venugopalan model. We discuss the longitudinal profiles of the energy-momentum tensor and the transv…
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We study the (3+1)D structure of the Glasma in the dilute approximation, which allows us to describe the longitudinal dynamics that arise from the three-dimensional nuclear structure. We employ a nuclear model with tunable longitudinal and transverse fluctuation scales that generalizes the McLerran-Venugopalan model. We discuss the longitudinal profiles of the energy-momentum tensor and the transverse structure of the local rest frame energy density.
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Submitted 28 August, 2025;
originally announced August 2025.
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Constraining hot and cold nuclear matter properties from heavy-ion collisions and deep-inelastic scattering
Authors:
Anton Andronic,
Nicolas Borghini,
Xiaojian Du,
Christian Klein-Bösing,
Renata Krupczak,
Hendrik Roch,
Sören Schlichting
Abstract:
We perform a global analysis of deep-inelastic $e+p$ scattering data from HERA and transverse energy distributions in $p+p$ and $p+\mathrm{Pb}$ collisions, alongside charged hadron multiplicities in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02\;\mathrm{TeV}$ from ALICE. Using a saturation-based initial state model grounded in high-energy QCD, we determine the early-time n…
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We perform a global analysis of deep-inelastic $e+p$ scattering data from HERA and transverse energy distributions in $p+p$ and $p+\mathrm{Pb}$ collisions, alongside charged hadron multiplicities in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02\;\mathrm{TeV}$ from ALICE. Using a saturation-based initial state model grounded in high-energy QCD, we determine the early-time non-equilibrium shear viscosity to entropy density ratio $η/s$ of the quark-gluon plasma. Our results provide new insights into the early-time transport properties of nuclear matter under extreme conditions.
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Submitted 30 July, 2025; v1 submitted 3 April, 2025;
originally announced April 2025.
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Limiting fragmentation in the dilute Glasma
Authors:
Andreas Ipp,
Markus Leuthner,
David I. Müller,
Sören Schlichting,
Kayran Schmidt,
Pragya Singh
Abstract:
We discuss the local longitudinal scaling behavior of the dilute Glasma. We gain insight into how the fragmentation region is dominated by the longitudinal structure of one of the two colliding nuclei in heavy-ion collisions and study the effect of the correlation scales of the nuclear color charge distributions. We compare with results from the full dilute Glasma framework and analyze the rapidit…
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We discuss the local longitudinal scaling behavior of the dilute Glasma. We gain insight into how the fragmentation region is dominated by the longitudinal structure of one of the two colliding nuclei in heavy-ion collisions and study the effect of the correlation scales of the nuclear color charge distributions. We compare with results from the full dilute Glasma framework and analyze the rapidity limits of the fragmentation region. From our findings, it follows that all scalar observables that can be constructed out of the dilute Glasma field strength tensor show limiting fragmentation behavior and the field strength tensor itself transforms locally via Lorentz boosts when changing the collision energy.
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Submitted 23 February, 2025;
originally announced February 2025.
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Stochastic baryon charge transport in relativistic hydrodynamics
Authors:
Nicolas Borghini,
Baochi Fu,
Sören Schlichting
Abstract:
We utilize 3+1D stochastic hydrodynamics to study correlations and fluctuations of baryon charge in high-energy heavy-ion collisions. The baryon charge fluctuations are important observables to probe the QCD phase diagram, yet a dynamical description with stochastic hydrodynamics remains challenging due to numerical instabilities and high computational demands. In this work, we employ a linearized…
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We utilize 3+1D stochastic hydrodynamics to study correlations and fluctuations of baryon charge in high-energy heavy-ion collisions. The baryon charge fluctuations are important observables to probe the QCD phase diagram, yet a dynamical description with stochastic hydrodynamics remains challenging due to numerical instabilities and high computational demands. In this work, we employ a linearized approach, allowing us to separately simulate the background energy-momentum evolution of a charge-neutral fluid and the stochastic baryon transport processes, thereby largely reducing computational cost while maintaining sufficient accuracy. We implement this linearized stochastic charge evolution in the viscous hydrodynamic code MUSIC, and find that it nicely describes the two-point correlation of 1+1D analytical solutions for various equations of state and transport coefficients. In particular, the hydrodynamic calculations demonstrate how different rapidity separations probe charge fluctuations originating at different times of the evolution. We also investigate the net baryon correlations after the Cooper--Frye freeze out, which show good consistency with the analytical calculations and indicate that these fluctuation-induced correlations are sensitive to the baryon diffusion coefficient.
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Submitted 16 February, 2025;
originally announced February 2025.
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Effective theories for nuclei at high energies
Authors:
Oscar Garcia-Montero,
Sören Schlichting
Abstract:
We discuss the application of the Color Glass Condensate (CGC), an effective field theory of Quantum Chromodynamics (QCD), to describe high-energy nuclear interactions. We first provide an introduction to the methods and language of the CGC, its role in understanding gluon saturation in heavy-ion collisions at the LHC and RHIC, and its relevance in various scattering processes such as Deep Inelast…
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We discuss the application of the Color Glass Condensate (CGC), an effective field theory of Quantum Chromodynamics (QCD), to describe high-energy nuclear interactions. We first provide an introduction to the methods and language of the CGC, its role in understanding gluon saturation in heavy-ion collisions at the LHC and RHIC, and its relevance in various scattering processes such as Deep Inelastic Scattering (DIS). The application of the CGC effective field theory to describe hadron-hadron collisions is discussed in the scope of asymmetric \textit{dilute-dense} collisions, and Heavy-Ion Collisions in the \textit{dense-dense} limit. The review covers theoretical foundations, recent advancements, and phenomenological applications, focusing on using the CGC to determine the initial conditions of heavy-ion collisions.
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Submitted 13 February, 2025;
originally announced February 2025.
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Effects of sub-nucleonic fluctuations on the longitudinal structure of heavy-ion collisions
Authors:
Oscar Garcia-Montero,
Sören Schlichting,
Jie Zhu
Abstract:
Sub-nuclear fluctuations in the initial state of heavy-ion collisions impact not only transverse long-range correlations of small systems, but also the creation of longitudinal structures, seen in particle detectors as longitudinal decorrelation observables. In this work, we study the emergence of long-range rapidity correlations in nuclear collisions based on the 3D resolved McDIPPER initial stat…
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Sub-nuclear fluctuations in the initial state of heavy-ion collisions impact not only transverse long-range correlations of small systems, but also the creation of longitudinal structures, seen in particle detectors as longitudinal decorrelation observables. In this work, we study the emergence of long-range rapidity correlations in nuclear collisions based on the 3D resolved McDIPPER initial state model, and for the first time, connect it to experimental observables using the 3+1D viscous hydrodynamics framework CLVisc. We include different sources of fluctuations at the nucleon and subnucleon level and study the effects of these additional fluctuation sources on the longitudinal structure of relevant observables, such as the flow decorrelations and directed flow.
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Submitted 1 April, 2025; v1 submitted 24 January, 2025;
originally announced January 2025.
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Collective dynamics in heavy and light-ion collisions -- II) Determining the origin of collective behavior in high-energy collisions
Authors:
Victor E. Ambrus,
Sören Schlichting,
Clemens Werthmann
Abstract:
Exploiting the first measurements of the same ion species in OO collisons at RHIC and LHC, we propose an observable to distinguish whether collective behavior builds up through a hydrodynamic expansion of a strongly interacting QGP or few final state re-scatterings. Our procedure allows to disentangle the effects of the initial state geometry and the dynamical response mechanism on anisotropic flo…
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Exploiting the first measurements of the same ion species in OO collisons at RHIC and LHC, we propose an observable to distinguish whether collective behavior builds up through a hydrodynamic expansion of a strongly interacting QGP or few final state re-scatterings. Our procedure allows to disentangle the effects of the initial state geometry and the dynamical response mechanism on anisotropic flow. We validate its ability to discriminate between systems with different interaction rates using results from event-by-event simulations in kinetic theory.
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Submitted 20 March, 2025; v1 submitted 29 November, 2024;
originally announced November 2024.
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Baryon stopping and charge deposition in heavy-ion collisions due to gluon saturation
Authors:
Oscar Garcia-Montero,
Sören Schlichting
Abstract:
We compute baryon and electric charge deposition in high-energy heavy-ion collisions using the Color Glass Condensate (CGC) Effective Field Theory, where at leading order charge is deposited through multiple scatterings of valence quarks with a saturated gluon target. A simplified phenomenological formula is derived to describe charge deposition, from which the parametrical dependence with collisi…
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We compute baryon and electric charge deposition in high-energy heavy-ion collisions using the Color Glass Condensate (CGC) Effective Field Theory, where at leading order charge is deposited through multiple scatterings of valence quarks with a saturated gluon target. A simplified phenomenological formula is derived to describe charge deposition, from which the parametrical dependence with collisional energy and geometry can be extracted. We present an approximate analytical prediction of the so-called baryon stopping parameter $α_B$, which shows excellent agreement with the state-of-the art extractions of $α_B$ from experimental data. These results are further validated using the McDIPPER framework, by computing charge deposition at midrapidity across a range of collision energies ($\sqrt{s_{\rm NN}}= 62.4 - 5020$ GeV).
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Submitted 18 February, 2025; v1 submitted 10 September, 2024;
originally announced September 2024.
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Pre-equilibrium Photon and Dilepton Production
Authors:
Oscar Garcia-Montero,
Aleksas Mazeliauskas,
Philip Plaschke,
Sören Schlichting
Abstract:
We use QCD kinetic theory to compute photon and dilepton production in the chemically equilibrating out-of-equilibrium quark-gluon plasma created in the early stages of high-energy heavy-ion collisions. We derive universal scaling functions for the pre-equilibrium spectra of photons and dileptons. These scaling functions can be used to make realistic predictions for the pre-equilibrium emission an…
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We use QCD kinetic theory to compute photon and dilepton production in the chemically equilibrating out-of-equilibrium quark-gluon plasma created in the early stages of high-energy heavy-ion collisions. We derive universal scaling functions for the pre-equilibrium spectra of photons and dileptons. These scaling functions can be used to make realistic predictions for the pre-equilibrium emission and consequently establish the significance of the pre-equilibrium phase for the production of electromagnetic probes in heavy-ion collisions.
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Submitted 3 April, 2024;
originally announced April 2024.
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Scaling of pre-equilibrium dilepton production in QCD Kinetic Theory
Authors:
Oscar Garcia-Montero,
Philip Plaschke,
Sören Schlichting
Abstract:
We use QCD kinetic theory to compute dilepton production coming from the pre-equilibrium phase of the Quark-Gluon Plasma created in high-energy heavy-ion collisions. We demonstrate that the dilepton spectrum exhibits a simple scaling in terms of the specific shear viscosity $η/s$ and entropy density $dS/dζ\sim {\scriptstyle \left(Tτ^{1/3}\right)_\infty^{3/2}}$, which can be derived from dimensiona…
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We use QCD kinetic theory to compute dilepton production coming from the pre-equilibrium phase of the Quark-Gluon Plasma created in high-energy heavy-ion collisions. We demonstrate that the dilepton spectrum exhibits a simple scaling in terms of the specific shear viscosity $η/s$ and entropy density $dS/dζ\sim {\scriptstyle \left(Tτ^{1/3}\right)_\infty^{3/2}}$, which can be derived from dimensional analysis in the presence of a pre-equilibrium attractor. Based on this scaling we perform event-by-event calculations of in-medium dilepton production and determine the invariant mass range where the pre-equilibrium yield is the leading contribution.
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Submitted 18 February, 2025; v1 submitted 7 March, 2024;
originally announced March 2024.
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Energy-momentum tensor of the dilute (3+1)D Glasma
Authors:
Andreas Ipp,
Markus Leuthner,
David I. Müller,
Sören Schlichting,
Kayran Schmidt,
Pragya Singh
Abstract:
We present a succinct formulation of the energy-momentum tensor of the Glasma characterizing the initial color fields in relativistic heavy-ion collisions in the Color Glass Condensate effective theory. We derive concise expressions for the (3+1)D dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with non-trivial…
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We present a succinct formulation of the energy-momentum tensor of the Glasma characterizing the initial color fields in relativistic heavy-ion collisions in the Color Glass Condensate effective theory. We derive concise expressions for the (3+1)D dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with non-trivial longitudinal correlations. Utilizing Monte Carlo integration, we calculate in unprecedented detail non-trivial rapidity profiles of early-time observables at RHIC and LHC energies, including transverse energy densities and eccentricities. For our setup with broken boost invariance, we carefully discuss the placement of the origin of the Milne frame and interpret the components of the energy-momentum tensor. We find longitudinal flow that deviates from standard Bjorken flow in the (3+1)D case and provide a geometric interpretation of this effect. Furthermore, we observe a universal shape in the flanks of the rapidity profiles regardless of collision energy and predict that limiting fragmentation should also hold at LHC energies.
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Submitted 27 May, 2024; v1 submitted 18 January, 2024;
originally announced January 2024.
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New theoretical developments on the early-time dynamics and approach to equilibrium in Heavy-Ion collisions
Authors:
Soeren Schlichting
Abstract:
We discuss recent theoretical developments in understanding the early pre-equilibrium dynamics and onset of hydrodynamic behavior in high-energy heavy-ion collisions. We highlight possible experimental signatures of the pre-equilibrium phase, and present recent progress in developing a consistent theoretical description of collective flow in small systems.
We discuss recent theoretical developments in understanding the early pre-equilibrium dynamics and onset of hydrodynamic behavior in high-energy heavy-ion collisions. We highlight possible experimental signatures of the pre-equilibrium phase, and present recent progress in developing a consistent theoretical description of collective flow in small systems.
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Submitted 8 January, 2024;
originally announced January 2024.
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Hot spots in a proton
Authors:
S. Demirci,
T. Lappi,
S. Schlichting
Abstract:
We explore the consequences of gluonic hot spots inside the proton for the initial eccentricities in a proton-nucleus collision, and the constraints on the parameters describing these hot spots from coherent and incoherent exclusive vector meson production cross sections in deep inelastic scattering. We show that geometric fluctuations of hot spots inside the proton are the dominant source of ecce…
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We explore the consequences of gluonic hot spots inside the proton for the initial eccentricities in a proton-nucleus collision, and the constraints on the parameters describing these hot spots from coherent and incoherent exclusive vector meson production cross sections in deep inelastic scattering. We show that geometric fluctuations of hot spots inside the proton are the dominant source of eccentricity whereas color charge fluctuations only give a negligible correction. We find that the coherent cross section is sensitive to both the size of the target and the structure of the probe. The incoherent cross section is dominated by color fluctuations at small transverse momentum transfer (t), by proton and hot spot sizes as well as the structure of the probe at medium -t and again by color fluctuations at large -t.
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Submitted 22 December, 2023;
originally announced December 2023.
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Event-by-event Kinetic Description of Pre-Equilibrium Charge Evolution in QCD Plasma
Authors:
Travis Dore,
Xiaojian Du,
Sören Schlichting
Abstract:
We use QCD effective kinetic theory to calculate far-from-equilibrium dynamics on an event-by-event basis within the KøMPøST framework. We present non-equilibrium charge response functions and the dynamical evolution of the conserved charge current pertinent to the early-time dynamics of heavy-ion collisions at the highest energies. The KøMPøST framework with conserved baryon, strangeness, and ele…
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We use QCD effective kinetic theory to calculate far-from-equilibrium dynamics on an event-by-event basis within the KøMPøST framework. We present non-equilibrium charge response functions and the dynamical evolution of the conserved charge current pertinent to the early-time dynamics of heavy-ion collisions at the highest energies. The KøMPøST framework with conserved baryon, strangeness, and electric charges can then be readily implemented into a multistage model allowing for the initialization of a non-equilibrium charge current in hydrodynamic simulations.
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Submitted 21 December, 2023;
originally announced December 2023.
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Heavy Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium
Authors:
Harshit Pandey,
Soeren Schlichting,
Sayantan Sharma
Abstract:
We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting non-perturbative features as a function o…
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We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting non-perturbative features as a function of time due to correlated momentum kicks it receives from the medium, eventually going over to a diffusive regime. We extract the momentum diffusion coefficient for a mass range describing charm and bottom quarks and find sizeable discrepancies from the heavy quark limit.
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Submitted 14 June, 2024; v1 submitted 19 December, 2023;
originally announced December 2023.
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Pre-equilibrium photon production in QCD Kinetic Theory
Authors:
Oscar Garcia-Montero,
Aleksas Mazeliauskas,
Philip Plaschke,
Sören Schlichting
Abstract:
We use QCD kinetic theory to compute photon production in the chemically equilibrating Quark-Gluon Plasma created in the early stages of high-energy heavy-ion collisions. We show that the photon spectrum radiated from an attractor evolution satisfies a simple scaling form in terms of the specific shear viscosity $η/s$ and entropy density…
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We use QCD kinetic theory to compute photon production in the chemically equilibrating Quark-Gluon Plasma created in the early stages of high-energy heavy-ion collisions. We show that the photon spectrum radiated from an attractor evolution satisfies a simple scaling form in terms of the specific shear viscosity $η/s$ and entropy density $dS/dζ\sim {\scriptstyle \left(Tτ^{1/3}\right)^{3/2}}_\infty$. We confirm the analytical predictions with numerical kinetic theory simulations. We use the extracted scaling function to compute the pre-equilibrium photon contribution in $\sqrt{s_{NN}}=2.76\,\text{TeV}$ 0-20% PbPb collisions. We demonstrate that our matching procedure allows for a smooth switching from pre-equilibrium kinetic to thermal hydrodynamic photon production.
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Submitted 14 December, 2023;
originally announced December 2023.
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Small-x structure of oxygen and neon isotopes as seen by the Large Hadron Collider
Authors:
Giuliano Giacalone,
Bjoern Schenke,
Soeren Schlichting,
Pragya Singh
Abstract:
Results on collisions of $^{16}$O nuclei performed at the Relativistic Heavy Ion Collider (RHIC) have been presented for the first time at Quark Matter 2023 by the STAR collaboration. $^{16}$O+$^{16}$O collisions are also expected to take place in the near future at the Large Hadron Collider (LHC) at much higher beam energies. We explore the potential of beam-energy-dependent studies for this syst…
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Results on collisions of $^{16}$O nuclei performed at the Relativistic Heavy Ion Collider (RHIC) have been presented for the first time at Quark Matter 2023 by the STAR collaboration. $^{16}$O+$^{16}$O collisions are also expected to take place in the near future at the Large Hadron Collider (LHC) at much higher beam energies. We explore the potential of beam-energy-dependent studies for this system to probe small-$x$ dynamics and QCD evolution. We perform 3+1D IP-Glasma simulations to predict the rapidity dependence of the initial geometry of light-ion collisions, focusing on $^{16}$O+$^{16}$O and $^{20}$Ne+$^{20}$Ne collisions at $\sqrt{s_{\rm NN}} = 70$ GeV and 7 TeV. The choice of $^{20}$Ne is motivated by its strongly elongated geometry, which may respond differently to the effect of the high-energy evolution compared to the more spherical $^{16}$O. We find that smearing induced by soft gluon production at high energy causes mild variations in the initial-state eccentricities as a function of the collision energy. These effects could be resolved in future experiments and deserve further investigation.
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Submitted 12 December, 2023;
originally announced December 2023.
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Charge and energy deposition in the McDIPPER framework
Authors:
Oscar Garcia-Montero,
Sören Schlichting,
Hannah Elfner
Abstract:
In this short note we present aspects of the energy and charge deposition within the McDIPPER, a novel 3D resolved model for the initial state of ultrarelativistic Heavy-Ion collisions based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. This framework is a initial-state Monte Carlo event generator which deposits the relevant conserved charges (energy, charge and baryon densit…
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In this short note we present aspects of the energy and charge deposition within the McDIPPER, a novel 3D resolved model for the initial state of ultrarelativistic Heavy-Ion collisions based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. This framework is a initial-state Monte Carlo event generator which deposits the relevant conserved charges (energy, charge and baryon densities) both in the midrapidity and forward/backward regions of the collision. The event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the conserved charges can be extracted directly. In this work we present the centrality and collision energy dependence for the deposited conserved quantities at midrapidity and the full event, the so-called $4π$ solid angle range.
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Submitted 6 November, 2023;
originally announced November 2023.
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Dilepton polarization as a signature of plasma anisotropy
Authors:
Maurice Coquet,
Xiaojian Du,
Jean-Yves Ollitrault,
Soeren Schlichting,
Michael Winn
Abstract:
We propose the angular distribution of lepton pairs produced in ultrarelativistic heavy-ion collisions as a probe of thermalization of the quark-gluon plasma. We focus on dileptons with invariant masses large enough that they are produced through quark-antiquark annihilation in the early stages of the collision. The angular distribution of the lepton in the rest frame of the pair then reflects the…
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We propose the angular distribution of lepton pairs produced in ultrarelativistic heavy-ion collisions as a probe of thermalization of the quark-gluon plasma. We focus on dileptons with invariant masses large enough that they are produced through quark-antiquark annihilation in the early stages of the collision. The angular distribution of the lepton in the rest frame of the pair then reflects the angular distribution of quark momenta. At early times, the transverse pressure of the quark-gluon plasma is larger than its longitudinal pressure as a result of the fast longitudinal expansion, which results in an oblate lepton distribution. By contrast, direct (Drell-Yan) production by quarks and antiquarks from incoming nuclei, whose momenta are essentially longitudinal, results in a prolate distribution. As the invariant mass increases, Drell-Yan gradually becomes the dominant source of dilepton production, and the lepton distribution evolves from oblate to prolate. The invariant mass at which the transition occurs is highly sensitive to the equilibration time of the quark-gluon plasma or, equivalently, the shear viscosity over entropy ratio $η/s$ in the early stages of the collision.
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Submitted 6 June, 2024; v1 submitted 1 September, 2023;
originally announced September 2023.
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The McDIPPER: A novel saturation-based 3+1D initial state model for Heavy Ion Collisions
Authors:
Oscar Garcia-Montero,
Hannah Elfner,
Sören Schlichting
Abstract:
We present a new 3D resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. The McDIPPER framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge and baryon densities) both in the midrapidity and f…
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We present a new 3D resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the $k_\perp$-factorized Color Glass Condensate hybrid approach. The McDIPPER framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge and baryon densities) both in the midrapidity and forward/backward regions of the collision. This event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the relevant conserved charges can be computed directly. In the present work we have included the leading order contributions to the light flavor parton densities. As a feature, the model can be systematically improved in the future by adding next-to-leading order calculations (in the CGC hybrid framework), and extended to lower energies by including sub-eikonal corrections the channels included. We present relevant observables, such as the eccentricities and flow decorrelation, as tests of this new approach.
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Submitted 22 August, 2023;
originally announced August 2023.
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Pre-equilibrium photons from the early stages of heavy-ion collisions
Authors:
Oscar Garcia-Montero,
Aleksas Mazeliauskas,
Philip Plaschke,
Sören Schlichting
Abstract:
We use QCD kinetic theory to compute photon production in the chemically equilibrating Quark-Gluon Plasma created in the early stages of high-energy heavy-ion collisions. We do a detailed comparison of pre-equilibrium photon rates to the thermal photon production. We show that the photon spectrum radiated from a hydrodynamic attractor evolution satisfies a simple scaling form in terms of the speci…
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We use QCD kinetic theory to compute photon production in the chemically equilibrating Quark-Gluon Plasma created in the early stages of high-energy heavy-ion collisions. We do a detailed comparison of pre-equilibrium photon rates to the thermal photon production. We show that the photon spectrum radiated from a hydrodynamic attractor evolution satisfies a simple scaling form in terms of the specific shear viscosity $η/s$ and entropy density $dS/dζ\sim {\scriptstyle \left(Tτ^{1/3}\right)^{3/2}}_\infty$. We confirm the analytical predictions with numerical kinetic theory simulations. We use the extracted scaling function to compute the pre-equilibrium photon contribution in $\sqrt{s_{NN}}=2.76\,\text{TeV}$ 0-20\% PbPb collisions. We demonstrate that our matching procedure allows for a smooth switching from pre-equilibrium kinetic to thermal hydrodynamic photon production. Finally, our publicly available implementation can be straightforwardly added to existing heavy ion models.
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Submitted 3 April, 2024; v1 submitted 18 August, 2023;
originally announced August 2023.
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Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field Theory
Authors:
Stephan Ochsenfeld,
Sören Schlichting
Abstract:
Viscous hydrodynamics serves as a successful mesoscopic description of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to investigate, how such an effective description emerges from the underlying microscopic dynamics we calculate the hydrodynamic and non-hydrodynamic modes of linear response in the sound channel from a first-principle calculation in kinetic theory.…
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Viscous hydrodynamics serves as a successful mesoscopic description of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to investigate, how such an effective description emerges from the underlying microscopic dynamics we calculate the hydrodynamic and non-hydrodynamic modes of linear response in the sound channel from a first-principle calculation in kinetic theory. We do this with a new approach wherein we discretize the collision kernel to directly calculate eigenvalues and eigenmodes of the evolution operator. This allows us to study the Green's functions at any point in the complex frequency space. Our study focuses on scalar theory with quartic interaction and we find that the analytic structure of Green's functions in the complex plane is far more complicated than just poles or cuts which is a first step towards an equivalent study in QCD kinetic theory.
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Submitted 15 November, 2023; v1 submitted 8 August, 2023;
originally announced August 2023.
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Universality of sound modes in kinetic theory
Authors:
Xiaojian Du,
Stephan Ochsenfeld,
Sören Schlichting
Abstract:
We present a simple approach to extract hydrodynamic sound modes and non-hydrodynamic modes in kinetic theories from response functions of the energy-momentum tensor. By comparing the response functions in four types of kinetic theories, namely the Relaxation-Time Approximation, scalar $φ^4$ theory, SU(3) Yang-Mills theory and QCD kinetic theory, we find a remarkable degree of universality for the…
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We present a simple approach to extract hydrodynamic sound modes and non-hydrodynamic modes in kinetic theories from response functions of the energy-momentum tensor. By comparing the response functions in four types of kinetic theories, namely the Relaxation-Time Approximation, scalar $φ^4$ theory, SU(3) Yang-Mills theory and QCD kinetic theory, we find a remarkable degree of universality for the sound mode, even beyond the hydrodynamic regime.
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Submitted 17 July, 2023;
originally announced July 2023.
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System size dependence of pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
Authors:
Victor E. Ambruş,
Sören Schlichting,
Clemens Werthmann
Abstract:
We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description, in order to determine the range of applicability of an effective description in relativistic viscous hydrodynamics. We find that hydrodynamics provides a quantitatively accurate description of collective flow when the average inverse Reynolds number $\mathrm{Re}^{-1}$ is sufficiently small and…
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We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description, in order to determine the range of applicability of an effective description in relativistic viscous hydrodynamics. We find that hydrodynamics provides a quantitatively accurate description of collective flow when the average inverse Reynolds number $\mathrm{Re}^{-1}$ is sufficiently small and the early pre-equilibrium stage is properly accounted for. By determining the breakdown of hydrodynamics as a function of system size and energy, we find that it is quantitatively accurate in central lead-lead collisions at LHC energies, but should not be used in typical proton-lead or proton-proton collisions, where the development of collective flow can not accurately be described within hydrodynamics.
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Submitted 17 July, 2023;
originally announced July 2023.
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Universality of energy-momentum response in kinetic theories
Authors:
Xiaojian Du,
Stephan Ochsenfeld,
Sören Schlichting
Abstract:
We study the response of the energy-momentum tensor in several kinetic theories, from the simple relaxation time approximation (RTA) to Quantum Chromodynamics (QCD). Irrespective of the differences in microscopic properties, we find a remarkable degree of universality in the response functions from conformal theories. We find that the response to scalar perturbations in kinetic theory can be effec…
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We study the response of the energy-momentum tensor in several kinetic theories, from the simple relaxation time approximation (RTA) to Quantum Chromodynamics (QCD). Irrespective of the differences in microscopic properties, we find a remarkable degree of universality in the response functions from conformal theories. We find that the response to scalar perturbations in kinetic theory can be effectively described by a pair of one hydrodynamic sound mode and one non-hydrodynamic mode. We find that even beyond the range of validity of hydrodynamics, the energy-momentum response in position space can be effectively described by one single mode with non-trivial dispersion relation and residue.
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Submitted 15 June, 2023;
originally announced June 2023.
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Attractors for Flow Observables in 2+1D Bjorken Flow
Authors:
Victor E. Ambruş,
Sören Schlichting,
Clemens Werthmann
Abstract:
We examine the capabilities of second-order Israel-Stewart-type hydrodynamics to capture the early-time behaviour of the quark-gluon plasma created in heavy-ion collisions. We point out that at very early times, the dynamics of the fireball is governed by the local 0+1-D Bjorken flow attractor due to the rapid expansion along the longitudinal direction. Discrepancies between hydrodynamics and kine…
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We examine the capabilities of second-order Israel-Stewart-type hydrodynamics to capture the early-time behaviour of the quark-gluon plasma created in heavy-ion collisions. We point out that at very early times, the dynamics of the fireball is governed by the local 0+1-D Bjorken flow attractor due to the rapid expansion along the longitudinal direction. Discrepancies between hydrodynamics and kinetic theory in this far-from-equilibrium regime leads to disagreement at the level of late-time observables, such as elliptic flow. We show that rescaling the initial energy-density profile for hydrodynamics accounts for such discrepancies, restoring agreement with kinetic theory for large opacities (small shear viscosity / large system size / high energy).
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Submitted 21 February, 2023;
originally announced February 2023.
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Pre-Equilibrium Evolution of Conserved Charges with ICCING Initial Conditions
Authors:
Patrick Carzon,
Mauricio Martinez,
Jacquelyn Noronha-Hostler,
Philip Plaschke,
Soeren Schlichting,
Matthew Sievert
Abstract:
Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far-from-equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. K$φ$MP$φ$ST is one such pre-equilibrium model that propagates the energy-moment…
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Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far-from-equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. K$φ$MP$φ$ST is one such pre-equilibrium model that propagates the energy-momentum tensor by decomposing it into the background and fluctuations around that background, whose evolution is captured by Green's functions. We extend this formalism to include conserved charges and calculate the corresponding non-equilibrium Green's functions in the relaxation time approximation. The ICCING algorithm initializes conserved charges in the initial state by sampling $g \rightarrow q\bar{q}$ splitting probabilities and is, thus, perfectly positioned to implement Green's functions for charge propagation. We show that this method alters the initial state charge geometries and is applicable in central to mid-central collisions.
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Submitted 6 December, 2023; v1 submitted 11 January, 2023;
originally announced January 2023.
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Studying the 3+1D structure of the Glasma using the weak field approximation
Authors:
Andreas Ipp,
Markus Leuthner,
David I. Müller,
Soeren Schlichting,
Pragya Singh
Abstract:
We extend the weak field approximation for the Glasma beyond the boost-invariant approximation, which allows us to compute rapidity-dependent observables in the early stages of heavy-ion collisions. We show that in the limit of small fields, the weak field approximation agrees quantitatively with non-perturbative lattice simulations. Furthermore, we demonstrate that the rapidity profile of the tra…
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We extend the weak field approximation for the Glasma beyond the boost-invariant approximation, which allows us to compute rapidity-dependent observables in the early stages of heavy-ion collisions. We show that in the limit of small fields, the weak field approximation agrees quantitatively with non-perturbative lattice simulations. Furthermore, we demonstrate that the rapidity profile of the transverse pressure is determined by longitudinal color correlations within the colliding nuclei.
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Submitted 19 December, 2022;
originally announced December 2022.
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Tracing the emergence of collectivity phenomena in small systems
Authors:
B Schenke,
S Schlichting,
P Singh
Abstract:
We study initial state momentum correlations and event-by-event geometry in p+Pb collisions at $\sqrt{s}=5.02~\rm TeV$ by following the approach of extending the IP-Glasma model to 3D using JIMWLK rapidity evolution. On examining the non-trivial rapidity dependence of the observables, we find that the geometry is correlated over large rapidity intervals, while the initial state momentum correlatio…
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We study initial state momentum correlations and event-by-event geometry in p+Pb collisions at $\sqrt{s}=5.02~\rm TeV$ by following the approach of extending the IP-Glasma model to 3D using JIMWLK rapidity evolution. On examining the non-trivial rapidity dependence of the observables, we find that the geometry is correlated over large rapidity intervals, while the initial state momentum correlations have a relatively short range in rapidity. Based on our results, we discuss implications for the relevance of both effects in explaining the origin of collective phenomena in small systems.
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Submitted 5 December, 2022;
originally announced December 2022.
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Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
Authors:
Victor E. Ambrus,
S. Schlichting,
C. Werthmann
Abstract:
We evaluate the full opacity dependence of collective flow in high-energy heavy-ion collisions within a microscopic kinetic description based on the Boltzmann equation in the conformal relaxation time approximation. By comparing kinetic theory calculations to hydrodynamic and hybrid simulations for an average initial state, we point out shortcomings and inaccuracies of hydrodynamic models and pres…
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We evaluate the full opacity dependence of collective flow in high-energy heavy-ion collisions within a microscopic kinetic description based on the Boltzmann equation in the conformal relaxation time approximation. By comparing kinetic theory calculations to hydrodynamic and hybrid simulations for an average initial state, we point out shortcomings and inaccuracies of hydrodynamic models and present modified simulation setups to improve them.
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Submitted 11 May, 2023; v1 submitted 25 November, 2022;
originally announced November 2022.
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Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
Authors:
Victor E. Ambrus,
S. Schlichting,
C. Werthmann
Abstract:
We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description in the conformal relaxation time approximation, in order to determine the range of applicability of an effective description in relativistic viscous hydrodynamics. We find that hydrodynamics provides a quantitatively accurate description of collective flow when the average inverse Reynolds numb…
▽ More
We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description in the conformal relaxation time approximation, in order to determine the range of applicability of an effective description in relativistic viscous hydrodynamics. We find that hydrodynamics provides a quantitatively accurate description of collective flow when the average inverse Reynolds number is sufficiently small and the early pre-equilibrium stage is properly accounted for. We further discuss the implications of our findings for the (in)applicability of hydrodynamics in proton-proton, proton-nucleus and light nucleus collisions.
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Submitted 18 April, 2023; v1 submitted 25 November, 2022;
originally announced November 2022.
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Chiral instabilities & the fate of chirality imbalance in non-Abelian plasmas
Authors:
Sören Schlichting,
Sayantan Sharma
Abstract:
We present a first principles study of chiral plasma instabilities and axial charge transfer in non-Abelian plasmas with a strong gauge-matter coupling $g^2N_f=64$, by performing $3+1$ D real-time classical-statistical lattice simulation with dynamical fermions. We explicitly demonstrate for the first time that -- unlike in an Abelian plasma -- the transfer of chirality from the matter sector to t…
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We present a first principles study of chiral plasma instabilities and axial charge transfer in non-Abelian plasmas with a strong gauge-matter coupling $g^2N_f=64$, by performing $3+1$ D real-time classical-statistical lattice simulation with dynamical fermions. We explicitly demonstrate for the first time that -- unlike in an Abelian plasma -- the transfer of chirality from the matter sector to the gauge fields occurs predominantly due to topological sphaleron transitions. We elaborate on the similarities and differences of the axial charge dynamics in cold Abelian $U(1)$ and non-Abelian $SU(2)$ plasmas, and comment on the implications of our findings for the study of anomalous transport phenomena, such as the chiral magnetic effect in QCD matter.
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Submitted 4 September, 2023; v1 submitted 21 November, 2022;
originally announced November 2022.
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Statistical analysis of initial state and final state response in heavy-ion collisions
Authors:
Nicolas Borghini,
Marc Borrell,
Nina Feld,
Hendrik Roch,
Sören Schlichting,
Clemens Werthmann
Abstract:
We develop a general decomposition of an ensemble of initial density profiles in terms of an average state and a basis of modes that represent the event-by-event fluctuations of the initial state. The basis is determined such that the probability distributions of the amplitudes of different modes are uncorrelated. Based on this decomposition, we quantify the different types and probabilities of ev…
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We develop a general decomposition of an ensemble of initial density profiles in terms of an average state and a basis of modes that represent the event-by-event fluctuations of the initial state. The basis is determined such that the probability distributions of the amplitudes of different modes are uncorrelated. Based on this decomposition, we quantify the different types and probabilities of event-by-event fluctuations in Glauber and Saturation models and investigate how the various modes affect different characteristics of the initial state. We perform simulations of the dynamical evolution with KoMPoST and MUSIC to investigate the impact of the modes on final-state observables and their correlations.
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Submitted 10 March, 2023; v1 submitted 2 September, 2022;
originally announced September 2022.
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Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
Authors:
Xiaojian Du,
Michal P. Heller,
Sören Schlichting,
Viktor Svensson
Abstract:
We use principal component analysis to study the hydrodynamic attractor in Yang-Mills kinetic theory undergoing the Bjorken expansion with Color Glass Condensate initial conditions. The late time hydrodynamic attractor is characterized by a single principal component determining the overall energy scale. How it is reached is governed by the disappearance of single subleading principal component ch…
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We use principal component analysis to study the hydrodynamic attractor in Yang-Mills kinetic theory undergoing the Bjorken expansion with Color Glass Condensate initial conditions. The late time hydrodynamic attractor is characterized by a single principal component determining the overall energy scale. How it is reached is governed by the disappearance of single subleading principal component characterizing deviations of the pressure anisotropy, the screening mass and the scattering rate. We find that for wide range of couplings the approach to the hydrodynamic attractor at late times is well described by an exponential. Its decay rate dependence on the coupling turns out to translate into a simple dependence on the shear viscosity to entropy density ratio.
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Submitted 30 March, 2022;
originally announced March 2022.
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Snowmass 2021 White Paper: Electron Ion Collider for High Energy Physics
Authors:
R. Abdul Khalek,
U. D'Alesio,
M. Arratia,
A. Bacchetta,
M. Battaglieri,
M. Begel,
M. Boglione,
R. Boughezal,
R. Boussarie,
G. Bozzi,
S. V. Chekanov,
F. G. Celiberto,
G. Chirilli,
T. Cridge,
R. Cruz-Torres,
R. Corliss,
C. Cotton,
H. Davoudiasl,
A. Deshpande,
X. Dong,
A. Emmert,
S. Fazio,
S. Forte,
Y. Furletova,
C. Gal
, et al. (83 additional authors not shown)
Abstract:
Electron Ion Collider (EIC) is a particle accelerator facility planned for construction at Brookhaven National Laboratory on Long Island, New York by the United States Department of Energy. EIC will provide capabilities of colliding beams of polarized electrons with polarized beams of proton and light ions. EIC will be one of the largest and most sophisticated new accelerator facilities worldwide,…
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Electron Ion Collider (EIC) is a particle accelerator facility planned for construction at Brookhaven National Laboratory on Long Island, New York by the United States Department of Energy. EIC will provide capabilities of colliding beams of polarized electrons with polarized beams of proton and light ions. EIC will be one of the largest and most sophisticated new accelerator facilities worldwide, and the only new large-scale accelerator facility planned for construction in the United States in the next few decades. The versatility, resolving power and intensity of EIC will present many new opportunities to address some of the crucial and fundamental open scientific questions in particle physics. This document provides an overview of the science case of EIC from the perspective of the high energy physics community.
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Submitted 17 October, 2022; v1 submitted 24 March, 2022;
originally announced March 2022.
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Rapidity dependence of initial state geometry and momentum correlations in p+Pb collisions
Authors:
Bjoern Schenke,
Soeren Schlichting,
Pragya Singh
Abstract:
Event geometry and initial state correlations have been invoked as possible explanations of long range azimuthal correlations observed in high multiplicity p+p and p+Pb collisions. We study the rapidity dependence of initial state momentum correlations and event-by-event geometry in $\sqrt{s}=5.02~\rm{TeV}$ p+Pb collisions within the 3+1D IP-Glasma model~\cite{Schenke:2016ksl}, where the longitudi…
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Event geometry and initial state correlations have been invoked as possible explanations of long range azimuthal correlations observed in high multiplicity p+p and p+Pb collisions. We study the rapidity dependence of initial state momentum correlations and event-by-event geometry in $\sqrt{s}=5.02~\rm{TeV}$ p+Pb collisions within the 3+1D IP-Glasma model~\cite{Schenke:2016ksl}, where the longitudinal structure is governed by JIMWLK rapidity evolution of the incoming nuclear gluon distributions. We find that the event geometry is correlated across large rapidity intervals whereas initial state momentum correlations are relatively short range in rapidity. Based on our results, we discuss implications for the relevance of both effects in explaining the origin of collective phenomena in small systems.
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Submitted 21 January, 2022;
originally announced January 2022.
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Transverse mass scaling of dilepton radiation off a quark-gluon plasma
Authors:
Maurice Coquet,
Xiaojian Du,
Jean-Yves Ollitrault,
Soeren Schlichting,
Michael Winn
Abstract:
The spectrum of dileptons produced by the quark-gluon plasma in an ultrarelativistic nucleus-nucleus collision depends only, to a good approximation, on the transverse mass M_t of the dilepton. This scaling is exact as long as transverse flow is negligible, and the system is in local thermal equilibrium. We implement a state-of-the-art modelization of kinetic and chemical equilibration in the earl…
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The spectrum of dileptons produced by the quark-gluon plasma in an ultrarelativistic nucleus-nucleus collision depends only, to a good approximation, on the transverse mass M_t of the dilepton. This scaling is exact as long as transverse flow is negligible, and the system is in local thermal equilibrium. We implement a state-of-the-art modelization of kinetic and chemical equilibration in the early stages of the evolution to study the modifications of the spectrum. Violations of M_t scaling resulting from these effects are evaluated as a function of the shear viscosity to entropy ratio (eta/s) that controls the equilibration time. We determine the dependence of the spectrum on system size, centrality, rapidity, and collision energy. We show that the quark-gluon plasma produces more dileptons than the Drell-Yan process up to invariant masses of order M = 4 GeV. Due to different kinematics, for a given M_t , the dependence of the dilepton yield on M is opposite for the two processes, so that experiment alone can in principle determine which process dominates.
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Submitted 29 November, 2022; v1 submitted 27 December, 2021;
originally announced December 2021.
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Fermion and gluon spectral functions far from equilibrium
Authors:
Kirill Boguslavski,
Tuomas Lappi,
Sören Schlichting
Abstract:
Motivated by the quark-gluon plasma, we develop a simulation method to obtain the spectral function of (Wilson) fermions non-perturbatively in a non-Abelian gauge theory with large gluon occupation numbers [arXiv:2106.11319]. We apply our method to a non-Abelian plasma close to its non-thermal fixed point, i.e., in a far-from-equilibrium self-similar regime, and find mostly very good agreement wit…
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Motivated by the quark-gluon plasma, we develop a simulation method to obtain the spectral function of (Wilson) fermions non-perturbatively in a non-Abelian gauge theory with large gluon occupation numbers [arXiv:2106.11319]. We apply our method to a non-Abelian plasma close to its non-thermal fixed point, i.e., in a far-from-equilibrium self-similar regime, and find mostly very good agreement with perturbative hard loop (HTL) calculations. For the first time, we extract the full momentum dependence of the damping rate of fermionic collective excitations and compare our results to recent non-perturbative extractions of gluonic spectral functions in two and three spatial dimensions [arXiv:2101.02715, arXiv:1804.01966].
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Submitted 30 November, 2021;
originally announced December 2021.
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Splitting rates in QCD plasmas from a non-perturbative determination of the momentum broadening kernel $C(q_{\bot})$
Authors:
Soeren Schlichting,
Ismail Soudi
Abstract:
We exploit a recent non-perturbative determination of the momentum broadening kernel $C(b_{\bot})$ in impact parameter space \cite{Moore:2021jwe}, to determine the momentum space broadening kernel $C(q_{\bot})$ in high-temperature QCD plasmas. We show how to use the non-pertubatively determined kernel $C(q_{\bot})$ to compute the medium-induced splitting rates in a QCD plasma of finite size. We co…
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We exploit a recent non-perturbative determination of the momentum broadening kernel $C(b_{\bot})$ in impact parameter space \cite{Moore:2021jwe}, to determine the momentum space broadening kernel $C(q_{\bot})$ in high-temperature QCD plasmas. We show how to use the non-pertubatively determined kernel $C(q_{\bot})$ to compute the medium-induced splitting rates in a QCD plasma of finite size. We compare the resulting in-medium splitting rates to the results obtained with leading-order and next-to-leading order perturbative determinations of $C(q_{\bot})$, as well as with various approximations of the splitting employed in the literature. Generally, we find that the differences in the splitting rates due to the momentum broadening kernel are larger than the errors associated with approximations of the splitting rate.
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Submitted 27 May, 2022; v1 submitted 26 November, 2021;
originally announced November 2021.
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Critical dynamics of relativistic diffusion
Authors:
Dominik Schweitzer,
Sören Schlichting,
Lorenz von Smekal
Abstract:
We study the dynamics of self-interacting scalar fields with $Z_2$ symmetry governed by a relativistic Israel-Stuart type diffusion equation in the vicinity of a critical point. We calculate spectral functions of the order parameter in mean-field approximation as well as using first-principles classical-statistical lattice simulations in real-time. We observe that the spectral functions are well-d…
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We study the dynamics of self-interacting scalar fields with $Z_2$ symmetry governed by a relativistic Israel-Stuart type diffusion equation in the vicinity of a critical point. We calculate spectral functions of the order parameter in mean-field approximation as well as using first-principles classical-statistical lattice simulations in real-time. We observe that the spectral functions are well-described by single Breit-Wigner shapes. Away from criticality, the dispersion matches the expectations from the mean-field approach. At the critical point, the spectral functions largely keep their Breit-Wigner shape, albeit with non-trivial power-law dispersion relations. We extract the characteristic time-scales as well as the dynamic critical exponent $z$, verifying the existence of a dynamic scaling regime. In addition, we derive the universal scaling functions implied by the Breit-Wigner shape with critical power-law dispersion and show that they match the data. Considering equations of motion for a system coupled to a heat bath as well as an isolated system, we perform this study for two different dynamic universality classes, both in two and three spatial dimensions.
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Submitted 4 September, 2022; v1 submitted 4 October, 2021;
originally announced October 2021.
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Space-time structure of 3+1D color fields in high energy nuclear collisions
Authors:
Andreas Ipp,
David I. Müller,
Soeren Schlichting,
Pragya Singh
Abstract:
We perform an analytic calculation of the color fields in heavy-ion collisions by considering the collision of longitudinally extended nuclei in the dilute limit of the Color Glass Condensate effective field theory of high-energy QCD. Based on general analytic expressions for the color fields in the future light cone, we evaluate the rapidity profile of the transverse pressure within a simple spec…
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We perform an analytic calculation of the color fields in heavy-ion collisions by considering the collision of longitudinally extended nuclei in the dilute limit of the Color Glass Condensate effective field theory of high-energy QCD. Based on general analytic expressions for the color fields in the future light cone, we evaluate the rapidity profile of the transverse pressure within a simple specific model of the nuclear collision geometry and compare our results to 3+1D classical Yang-Mills simulations.
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Submitted 26 July, 2022; v1 submitted 10 September, 2021;
originally announced September 2021.
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Spectral function of fermions in a highly occupied non-Abelian plasma
Authors:
Kirill Boguslavski,
Tuomas Lappi,
Mark Mace,
Sören Schlichting
Abstract:
We develop a method to obtain fermion spectral functions non-perturbatively in a non-Abelian gauge theory with high occupation numbers of gauge fields. After recovering the free field case, we extract the spectral function of fermions in a highly occupied non-Abelian plasma close to its non-thermal fixed point, i.e., in a self-similar regime of the non-equilibrium dynamics. We find good agreement…
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We develop a method to obtain fermion spectral functions non-perturbatively in a non-Abelian gauge theory with high occupation numbers of gauge fields. After recovering the free field case, we extract the spectral function of fermions in a highly occupied non-Abelian plasma close to its non-thermal fixed point, i.e., in a self-similar regime of the non-equilibrium dynamics. We find good agreement with hard loop perturbation theory for medium-induced masses, dispersion relations and quasiparticle residues. We also extract the full momentum dependence of the damping rate of the collective excitations.
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Submitted 8 December, 2022; v1 submitted 21 June, 2021;
originally announced June 2021.
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Intermediate mass dileptons as pre-equilibrium probes in heavy ion collisions
Authors:
Maurice Coquet,
Xiaojian Du,
Jean-Yves Ollitrault,
Soeren Schlichting,
Michael Winn
Abstract:
The production of dileptons with an invariant mass in the range 1 GeV < M < 5 GeV provides unique insight into the approach to thermal equilibrium in ultrarelativistic nucleus-nucleus collisions. In this mass range, they are produced through the annihilation of quark-antiquark pairs in the early stages of the collision. They are sensitive to the anisotropy of the quark momentum distribution, and a…
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The production of dileptons with an invariant mass in the range 1 GeV < M < 5 GeV provides unique insight into the approach to thermal equilibrium in ultrarelativistic nucleus-nucleus collisions. In this mass range, they are produced through the annihilation of quark-antiquark pairs in the early stages of the collision. They are sensitive to the anisotropy of the quark momentum distribution, and also to the quark abundance, which is expected to be underpopulated relative to thermal equilibrium. We take into account both effects based on recent theoretical developments in QCD kinetic theory, and study how the dilepton mass spectrum depends on the shear viscosity to entropy ratio that controls the equilibration time. We evaluate the background from the Drell-Yan process and argue that future detector developments can suppress the additional background from semileptonic decays of heavy flavors.
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Submitted 20 September, 2021; v1 submitted 15 April, 2021;
originally announced April 2021.
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Hot spots and gluon field fluctuations as causes of eccentricity in small systems
Authors:
S. Demirci,
T. Lappi,
S. Schlichting
Abstract:
We calculate eccentricities in high energy proton-nucleus collisions, by calculating correlation functions of the energy density field of the Glasma immediately after the collision event at proper time tau = 0. We separately consider the effects of color charge and geometrical hot spot fluctuations, analytically performing the averages over both in a dilute-dense limit. We show that geometric fluc…
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We calculate eccentricities in high energy proton-nucleus collisions, by calculating correlation functions of the energy density field of the Glasma immediately after the collision event at proper time tau = 0. We separately consider the effects of color charge and geometrical hot spot fluctuations, analytically performing the averages over both in a dilute-dense limit. We show that geometric fluctuations of hot spots inside the proton are the dominant source of eccentricity whereas color charge fluctuations only give a negligible correction. The size and number of hot spots are the most important parameters characterizing the eccentricities.
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Submitted 11 January, 2021;
originally announced January 2021.
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Equilibration of weakly coupled QCD plasmas
Authors:
Xiaojian Du,
Sören Schlichting
Abstract:
We employ a non-equilibrium Quantum Chromodynamics (QCD) kinetic description to study the kinetic and chemical equilibration of the Quark-Gluon Plasma (QGP) at weak coupling. Based on our numerical framework, which explicitly includes all leading order processes involving light flavor degrees of freedom, we investigate the thermalization process of homogeneous and isotropic plasmas far-from equili…
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We employ a non-equilibrium Quantum Chromodynamics (QCD) kinetic description to study the kinetic and chemical equilibration of the Quark-Gluon Plasma (QGP) at weak coupling. Based on our numerical framework, which explicitly includes all leading order processes involving light flavor degrees of freedom, we investigate the thermalization process of homogeneous and isotropic plasmas far-from equilibrium and determine the relevant time scales for kinetic and chemical equilibration. We further simulate the longitudinally expanding pre-equilibrium plasma created in ultrarelativistic heavy-ion collisions at zero and non-zero density of the conserved charges and study its microscopic and macroscopic evolution towards equilibrium.
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Submitted 16 December, 2020;
originally announced December 2020.
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Equilibration of the Quark-Gluon Plasma at finite net-baryon density in QCD kinetic theory
Authors:
Xiaojian Du,
Sören Schlichting
Abstract:
We explore the out-of-equilibrium dynamics of the Quark-Gluon Plasma at zero and finite net-baryon density based on an effective kinetic theory of Quantum Chromo Dynamics (QCD). By investigating the isotropization of the longitudinal pressure, we determine the relevant time and temperature scales for the onset of viscous hydrodynamics, and quantify the dependence on the chemical composition of the…
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We explore the out-of-equilibrium dynamics of the Quark-Gluon Plasma at zero and finite net-baryon density based on an effective kinetic theory of Quantum Chromo Dynamics (QCD). By investigating the isotropization of the longitudinal pressure, we determine the relevant time and temperature scales for the onset of viscous hydrodynamics, and quantify the dependence on the chemical composition of the QGP. By extrapolating our results to realistic coupling strength, we discuss phenomenological consequences regarding the role of the pre-equilibrium phase at different collision energies.
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Submitted 16 December, 2020;
originally announced December 2020.
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Hadronization of correlated gluon fields
Authors:
Moritz Greif,
Carsten Greiner,
Simon Plätzer,
Björn Schenke,
Sören Schlichting
Abstract:
Following an explicit example, we present the chain of steps required for an event-by-event description of hadron production in high energy hadronic and nuclear collisions. We start from incoming nuclei, described in the Color Glass Condensate effective theory, whose collision creates the gluon fields of the glasma. Individual gluons are then sampled from the gluon fields' Husimi (smeared Wigner)…
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Following an explicit example, we present the chain of steps required for an event-by-event description of hadron production in high energy hadronic and nuclear collisions. We start from incoming nuclei, described in the Color Glass Condensate effective theory, whose collision creates the gluon fields of the glasma. Individual gluons are then sampled from the gluon fields' Husimi (smeared Wigner) distributions, and clustered using a new spacetime based algorithm. Clusters are fed into the Herwig event generator, which performs the hadronization, conserving energy and momentum. We discuss the physical implications of smearing and problems with the quasi particle picture for the studied processes. We compute spectra of charged hadrons and identified particles and their azimuthal momentum anisotropies, and address systematic uncertainties on observables, resulting from the general lack of detailed knowledge of the hadronization mechanism.
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Submitted 15 December, 2020;
originally announced December 2020.
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Kinetic and Chemical Equilibration of Quark-Gluon Plasma
Authors:
Xiaojian Du,
Sören Schlichting
Abstract:
We solve a leading-order QCD kinetic theory with light quarks and gluon degrees of freedom to study the non-equilibrium dynamics of the quark-gluon plasma (QGP). By including both elastic and inelastic scatterings for quarks and gluon, the model is proficient to describe kinetic and chemical equilibration of the QGP, and thus connects the initial (semi-) hard production of partons at early times w…
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We solve a leading-order QCD kinetic theory with light quarks and gluon degrees of freedom to study the non-equilibrium dynamics of the quark-gluon plasma (QGP). By including both elastic and inelastic scatterings for quarks and gluon, the model is proficient to describe kinetic and chemical equilibration of the QGP, and thus connects the initial (semi-) hard production of partons at early times with the hydrodynamic description of a near-thermalized quark-gluon plasma after the first fm/c of the collision. Within this approach, we investigate the time scales and mechanisms for kinetic and chemical equilibration of the QGP at zero and non-zero net-baryon density and elaborate on the connections to jet quenching physics and hydrodynamics.
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Submitted 26 October, 2020;
originally announced October 2020.