Evolution of Flow and Effective Temperatures of the Parton Matter from the AMPT Model

Zi-Wei Lin （林子威） Department of Physics East Carolina University

This study was motivated by Miklos

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Miklos as the PhD Advisor

My 1st Quark Matter, Monterey 1995 My 1st heavy ion workshop, Berkeley 1993

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Miklos as the PhD Advisor We also learned to work hard

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Columbia 1996

September 25-26, 2015 at CCNU

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To simulate high energy heavy ion collisions Choices: We need: Initial particle/energy production Soft+hard model (+ string melting), CGC, pQCD, ... Parton cascade (ZPC, MPC, BAMPS), equilibration, thermalization, initial flow CGC, AdS/CFT, … Pre-equilibrium interactions:

Space-time evolution of QGP

Parton cascade (ZPC, MPC, BAMPS), (ideal, viscous, anisotropic) hydrodynamics, ...

Hadronization /QCD phase transition

Quark coalescence/parton recombination, string fragmentation, Cooper-Frye, statistical hadronization, independent fragmentation, rate equations, ...

Hadronic interactions

Hadron cascade (ART, RQMD, UrQMD, ...), thermal model (w/ freezeout temperatures), …

AMPT currently includes the green components. GyulassyFest: A symposium on future RHIC and LHC Physics

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Structure of AMPT v2.xx (String Melting version)

A+B

HIJING1.0: minijet partons (hard), excited strings (soft), spectator nucleons

Generate parton space-time

“Melt” strings to q & qbar via intermediate hadrons

ZPC (parton cascade) Partons freeze out Hadronization (Quark Coalescence)

Extended ART (hadron cascade) Hadrons freeze out (at a global cut-off time); then strong-decay all remaining resonances

Final particle spectra GyulassyFest: A symposium on future RHIC and LHC Physics

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Structure of AMPT v2.xx (String Melting version)

A+B

HIJING1.0: minijet partons (hard), excited strings (soft), spectator nucleons

LBNL Symposium, 2009

Miklos & Xin-Nian Wang: PRD44 (1991) …, Comput.Phys.Commun.83 (1994). çMiklos

around that time: LBNL Workshop, 1993

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Structure of AMPT v2.xx (String Melting version)

A+B

HIJING1.0: minijet partons (hard), excited strings (soft), spectator nucleons

ZPC (parton cascade) Miklos & Bin Zhang / Yang Pang: PRC58 (1998), Comput.Phys.Commun.109 (1998)

Quark Matter, Monterey 1995 GyulassyFest: A symposium on future RHIC and LHC Physics

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1 central Au+Au event at 200AGeV from String Melting (SM) AMPT σp=3mb 60fm-long box Beam axes

See, e.g. in middle region (near mid-rapidity):

coalescence of q (red) and qbar (cyan)

Particle # vs time GyulassyFest: A symposium on future RHIC and LHC Physics

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Motivation of this study Use thermodynamic variables to describe the bulk parton matter as modeled by a transport model (usually in non-equilibrium)

This provides •  a link between transport model and hydrodynamics •  a transport-model soft background for jet quenching studies Results mostly from arXiv:1403.6321 = PRC 90, 014904 (2014). We only consider partons within mid space-time rapidity |η|<1/2 GyulassyFest: A symposium on future RHIC and LHC Physics

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Constraining parameters of the String Melting AMPT model Goal: fit low-pt (<2GeV/c) π & K data on dN/dy, pT –spectra & v2(pT) in central (0-5%) and mid-central (20-30%) 200AGeV Au+Au collisions (RHIC) and 2760AGeV Pb+Pb collisions (LHC). HIJING1.0

SM-AMPT [1]

SM-AMPT in [2]

SM-AMPT in this Study [3]

Lund string

a

0.5

2.2

0.5

0.55 for RHIC, 0.30 for LHC

Lund string

b (GeV-2)

0.9

0.5

0.9

0.15

αs in parton cascade

N/A

0.47

0.33

0.33

Parton cross section

N/A

~ 6 mb

1.5 mb

3 mb

Model describes

pp, …

v2 & HBT dN/dy & v2 (LHC) dN/dy, pT & v2 not dN/dy or pT not pT (RHIC & LHC) [1] ZWL, Ko, Li, Zhang and Pal, PRC72 (2005); etc. [2] Xu and Ko, PRC83 (2011). [3] ZWL, PRC90 (2014).

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Constraining parameters of the String Melting AMPT model dN/dy of π & K:

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Constraining parameters of the String Melting AMPT model pT -spectra of π & K (in central collisions):

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Constraining parameters of the String Melting AMPT model v2 of π & K (in mid-central collisions):

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Evolution of flow, parton densities and energy-momentum Flow velocity for a cell is defined here as ! ! β = ∑ pi / ∑ Ei

(

)(

)

X

X

Transverse flow in central RHIC collisions:

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Evolution of flow, parton densities and energy-momentum Transverse flow in central RHIC collisions at 2 locations along x:

βy≈0 due to symmetry Flow ≈ βx : shape depends on location; decrease seen at late times; develops earlier near edge of overlap volume

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Evolution of flow, parton densities and energy-momentum Transverse flow in central RHIC collisions: dependence on x-position:

Significant flow velocity near the edge even at t=1fm/c Flow at early times: ~ Pre-equilibrium flow, modeled by elastic parton cascade here

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Evolution of flow, parton densities and energy-momentum We then evaluate variables in the local rest frame of partons in each volume cell: energy density ε number density n average PT, P, ET, E, then use each variable v to extract the “effective” temperature Tv.

If partons in a sub-volume are in complete chemical and thermal equilibrium, then all these “effective” temperatures would be the same. If these “effective” temperatures are different in a sub-volume, then the partons are not in full (chemical and thermal) equilibrium.

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Evolution of extracted effective temperatures è Extract effective temperatures using relations for a massless ideal QGP with the Boltzmann momentum distribution:

Tε4 ε = 3gB 2 π Tε4T εT = 3gB 4π Tn3 n = gB 2 π

< p> T< p> = 3 4 < pT > T< pT > = 3π < pT2 > T< p2 > = , T 8

The center 1 fm2 cell in central RHIC GyulassyFest: A symposium on future RHIC and LHC Physics

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Evolution of extracted effective temperatures The effective temperatures are all different;

Tn > Tε >> T è

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in the plasma phase.

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Evolution of extracted effective temperatures Tε >> T is the case for the center cell of all 4 collision systems:

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Evolution of extracted effective temperatures How about other transverse locations within |η|<1/2 ?

è Tε > T over the inner part of the overlap volume, is the opposite over the outer part. This is the case for all 4 collision systems. GyulassyFest: A symposium on future RHIC and LHC Physics

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Summary Using the String Melting AMPT model, we find: effective temperatures extracted from different variables (ε, n, , , … in the rest frame of each cell) can be quite different è the parton matter from AMPT is far from full equilibrium

Tn > T< pT > and Tε > T over the inner part of the overlap volume è

The parton system is over-populated there: the parton density n & ε >> the expected density for an ideal QGP at temperature T< pT >

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Miklos as a Friend Thanks to Miklos, I gained •  PhD degree •  Love for good coffee •  Love for sushi/sashimi •  … •  Sensitivity to MSG (味精) Columbia 1996

To dear Miklos: Enjoy life after retirement. Enjoy your beautiful wife & wonderful children. May your heart stay forever young. GyulassyFest: A symposium on future RHIC and LHC Physics

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Extra Slides

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Outline

Introduction to A Multi-Phase Transport (AMPT) model Constraining parameters of the AMPT model Evolution of flow, densities and energy-momentum Evolution of extracted effective temperatures Summary

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Structure of AMPT v1.xx (default version)

A+B

HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectators

ZPC (parton cascade) Partons freeze out Hadronization (Lund string fragmentation)

Extended ART Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances

Final particle spectra GyulassyFest: A symposium on future RHIC and LHC Physics

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Individual components of AMPT HIJING1.0

Two component model

ZPC

parton cascade

(soft strings + hard minijets)

(elastic collisions only)

Hadronization Lund string fragmentation (Default AMPT) or Quark coalescence (String Melting AMPT) Extended ART Hadron cascade, including secondary interactions for π ρ ω η K K* φ n p Δ N * (1440) N * (1535) Λ Σ Ξ Ω

deuteron

All other particles with PYTHIA flavor codes have no secondary interactions, but they can be produced (from HIJING, string fragmentation, or quark coalescence), e.g. D Ds J /Ψ B ϒ. Each hadron has an explicit isospin/charge. KS0 and KL0 are also produced at the end of hadron cascade. GyulassyFest: A symposium on future RHIC and LHC Physics

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A Multi-Phase Transport (AMPT) model First public release of AMPT source codes: ~ April 2004. Detailed physics descriptions in the long paper: ZWL, Ko, Li, Zhang & Pal, PRC 72, 064901 (2005). "Official" versions v1.11/v2.11 (2004) and v1.21/v2.21 (2008) are available at https://karman.physics.purdue.edu/OSCAR & http://myweb.ecu.edu/linz/ampt/ More versions, including later test (t) versions, are available at http://myweb.ecu.edu/linz/ampt/

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Individual components of AMPT: parton cascade Cross section based on gg → gg in leading-order pQCD:

A screening mass μ regulates the divergence:

Elastic collisions only:

gg → gg

in Default AMPT, massless gluons.

in String Melting AMPT, but using the same gg cross section; using current quark masses: u 5.6MeV, d 9.9MeV, s 199MeV, c 1.35 GeV, …

qi q j → qi q j , qi q j → qi q j , qi q j → qi q j

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The same Au+Au event at 200AGeV from the Default AMPT model

Beam axes

Dynamics is time-dilated at large rapidities

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A central Au+Au event at 200AGeV from the default AMPT σp=3mb 60fm-long box Beam axes

Dynamics is time-dilated at large rapidities

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Structure of AMPT v1.xx (Default version)

A+B

HIJING1.0: minijet partons (hard), excited strings (soft), spectator nucleons

Generate parton space-time ZPC (parton cascade) Partons freeze out Hadronization (Lund string fragmentation)

Extended ART (hadron cascade) Hadrons freeze out (at a global cut-off time); then strong-decay all remaining resonances

Final particle spectra GyulassyFest: A symposium on future RHIC and LHC Physics

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A Multi-Phase Transport (AMPT) model Why string melting version of AMPT? Estimate the initial energy density in AA collisions:

dET / dy dET / dy ε0 ~ ≈ 6 2 3 ~ 2.5 πR τ0 150 fm SPS RHIC Nuclear radius Proper formation time, taken as 1 fm/c

20 GeV/fm3 LHC

>>critical energy density for QCD phase transition: εc ~ O(1) GeV/fm3

èAt high-enough energies, hadronic matter such as strings cannot exist early on, they should be represented by a high density partonic matter: è

the string melting version of AMPT

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Lin&Ko, PRC65

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A central Au+Au event at 200AGeV from the String Melting AMPT View on the beam axis

σp=3mb Box size 60fm

E.g. middle region (near mid-rapidity):

coalescence of q (red) and qbar (cyan) GyulassyFest: A symposium on future RHIC and LHC Physics

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A Multi-Phase Transport (AMPT) model In default version of AMPT: strings are in the high density overlap area, but not in parton cascade. At high energies: èstrings should not exist, instead the energy should be in partonic matter.

Initial condition in default AMPT: soft (strings) & hard (minijets) ¤ Beam axis

minijets

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A Multi-Phase Transport (AMPT) model The same central 200AGeV Au+Au event (at t=5 fm/c) from AMPT-Default vs AMPT-String Melting (SM)

Beams from the left & right sides

AMPT-Default: only minijets are in parton cascade, dense hadron stage starts early.

AMPT-SM: early parton stage dominates; hadron stage starts later.

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A b=10fm Au+Au event at 200AGeV from String Melting AMPT

View on the beam axis

Initial overlap region has an irregular geometry

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Evolution of flow, parton densities and energy-momentum

Example: the center cell in RHIC central

All evaluated in the rest frame of each cell GyulassyFest: A symposium on future RHIC and LHC Physics

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Evolution of extracted effective temperatures Check temperature in a side cell: its rest frame Tε in cms vs Tε in the center-of-mass frame

For massless partons in a cell that can be described by ε and P, we can obtain 1/4

Tεexpected

2 % " 1− β = Tεcms $ ' 2 # 1+ β / 3 &

β: flow of the cell in the center-of-mass frame GyulassyFest: A symposium on future RHIC and LHC Physics

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Evolution of extracted effective temperatures

Tε >> T is true for the center cell of all 4 collision systems:

4 3 Note: we find Tε ≈ Tn T , so

Tε > T gives Tn > Tε > T

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Over-population of partons

Tε > T for each cell in the inner part of the overlap volume è Energy and number densities ε, n are too high, relative to the expected values for an ideal QGP at T (that has the same as partons in the cell) è The local parton system is over-populated. GyulassyFest: A symposium on future RHIC and LHC Physics

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Over-population of partons Transverse plane of LHC mid-central (b=7.8fm) Let us define 2 terms:

yHfmL 8

QGP cell: cell with ε >1.05 GeV/fm3 Over-populated cell: QGP cell with

6 ‡ ‡

Tε > T

-8

Ÿ QGP cells at t=0.2 fm/c n Over-populated cells at t=0.2 fm/c Δ Over-populated cells at t=3 fm/c

-6

‡ Û ‡ Û -4 ‡ Û Û

‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡

‡ Û ‡ Û ‡ Û ‡ Û ‡ Û -2 ‡ Û ‡ Û ‡ Û ‡ Û ‡

‡ Û ‡ 4Û ‡ Û ‡ Û ‡ Û ‡ 2Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û 0 ‡ Û ‡ Û ‡-2Û ‡ Û ‡ Û ‡ Û ‡-4Û ‡ Û

‡

‡

‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û

‡ Û ‡ Û ‡ Û ‡ Û ‡ Û 2 ‡ Û ‡ Û ‡ Û ‡ Û

‡

‡

‡

‡

‡

‡ ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û ‡ Û

‡ ‡ Û ‡ Û 4 ‡ Û Û

6

8

xHfmL

‡

-6

Over-population in inner part of overlap volume; many over-populated cells even after several fm/c GyulassyFest: A symposium on future RHIC and LHC Physics

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Over-population of partons

Transverse area: 50-70% of initial QGP cells are over-populated. After 2-3 fm/c, all QGP cells are over-p.

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Over-population of partons Evaluate parton phase-space density function f(p) in center cell of LHC central: then compare with equilibrium functions 12N f 16 − p/T fQGP ( p) = gB e , or quantum fQGP ( p) = p/T + p/T . e −1 e +1 fails in magnitude fails in slope

If quarks/antiquark densities are limited by the Pauli principle è Gluons must be over-populated. GyulassyFest: A symposium on future RHIC and LHC Physics

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Over-population of partons Compare f(p) in center cell of LHC central with non-equilibrium functions: 16γ g 12N f γ q − p/T non−eq fQGP,Boltzmann ( p) = (16γ g +12N f γ q ) e , or fQGP ( p) = p/T + p/T . e −1 e +1

γ g & γ q are gluon & quark phase-space occupancy factors, respectively Set T as T , then match ε of the cell èan equation for γ g and γ q

γ g ∈ [23.1,25.1]

γ g ∈ [11.1,13.1]

Pauli principle γ q ∈ [0,1]

⇒ γ gmax & γ gmin : range of γ g

f(p) can be described well by non-equilibrium functions, with γ g >> 1 GyulassyFest: A symposium on future RHIC and LHC Physics

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Over-population of partons We may use another set of non-equilibrium functions: µ g /T 12N f 16e non−eq fQGP ( p) = p/T + ( p−µq )/T . e −1 e +1 µ g & µq are gluon & quark/antiquark “chemical potential”, respectively

µq ∈ (-∞,µqmax ) ⇒ µ gmax & µ gmin : µ g ∈ (µ gmin ,0.36) GeV

µ g ∈ (µ gmin ,1.0) GeV

range of µ g Will get a new figure: same

µ gmax

as before

f(p) can be described well by non-equilibrium functions, with µ g >> T GyulassyFest: A symposium on future RHIC and LHC Physics

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Over-population of partons Can also use gluon “chemical potential” µ g to represent gluon over-population:

γg ≡ e

" % $ µg ' $$ T ''

# T &

,

range of γ g ⇒ range of µ g

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Over-population of partons For the center cell: Tε 548MeV = ≈ 1.7 T 322MeV

εT = ET n ⇒ T<4εT=> TTn3 ⇒ Tε4 ≈ TTn3

3

4

" T % " T % n ⇒ = $$ n '' ≈ $$ ε '' = 1.74 ≈ 8.4 n (T ) # T & # T & The actual parton density n >> expected density for an ideal QGP at temperature T

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Evolution of extracted effective temperatures

Tε in RHIC central over the transverse plane:

Note again: for partons within |η|<1/2

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Evolution of extracted effective temperatures This is the case in all 4 collision systems:

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Summary Effective temperatures extracted from different variables (ε, n, , , … in the rest frame of each cell) can be quite different è the parton matter from AMPT-SM is not in full equilibrium

Tε > T is seen over the inner part of the overlap volume

èThe parton system (at least the gluons) is over-populated there, often by a large factor.

Parton phase-space distributions from the constrained AMPT-SM model •  cannot be described by QGP in full equilibrium (Boltzmann or quantum) •  can be described well by non-equilibrium QGP (with phase-space occupancy factors γ g & γ q ) A large gluon over-population gives GyulassyFest: A symposium on future RHIC and LHC Physics

γ g >> 1, or µ g >> T September 25-26, 2015 at CCNU

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