Dynamical Thermalization in Heavy-Ion Collisions - Indico
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Dynamical Thermalization in Heavy-Ion
Collisions
Mahbobeh Jafarpour
Ph.D Supervisor: Prof. Klaus Werner
with:
Prof. Elena Bratkovskaya & Dr. Vadym Voronyuk
Collaboration of Nantes-Frankfurt-Dubna groups
RPP 6-9 Apr. 2021
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Outline Outline
Introduction
QGP, Particle accelerators
Heavy-ion collision Models
EPOS
Initial condition, PBGRT
From participants to prehadrons
EPOS2PHSD interface
PHSD
Non-equilibrium Quantum Field Theory
QGP, DQPM, Generalized transport equation and hadronization
Formation of hadrons and partons
Results
Particle Production, Elliptic Flow, Transverse Momentum,
Transverse Mass
Conclusion and outlook
Appendix
References
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Introduction Quark-Gluon Plasma, Particle accelerators
From QCD to QGP:
At low Tc and low µB → Hadronic
gas
At low Tc and high µB → gas of
neutron
For Tc > 175M eV → QGP
At high Tc and µB → 0, Big Bang
Figure: Phase diagram of nuclear
matter [1].
Current Accelerators:
SPS & LHC, CERN
RHIC, BNL, New York
Future Accelerators:
FAIR, Germany
Figure: Space-time evolution of NICA, Russia
HIC. 3/27
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Introduction Heavy-ion collision Models
EPOS: Energy conserving multiple scattering Partons, parton ladder
and strings Off-shell remnantes Saturation [2, 3].
INITIAL CONDITION: A Gribov-Regge multiple scattering approach is employed (PBGRT).
CORE-CORONA SEPARATION: based on momentum and density of string segments.
VISCOUS HYDRODYNAMIC EXPANSION: Using core part and cross-over equation of state
(EOS) compatible with lattice QCD.
STATISTICAL HADRONIZATION: employing Cooper-Frye procedure and equilibrium hadron
distribution.
FINAL STATE HADRONIC CASCADE: applying the UrQMD model.
PHSD: Parton Hadron String Dynamics [4, 5].
INITIAL A+A COLLISION: leads to formation of strings that decays to pre-hadrons, done by
PYTHIA.
QGP FORMATION: based on local energy-density.
QGP STAGE: evolution based on off-shell transport eqs. derived by Kadanoff-Baym eqs. with the
DQPM defining the parton spectral function i.e. masses and widths.
HADRONIZATION: massive off-shell partons with broad spectral functions hadronize to off-shell
baryons and mesons.
HADRONIC PHASE: evolution based on the off-shell transport eqs. with hadron-hadron
interaction. 4/27
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Introduction Purpose
Purpose: We endeavor to employ a sophisticated EPOS approach to
determine the initial distribution of matter (partons/hadrons) and then
use PHSD for the evolution of matter in a non-equilibrium transport
approach.
Figure: EPOS particles production hyper-surface initial condition for PHSD model. Zero time
corresponds to maximum overlapping.
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EPOS Initial Condition and PBGRT
Initial Condition in EPOS:
Parton Based Gribov Regge Theory (PBGRT) [6]:
Hard/Soft processes, Energy conservation by multiple Pomeron
exchange
Calculation of elastic/inelastic Cross-Sections (uncut ladder, soft
contribution)
Particle production [7] (cut ladder, semi-hard/hard contribution)
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EPOS Pre-hadrons
From participants to pre-hadrons
Constituting the ”initial condition” to ”pre-hadronization”:
ZB1 ZB1
ZA1 ZA1
rope
ZB2 ZB2
ZA2 ZA2
projectile+target → pomerons → string segments → core/corona
part → rope segments → core/corona pre-hadrons
rope segments: longitudinal color field, consider in 3D, larger
string tension and transverse momentum.
core pre-hadrons : decay of rope segments/clusters based on
Microcanonical treatment.
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EPOS Microcanonical decay
Microcanonical decay
The Monte Carlo approaches are applied to generate ensembles of n
hadrons hi with their four-momenta pi based on probability
distribution [8]:
dP = Cvol Cdeg Cident Cf lav dΦN RP S (1)
n
3
Y
dΦN RP S = δ(M − ΣEi )δ(Σp~i ) d pi f or large n (2)
i=1
Z n
Z Y
dΦN RP S = 2Ei × dΦLIP S (3)
i=1
π(2π)n−2 n−1
Y n−1
Y
dΦLIP S (M ; m1 , ..., mn ) = p(Mi+1 ; Mi , mi+1 ) dMi f or small n (4)
M i=1 i=2
ΦLIP S for two body decay:
π
ΦLIP S (M ; ma , mb ) = p(M ; ma , mb ) (5)
M
The integration limits for n-body:
Figure: Successive two-body
Mi−1 + mi ≤ Mi (6) decays. 8/27
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EPOS2PHSD Interface
EPOS+PHSD overview
Z
to PHSD
t=0
The principle problem: EPOS uses light-cone dynamics, PHSD
uses real-time dynamics.
EPOS/PHSD ”core pre-hadrons”: parents/children of rope
segments
EPOS/PHSD ”corona pre-hadrons”: spectators, high pt particles,
particles that formed before start time of PHSD
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PHSD Initial condition to start QGP
The energy momentum tensor T µν in PHSD in each cell [9]:
pµi pνi
Z ∞ 3
d pi
T µν (x) = g fi (Ei ) (7)
0 (2π)3 Ei
Qx Qy Qz ( = energy density
−Qx P π xy π xz
µν x with P = pressure
T = −Qy −π xy (8)
Py π yz Q = momentum density
π = shear stress
−Qz −π xz −π yz Pz
The energy density of the cells in Local Rest Frame (LRF) in PHSD4
is:
E0 E/γ
0 = 0 = = 2 (9)
V V ×γ γ
where p
γ = 1/ 1 − β 2 , β~ = Σi p~i /Σi Ei , = Σi Ei /Vcell , Vcell = ∆x∆y∆z
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 10 / 27PHSD Energy density evolution in PHSD
Energy density evolution in PHSD
Au-Au@200GeV,b=7fm,Num=20, STPHSD=0.05, yl=2.3, yr=0.9
time = 0.055 fm/c .ime = 0.064 fm/c .ime = 0.699 fm/c
5000 30
10 Energy Density (GeV/fm^3)
4000
4000 25
5
3000 20
3000
0 15
2000 2000
−5 10
1000 1000
5
−10 PHSD, P ,tons+Hadrons
EPOS+PHSD
0 0 0
time = 1.504 fm/c .ime = 3.11 fm/c .ime = 6.31 fm/c
2.5 1.0
10 8
2.0 0.8
5 6
1.5 0.6
1(fm)
0
4
1.0 0.4
−5
2 0.5 0.2
−10
0 0.0 0.0
.ime = 12.687 fm/c time = 33.5 fm/c .ime = 88.156 fm/c
0.35 0.04
10 0.10
0.30
5 0.08 0.03
0.25
0.20 0.06
0 0.02
0.15 0.04
−5 0.10 0.01
0.02
0.05
−10
0.00 0.00 0.00
−10 −5 0 5 10 210 25 0 5 10 −10 −5 0 5 10
0(fm) 11/27
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Nonequilibrium Quantum Field Theory in PHSD
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Time evolution of particles in PHSD space time
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RESULTS
Comparing the
Particle Production, Elliptic Flow (v2 ), Transverse Momentum (pT )
and Transverse Mass (mT ) for Au-Au@200GeV
With different simulations:
EPOS+PHSD, EPOS+hydro, EPOS-hydro, pure PHSD
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 14 / 27Results Particle Production
Particle Production:
Au-Au@200GeV
(b) EPOS+PHSD, EPOS+hydro
(a) EPOS+PHSD EPOS-hydro
Good agreement to the real DATA X
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 15 / 27Results Elliptic Flow
Elliptic Flow v2 :
3 2 P∞
1
E d 3N = 2π d N
pt dpt dy
(1 + n=1 2vn cos(n(φ − ΨRP )))
d p
vn (pt , y) =< cos(n(φ − ΨRP )) >, v2 = elliptic flow,
ΨRP =reaction plane angle [10].
Au-Au@200GeV
Figure: EPOS+PHSD, EPOS+hydro, EPOS-hydro, pure PHSD
NEAR TO THE THERMALIZATION X 16/27
Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 16 / 27Results Transverse Momentum and Transverse Mass
Transverse Momentum and Transverse Mass: Au-Au@200GeV
Figure: EPOS+PHSD, EPOS+hydro, EPOS-hydro, pure PHSD
Figure: EPOS+PHSD, EPOS+hydro, EPOS-hydro, pure PHSD
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 17 / 27Conclusion and Outlook Summary and Conclusion
Summary and Conclusion:
The project done to merge the two models commenting the issue of
different framework (Miles coordinates and Minkowski space-time).
Comparison of space-time evolution by EPOS+PHSD with
EPOS+hydro also EPOS-hydro and pure PHSD.
Considering observables like charged particles production, v2 , pT ,
mT . High pT has not been improved yet by EPOS+PHSD.
Outlook:
Comparison EPOS+PHSD with different range energies from
RHIC to LHC for various systems like p-p and Au-Au collisions.
Investigation of other ”flow behaviors”; vn =1; 3; 4; ...
Investigation of electromagnetic probes, photon and dilepton
production.
Checking heavy flavor particles behavior
Checking EPOS(+hydo)+PHSD to study the high pt part
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 19 / 27Appendix Elliptic Flow
Appendix
Anistropic radial Flow (Depends on Initial State Fluctuation):
Fourier expansion:
3 1 d2 N P∞
E dd3Np = 2π pt dpt dy (1 + n=1 2vn cos(n(φ − ΨRP )))
vn (pt , y) =< cos(n(φ − ΨRP )) >, v1 =directed flow, v2 = elliptic flow,
v3 =triangle flow, ΨRP =reaction plane angle
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PHSD group:
Figure: https://theory.gsi.de/ ebratkov/phsd-project/PHSD/index5.html
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 21 / 27Appendix PHSD, QGP, DQPM
QGP phase in PHSD
To investigate the dynamics and properties of the medium, one can
employ the transport equation and spectral function:
Using spectral function A in DQPM [11]:
P˜
A(p) = 2γp0
(pµ pµ −M 2 )2 +4γ 2 p20
, Γ̃ = 2γp0 , M2 = m2 + Re R
To have Masses M 2 and widths γ of partons.
Entropy density sdqp is a grandcanonical quantity in DQPM which
leads to measure the pressure s = ∂P
∂T , energy density = T s − P ,
interaction measure W (T ) = (T ) − 3P (T ) and scalar mean-field
dVp (ρs )
Us (ρs ) = dρ s
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 22 / 27Appendix QGP, Transport equation and Hadronization
Generalized transport equation [12]:
1 < 1 <
P¯< > P¯> <
2 ĀΓ̄[{M̄ , iG } − Γ̄ {Γ̄, M̄ .iG }] = i iḠ − iḠ
Ā =spectral function, Γ̄ =Width, M̄ = mass function in Wigner-space, ¯ =self-energy
P
Collision term = i ¯< iḠ> − ¯> iḠ<
P P
Employing the test-particle Ansatz
iG< (P0 , P, t, X) ≈
PN 1
i=1 2P0 δ (3) (X − Xi (t))δ (3) (P − Pi (t))δ(P0 − i (t))
to transport equation → derive the equation of motion by
neglecting the collision term → dXi /dt, dPi /dt, di /dt, obtain the
coordinates, momentum and energy of particles in time t.
Hadronization:
As the system expands and cools down, the energy density drops
until hadronization occurs. The colored off-shell partons with
broad spectral function are combined into off-shell colorless
hadrons.
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Masses and widths of quarks/antiquarks and gluons in DQPM:
2 P µ2 2
Mg2 (T ) = g6 [(Nc + 21 Nf )T 2 + 12 g πq2 ], γg (T ) = Nc g8πT ln g2c2
Nc2 −1 2 2 µ2q/q̄ Nc2 −1 g 2 T 2c
2 (T ) =
Mq/q̄ 8Nc g [T + π2
], γq/q̄ (T ) = 2Nc 8π ln g 2
g 2 (T /Tc ) =running coupling, µ=chemicl potential, Nc , Nf : Number of color and flavor
Entropy density in DQPM:
R d4 p ∂nB (p0 /T )
sdqp = −dg (2π) 4 ∂T (Imln(−∆− 1) + ImΠRe∆) −
R d4 p ∂nF ((p0 −µq )/T )
(Imln(−Sq−1 ) + Im q ReSq ) −
P
dq (2π)4 ∂T
R d4 p ∂nF ((p0 +µq )/T )
(Imln(−Sq̄−1 ) + Im q̄ ReSq̄ )
P
dq̄ (2π) 4 ∂T
Bose distribution function=nB (p0 /T ) = (exp(p0 /T ))−1
Fermi distribution function=nF ((p0 − µq )/T ) = (exp((p0 − µq )/T ) + 1)−1
propagator of gluon: ∆−1 = pµ pµ − Π, quasiparticle self-energy for gluon= Π
propagator of quark: Sq−1 = pµ pµ − q ,
P P
quasiparticle self-energy for quark: q
propagator of antiquark: Sq̄ = pµ pµ − q̄ ,
P P
quasiparticle self-energy for antiquark: q̄
degeneracy: dq = dq̄ = 2Nc Nf = 18, dg = 2(Nc2 − 1) = 16
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The equation of motion for testparticles in transport equation:
P˜
P˜R 2i −Pi2 −M02 −Re R
dXi 1 1
dt = 1−Ci 2i [2Pi + ∆pi Re (i) + Γ˜
(i)
∆pi Γ˜(i) ]
(i)
P˜
P˜ 2i −Pi2 −M02 −Re R
dPi
dt
1
= 1−C 1
i 2i
[∆xi Re R(i) + Γ˜(i)
(i)
∆pi Γ˜(i) ]
P˜R P˜
di 1 1 ∂Re (i) 2i −Pi2 −M02 −Re R ˜
(i) ∂ Γ(i)
dt = 1−Ci 2i [ ∂t + Γ˜(i) ∂t ]
Ci stands the function of a Lorentz-factor and transforms the system time t to the eigentime of
particles i which is given by the energy derivatives:
P˜R P˜
1 ∂Re (i) 2i −Pi2 −M02 −Re R (i) ∂ Γ˜(i)
C(i) = 2i [ ∂i + Γ˜(i) ∂i ]
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References I
[1] J. C. Collins and M. J. Perry, “Superdense matter: neutrons or asymptotically free quarks?,”
Physical Review Letters, vol. 34, no. 21, p. 1353, 1975.
[2] K. Werner, F.-M. Liu, and T. Pierog, “Parton ladder splitting and the rapidity dependence of
transverse momentum spectra in deuteron-gold collisions at the bnl relativistic heavy ion collider,”
Physical Review C, vol. 74, no. 4, p. 044902, 2006.
[3] T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner, “Epos lhc: Test of collective
hadronization with data measured at the cern large hadron collider,” Physical Review C, vol. 92,
no. 3, p. 034906, 2015.
[4] W. Cassing and E. Bratkovskaya, “Parton transport and hadronization from the dynamical
quasiparticle point of view,” Physical Review C, vol. 78, no. 3, p. 034919, 2008.
[5] W. Cassing and E. Bratkovskaya, “Parton–hadron–string dynamics: An off-shell transport approach
for relativistic energies,” Nuclear Physics A, vol. 831, no. 3-4, pp. 215–242, 2009.
[6] H. J. Drescher, M. Hladik, S. Ostapchenko, T. Pierog, and K. Werner, “Parton-based gribov–regge
theory,” Physics Reports, vol. 350, no. 2-4, pp. 93–289, 2001.
[7] K. Werner, B. Guiot, I. Karpenko, and T. Pierog, “Analyzing radial flow features in p-pb and p-p
collisions at several tev by studying identified-particle production with the event generator epos3,”
Physical Review C, vol. 89, no. 6, p. 064903, 2014.
[8] K. Werner and J. Aichelin, “Microcanonical treatment of hadronizing the quark-gluon plasma,”
Physical Review C, vol. 52, no. 3, p. 1584, 1995.
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Mahbobeh Jafarpour Dynamical Thermalization in HIC RPP 6-9 Apr. 2021 26 / 27References
References II
[9] R. Marty, E. Bratkovskaya, W. Cassing, and J. Aichelin, “Observables in ultrarelativistic heavy-ion
collisions from two different transport approaches for the same initial conditions,” Physical Review C,
vol. 92, no. 1, p. 015201, 2015.
[10] R. Snellings, “Elliptic flow: a brief review,” New Journal of Physics, vol. 13, no. 5, p. 055008, 2011.
[11] W. Cassing, “From kadanoff-baym dynamics to off-shell parton transport,” The European Physical
Journal Special Topics, vol. 168, no. 1, pp. 3–87, 2009.
[12] W. Cassing and S. Juchem, “Semiclassical transport of particles with dynamical spectral functions,”
Nuclear Physics A, vol. 665, no. 3-4, pp. 377–400, 2000.
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