Gaussian rapidity profile from collisions in Glasma simulations - PowerPoint PPT Presentation

Gaussian rapidity profile from collisions in Glasma simulations SEWM 2018, Barcelona, Spain June 28, 2018 Andreas Ipp based on D. Gelfand, AI, D. Müller, Phys. Rev. D94 (2016) no.1, 014020 AI, D. Müller, Phys. Lett. B (2017) 771 AI, D. Müller, arXiv:1804.01995 Institute for Theoretical Physics, Vienna University of Technology, Austria

Outline Simulation of early stages of heavy-ion collisions ● color-glass-condensate (CGC) framework – colored particle-in-cell (CPIC) – beyond boost-invariance – Numerical results ● energy density at different rapidities – comparison to RHIC data – Berndt Müller, arXiv:1309.7616 SEWM, June 28, 2018 Andreas Ipp 2

Stages of a heavy-ion collision Freeze-out ( τ ≈ 15 fm/ c ): interactjons stop Hadronic gas ( τ ≈ 10 - 15 fm/ c ) : hadrons (kinetjc transport theory) Hadronizatjon ( τ ≈ 10 fm/ c ) : confjnement transitjon → hadron formatjon QGP ( τ ≈ 1 - 10 fm/ c ) : quarks and gluons (relatjvistjc viscous hydrodynamics) (almost) isotropic and in thermal equilibrium Glasma ( τ ≈ 0 - 1 fm/ c ) : quasi-classical fjelds (classical fjeld equatjons) Collision event 0 Initjal state: Lorentz-contracted nuclei (color glass condensate) − 24 s ≈ 3.3ys 1fm / c ≈ 3.3 ⋅ 10 scope of this project SEWM, June 28, 2018 Andreas Ipp 3

Color glass condensate Nuclei at ultrarelatjvistjc speeds can be described by classical efgectjve theory in the color glass condensate (CGC) framework. [Gelis, Iancu, Jalilian-Marian, Venugopalan, Ann.Rev.Nucl.Part.Sci.60:463-489,2010] Large gluon occupatjon numbers → coherent, classical gluon fjeld Split degrees of freedom into ... o Hard partons = classical color charges generates.. o Sofu gluons = classical gauge fjeld • Statjc fjeld confjguratjon due to tjme dilatjon. • Collision of two such classical fjelds creates the Glasma . [Gelis, Int.J.Mod.Phys. A28 (2013) 1330001] Figure from L. McLerran: Proceedings of ISMD08, p.3-18 (2008) SEWM, June 28, 2018 Andreas Ipp 4

Boost-invariant CGC collision • color glass condensate (CGC): hard and soft degrees of freedom, weak coupling • infinitely thin color currents • boost-invariant solution • solve Yang-Mills equations numerically in 2+1 D μ ν (τ , x T )= 0 D μ F SEWM, June 28, 2018 Andreas Ipp 5

Finite nucleus thickness • extended color currents • boost-invariance lost • solve full 3+1 D Yang-Mills equation with currents μ ν ( t , z , x T )= J 1 ν + J 2 ν D μ F μ ( t , z , x T )= 0 D μ J D μ ≡∂ μ + ig [ A μ , ⋅] → use Colored particle-in-cell (CPIC) in laboratory frame SEWM, June 28, 2018 Andreas Ipp 6

Colored particle-in-cell (CPIC) CPIC: non-Abelian generalization of the particle-in-cell method from plasma physics. [A. Dumitru, Y. Nara, M. Strickland: PRD75:025016 (2007)] Nucleus model: 2D McLerran- Venugopalan (MV) model . [McLerran, Venugopalan: PRDD49 (1994) 3352-3355] a ( x T )^ b ( x ' T )⟩= g 2 μ 2 δ ( 2 ) ( x T − x ' T )δ ab ⟨ ^ ρ ρ 2 ≈ 0.5GeV μ (Au, RHIC) Gaussian profjle with thickness σ . Infrared regulatjon σ≈ R / γ m ≈ 200 MeV (no random longitudinal structure) SEWM, June 28, 2018 Andreas Ipp 7

Implementation Lappi, Phys.Letu. B643 (2006) 11-16 Contjnuum equatjons of motjon Lattjce equatjons of motjon Parallel transporters (gauge links): SEWM, June 28, 2018 Andreas Ipp 8

3D energy density SEWM, June 28, 2018 Andreas Ipp 9

3D energy density SEWM, June 28, 2018 Andreas Ipp 10

3D energy density SEWM, June 28, 2018 Andreas Ipp 11

3D energy density SEWM, June 28, 2018 Andreas Ipp 12

3D energy density SEWM, June 28, 2018 Andreas Ipp 13

3D energy density SEWM, June 28, 2018 Andreas Ipp 14

Observables μ ν ( x ) T Main observable: energy-momentum tensor μ ν ( x ) a ( x ) , B i a ( x ) • T E i Build from electric and magnetjc fjelds • Average over confjguratjons and integrate over transverse plane • Diagonalize, obtain local rest-frame energy density SEWM, June 28, 2018 Andreas Ipp 15

Rapidity profiles Plot (space-tjme) rapidity profjle of local rest-frame energy density Compare to measured rapidity profjle of partjcle multjplicity (RHIC) and Landau model predictjon • Simulatjon data in interval τ= 1fm / c η s ∈(− 1,1 ) at • Fit to Gaussian profjle (dashed) • Dependency on thickness (or √ s rather ) • Strong dependency on IR m = 0.2GeV regulator, but gives realistjc shape • However: no hydrodynamic expansion included • Limited rapidity interval ( a ) m = 0.2GeV ( b ) m = 0.4GeV [RHIC data: Bearden et al., PRL 94 (2005) 162301] ( c ) m = 0.8GeV SEWM, June 28, 2018 Andreas Ipp 16

Rapidity profiles Plot (space-tjme) rapidity profjle of local rest-frame energy density Compare to measured rapidity profjle of partjcle multjplicity (RHIC) and Landau model predictjon • Simulatjon data in interval τ= 1fm / c η s ∈(− 1,1 ) at • Fit to Gaussian profjle (dashed) • Dependency on thickness (or √ s rather ) • Strong dependency on IR m = 0.2GeV regulator, but gives realistjc shape • However: no hydrodynamic expansion included • Limited rapidity interval ( a ) m = 0.2GeV ( b ) m = 0.4GeV ( c ) m = 0.8GeV SEWM, June 28, 2018 Andreas Ipp 17

Free streaming glasma τ= 1 τ= 2 Compare local velocity of glasma to free streaming v = z / t conditjon Lines (almost) on top of each other. Black solid: measured v z Red dashed: free streaming v fs = z / t SEWM, June 28, 2018 Andreas Ipp 18

Transverse pressure distribution • p T ( x ) Transverse pressure generated by longitudinal fjelds • τ= 0 Boost-invariant case : initjal conditjons at for longitudinal E and p T B fjelds, i.e. constant along the boundary of the forward light cone 3+1 Yang-Mills Holographic model [Casalderrey-Solana et al., PRL (2013) 181601] SEWM, June 28, 2018 Andreas Ipp 19

Dispersion-free propagation Standard Wilson action : Variational integrator : Discretized equations of motion from discretized action Discretized action for the semi-implicit scheme : semi-implicit part implicit part For details see: AI, D. Müller, arXiv:1804.01995 with etc. SEWM, June 28, 2018 Andreas Ipp 20

Conclusions & Outlook • Simulate CGC collisions in 3D+1 using Colored Partjcle-In-Cell is viable • Finite thickness breaks boost invariance → Gaussian rapidity profjles • Outlook : – Study efgect of random longitudinal structure – Observables at early tjmes: gluon productjon, two-partjcle correlatjons in rapidity, ... D. Gelfand, AI, D. Müller, Phys. Rev. D94 (2016) no.1, 014020 AI, D. Müller, Phys. Lett. B (2017) 771 AI, D. Müller, arXiv:1804.01995 open source: github.com/openpixi/openpixi (Java) gitlab.com/monolithu/pyglasma3d (Python, Cython) C++ version in preparation SEWM, June 28, 2018 Andreas Ipp 21

Backup slides SEWM, June 28, 2018 Andreas Ipp 22

Pressure anisotropy at midrapidity longitudinal pressure p L ( z ) observe very slow isotropization transverse pressure p T ( z ) SEWM, June 28, 2018 Andreas Ipp 23