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

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

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Gaussian rapidity profile from collisions in Glasma simulations SEWM 2018, Barcelona, Spain June 28, 2018 Andreas Ipp based on D. Gelfand, AI, D. Mller, Phys. Rev. D94 (2016) no.1, 014020 AI, D. Mller, Phys. Lett. B (2017) 771 AI, D.

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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

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SEWM, June 28, 2018 Andreas Ipp 2

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

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SEWM, June 28, 2018 Andreas Ipp 3

Initjal state: Lorentz-contracted nuclei (color glass condensate)

Collision event

Glasma (τ ≈ 0 - 1 fm/c): quasi-classical fjelds (classical fjeld equatjons) QGP (τ ≈ 1 - 10 fm/c): quarks and gluons (relatjvistjc viscous hydrodynamics) (almost) isotropic and in thermal equilibrium Hadronizatjon (τ ≈ 10 fm/c): confjnement transitjon → hadron formatjon Hadronic gas (τ ≈ 10 - 15 fm/c): hadrons (kinetjc transport theory) Freeze-out (τ ≈ 15 fm/c): interactjons stop

scope of this project

Stages of a heavy-ion collision

1fm/c≈3.3⋅10

−24s≈3.3ys

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SEWM, June 28, 2018 Andreas Ipp 4 Figure from L. McLerran: Proceedings of ISMD08, p.3-18 (2008)

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 ...

  • Hard partons = classical color charges
  • 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]

generates..

Color glass condensate

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SEWM, June 28, 2018 Andreas Ipp 5

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

Dμ F

μ ν(τ, xT)=0

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SEWM, June 28, 2018 Andreas Ipp 6

Finite nucleus thickness

  • extended color currents
  • boost-invariance lost
  • solve full 3+1 D Yang-Mills

equation with currents → use Colored particle-in-cell (CPIC) in laboratory frame

Dμ F

μ ν(t , z , xT)=J1 ν+J2 ν

DμJ

μ(t , z , xT)=0

Dμ≡∂μ+ig[Aμ,⋅]

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SEWM, June 28, 2018 Andreas Ipp 7

Colored particle-in-cell (CPIC)

[A. Dumitru, Y. Nara, M. Strickland: PRD75:025016 (2007)]

CPIC: non-Abelian generalization of the particle-in-cell method from plasma physics.

Gaussian profjle with thickness σ.

σ≈R/ γ

[McLerran, Venugopalan: PRDD49 (1994) 3352-3355]

(Au, RHIC)

⟨ ^ ρ

a(xT)^

ρ

b(x' T)⟩=g 2μ 2δ (2)(xT−x'T)δ ab

μ

2≈0.5GeV

Nucleus model: 2D McLerran- Venugopalan (MV) model . Infrared regulatjon

m≈200 MeV

(no random longitudinal structure)

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SEWM, June 28, 2018 Andreas Ipp 8

Implementation

Lappi, Phys.Letu. B643 (2006) 11-16

Lattjce equatjons of motjon Contjnuum equatjons of motjon Parallel transporters (gauge links):

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SEWM, June 28, 2018 Andreas Ipp 9

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 10

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 11

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 12

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 13

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 14

3D energy density

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SEWM, June 28, 2018 Andreas Ipp 15

Main observable: energy-momentum tensor

  • Build from electric and magnetjc fjelds
  • Average over confjguratjons and integrate over transverse plane
  • Diagonalize, obtain local rest-frame energy density

Observables

T

μ ν(x)

T

μ ν(x)

Ei

a(x), Bi a(x)

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SEWM, June 28, 2018 Andreas Ipp 16

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

at

  • Fit to Gaussian profjle (dashed)
  • Dependency on thickness (or

rather )

  • Strong dependency on IR

regulator, but gives realistjc shape

  • However: no hydrodynamic

expansion included

  • Limited rapidity interval

Rapidity profiles

(a)m=0.2GeV (b)m=0.4GeV (c)m=0.8GeV

ηs∈(−1,1) τ=1fm/c

√s

m=0.2GeV

[RHIC data: Bearden et al., PRL 94 (2005) 162301]

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SEWM, June 28, 2018 Andreas Ipp 17

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

at

  • Fit to Gaussian profjle (dashed)
  • Dependency on thickness (or

rather )

  • Strong dependency on IR

regulator, but gives realistjc shape

  • However: no hydrodynamic

expansion included

  • Limited rapidity interval

Rapidity profiles

ηs∈(−1,1) τ=1fm/c

√s

m=0.2GeV

(a)m=0.2GeV (b)m=0.4GeV (c)m=0.8GeV

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SEWM, June 28, 2018 Andreas Ipp 18

Compare local velocity

  • f glasma to free streaming

conditjon

Free streaming glasma

τ=1 τ=2 v=z/t

Lines (almost) on top of each

  • ther.

Black solid: measured vz Red dashed: free streaming vfs = z/t

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SEWM, June 28, 2018 Andreas Ipp 19

  • Transverse pressure generated by longitudinal fjelds
  • Boost-invariant case: initjal conditjons at for longitudinal E and

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]

Transverse pressure distribution

pT(x) τ=0 pT

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SEWM, June 28, 2018 Andreas Ipp 20

Dispersion-free propagation

For details see: AI, D. Müller, arXiv:1804.01995

Standard Wilson action: implicit part semi-implicit part Discretized action for the semi-implicit scheme:

etc.

Variational integrator: Discretized equations of motion from discretized action

with

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SEWM, June 28, 2018 Andreas Ipp 21

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

  • pen source:

github.com/openpixi/openpixi (Java) gitlab.com/monolithu/pyglasma3d (Python, Cython) C++ version in preparation

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SEWM, June 28, 2018 Andreas Ipp 22

Backup slides

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SEWM, June 28, 2018 Andreas Ipp 23

Pressure anisotropy at midrapidity

  • bserve very slow isotropization

longitudinal pressure pL(z) transverse pressure pT(z)