Electromagnetic probes of a pure-glue initial state in
nucleus-nucleus collisions at LHC
Volodymyr Vovchenko
In collaboration with Iurii Karpenko, Mark Gorenstein, Leonid Satarov,
Igor Mishustin, Burkhard Kämpfer, and Horst Stoecker
based on arXiv:1604.06346
Transport Meeting
ITP, Frankfurt
24 May 2016
HGS-HIRe
Helmholtz Graduate School for Hadron and Ion Research
1 / 23
Outline
1
Introduction
2
Equation of state for chemically non-equilibrium QCD matter
3
Hydrodynamic modeling
4
Entropy production
5
Electromagnetic probes of pure glue initial state at LHC
6
Summary
2 / 23
Pure glue scenario
Pure glue scenario for ultrarelativistic HIC
Created system is initially quarkless
Yang-Mills theory is relevant
Possible appearance of deconfinement first-order phase transition
H. Stoecker et al., J. Phys. G 43, 015105 (2016).
3 / 23
(2+1)-flavor vs YM: equation of state
Equation of state for two limiting cases is known from lattice
(2+1)-flavor QCD
Pure SU(3)
Crossover transition from
hadrons to QGP
First-order deconfinement PT
Critical temperature at
Tc ' 270 MeV
No phase transitions at µ = 0
Borsanyi et al., PLB (2014)
Borsanyi et al., JHEP (2012)
6
30
Full QCD
5
Full QCD
5.21
Pure glue
Pure glue
25
3
P (GeV/fm )
= 3P
P/T
4
4
3
2
1.75
1
20
15
3
10
2
1
5
(a)
0
0
0
100
2
4
6
8
10
0
200
300
400
500
T (MeV)
600
700
800
0
20
40
60
80
100
3
(GeV/fm )
Very different number of degrees of freedom and temperature dependence,
but very similar p(e) dependence at high densities
4 / 23
(2+1)-flavor vs YM: ideal hydro results
Hydro evolution in limiting cases looks very different
Simulation: Glauber IC, normalization to get same T0 , top RHIC energy
Much longer evolution in pure SU(3) case, long phase transition,
glueballs at freeze-out
L.G. Pang, V. Vovchenko, H. Niemi, H. Stoecker, in preparation.
5 / 23
Modeling chemical non-equilibrium
In a more realistic scenario quarks appear after some time
Slow chem. equil. of quarks
Quarks suppressed compared to
gluons
1
PYTHIA init.cond.
b = 0fm
xT < 1.5 fm
|ηs|<0.5
fugacity
0.8
0.6
Rough estimates of equil. time
from transport models
0.4
0.2
gluons
quarks
0
0
1
2
3
4
5
t [fm]
T.S. Biro et al., PRC (1993)
Z. Xu, C. Greiner, PRC (2005)
J.P. Blaizot et al., NPA (2013)
1.0
Model by time-dependent
(anti)quark fugacity
Ansatz: λq (τ ) = 1 − exp ττ0 −τ
eq.
0.8
0.6
=0 fm/c
*
0.4
∗
Equation of state becomes
time-dependent
=1 fm/c
*
=5 fm/c
0.2
*
=10 fm/c
*
0.0
0.1
2
4
6
(fm/c)
8
10
12
6 / 23
Equation of state for chemical non-equilibrium QCD
Equation of state for intermediate 0 < λ < 1 needed
Lattice-based EoS for chemical non-equilibrium QCD
Ansatz: P (T , λ) = λ PFQ (T ) + (1 − λ) PPG (T )
Linear interpolation between limiting cases
Can be obtained in several analytic models,
i.e. within massless gas of partons1 and modified bag model
Pure glue
Pure glue
Full QCD
400
Full QCD
400
3
P (GeV/fm )
4
350
2
3
(GeV/fm )
12
350
300
300
10
3
0.05 GeV/fm
200
2
150
T (MeV)
T (MeV)
3
250
250
8
3
0.5 GeV/fm
200
6
150
4
1
100
100
2
50
50
(a)
(b)
0
0
0
1 V.
0.2
0.4
0.6
0.8
1
0
0
0
0.2
0.4
0.6
0.8
1
Vovchenko et al., Phys. Rev. C 93, 014906 (2016).
Begun, M.I. Gorenstein, O.A. Mogilevksy, IJMPE 20, 1805 (2011).
2 V.V.
7 / 23
Hydrodynamic modeling of a pure glue scenario
Modeling: longitudinally boost-invariant (2+1)D ideal hydro to describe
√
ALICE Pb+Pb collisions at sNN = 2.76 TeV
Code: modified vHLLE (viscous Harten-Lax-van Leer-Einfeldt)3 , Milne
coordinates (τ, x, y , η)
Modifications:
Solution for the space-time profile of the proper time τP of a fluid cell
element
u µ ∂µ τP (x) = 1 ,
τP (τ0 , x, y , η) = τ0 .
Explicit dependence of equation of state on τP
Calculation of electromagnetic observables (photons and dileptons)
The dependence P = P(ε, λ) determined from
P (T , λ) = λ PFQ (T ) + (1 − λ) PPG (T ) ,
ε (T , λ) = λ εFQ (T ) + (1 − λ) εPG (T ) .
3 Iu.
Karpenko et al., Comput. Phys. Commun. 185, 3016 (2014)
code available at GitHub github.com/yukarpenko/vhlle
8 / 23
Initial conditions and hadron spectra
Initial conditions: τ0 = 0.1 fm/c and averaged MC-Glauber ε(x, y ) profile
Normalization fixed to reproduce hadron spectra in chemical equilibrium,
same initial profile used for all other scenarios
ALICE, c=0-5%
ALICE, c=10-20%
ALICE, c=20-30%
ALICE, c=30-40%
10
T
T
T
10
-
K
d2 N/(2 pi p dp dy) [GeV-2]
102
T
d2 N/(2 pi p dp dy) [GeV-2]
c=0-5% hybrid, <vT>=0.021
c=0-5% hHKM, <vT>=0.042
10-20% hybrid, <vT>=0.022
10-20% hHKM, <vT>=0.022
20-30% hybrid, <vT>=0.023
30-40% hybrid, <vT>=0.025
π-
3
10
1
10-1
1
10-1
10-20
0.5
1
1.5
pT [GeV]
2
2.5
3
10
0
0.5
1.5
pT [GeV]
2
2.5
3
0.25
antiprotons
ALICE 10-20%
ALICE 20-30%
ALICE 30-40%
0.2
v2(p ) all charged
T
1
0.15
T
v2
T
d2 N/(2 pi p dp dy) [GeV-2]
1
0.1
10-1
ALICE, c=0-5%
ALICE, c=10-20%
ALICE, c=20-30%
ALICE, c=30-40%
0.05
-2
10 0
0.5
1
1.5
pT [GeV]
2
2.5
3
0
0
0.2
0.4
0.6
0.8
1
1.2
pT [GeV]
1.4
1.6
1.8
2
Iu. Karpenko, Yu. Sinyukov, K. Werner, Phys. Rev. C 87, 024914 (2013).
9 / 23
Hydrodynamic evolution
12
0.9
=5 fm/c
*
1
155 MeV
10
ALICE 0-20% central Pb+Pb
√
sNN = 2.76 TeV
0.9
0.8
0.7
0.75
0.6
6
τ∗ = 5 fm/c
0.5
0.4
4
0.5
2
0.25
λ close to 1 at the end
0.3
0.2
(a)
-15
However still smaller than 1 →
baryon suppression?
0.1
0
-10
-5
0
5
10
15
x (fm)
1.1
Initial temperatures much higher
in PG scenario
Very similar T -depedence at the
later stages of hydro evolution
In PG scenario matter undergoes
FOPT
1/2
0-20% Pb+Pb, s
1.0
=2.76 TeV
central cell
0.9
=0 fm/c, EoS-FQ
0.8
T (GeV)
(fm/c)
8
*
0.7
=5 fm/c, EoS-LI
*
0.6
=5 fm/c, ultrarelativistic EoS ( =3P)
*
0.5
0.4
0.3
0.2
0.1
With ideal gas QGP EoS cools
down too quickly
0.0
0.1
2
4
6
8
10
12
(fm/c)
10 / 23
Hydrodynamic evolution: temperature profile
ALICE 0-20% central Pb+Pb @
√
sNN = 2.76 TeV
Temperature profile
τ∗ = 0 fm/c
τ∗ = 5 fm/c
12
T (MeV)
12
=0 fm/c
T (MeV)
=5 fm/c
*
155
*
400
155
10
Dashed:
=0
*
400
10
350
350
8
300
200
250
6
200
4
270
2
350
150
(fm/c)
(fm/c)
8
300
200
250
6
270
200
FOPT
4
150
350
100
100
2
50
50
(a)
-15
(b)
-10
-5
0
5
10
15
x (fm)
-15
-10
-5
0
5
10
15
x (fm)
Longer evolution in PG initial scenario compared to equilibrium case
Region with FOPT at T = 270 MeV
Much higher temperatures at the initial stage in PG
11 / 23
Entropy production
Entropy for chemical non-equilibrium EoS
s (T , λ) = λ sFQ (T ) + (1 − λ) sPG (T ) − nq (T , λ) ln λ,
λ
nq (T , λ) = (PFQ − PPG ).
T
Initially λ = 0, in the end λ ' 1, in non-equilibrium S not conserved
Simple model: gas of massless partons (ε = 3P) and Bjorken-like hydro4
Box
Bjorken-like hydro, 2.76 TeV
18
x 10
-3
17
16
Equilibrium QGP
15
uQGP,
dS/d
14
uQGP,
uQGP,
13
12
0
*
*
*
= 1 fm/c
= 5 fm/c
= 10 fm/c
= 0.1 fm/c
11
(a)
10
0.1
2
4
6
8
10
12
14
(fm/c)
4 V.
Vovchenko et al., Phys. Rev. C 93, 014906 (2016).
12 / 23
Entropy production
√
ALICE 0-20% central Pb+Pb @ sNN = 2.76 TeV
(2+1) hydro with lattice-based EoS
Z
dS (τ )
= τ d 2 x⊥ γ⊥ (τ, x⊥ )s(τ, x⊥ ) .
dη
12
10
=1 fm/c
*
6
=5 fm/c
*
10
-3
dS/d
=0 fm/c
*
8
4
2
1/2
0-20% Pb+Pb, s
=2.76 TeV
0
0.1
2
4
6
8
10
12
(fm/c)
About 25% of total entropy generated during ideal hydro evolution
13 / 23
Electromagnetic probes
Photons and dileptons irradiated from all stages of HIC
Potentially carry more information about initial stage than hadrons
Measured by different experiments: HADES, NA49, RHIC BES, ALICE
Models for description
Hydrodynamics
J.F. Paquet et al., Phys.Rev. C 93, 044906 (2016)
H. Hees et al., Nucl. Phys. A 933, 256 (2015)
R. Chatterjee et al., Phys. Rev. C 85, 064910 (2012)
Coarse-grained transport
S. Endres et al., Phys. Rev. C 93, 054901 (2016)
T. Galatyuk et al., Eur. Phys. J. A 52, 131 (2016)
Microscopic transport
O. Linnyk et al., Prog. Part. Nucl. Phys. 87, 50 (2016)
M. Greif et al. (2016)
14 / 23
Photons in hydro models
Photon production rate Γ(Ẽ, T , λ) convoluted with hydro space-time profile
dNγth
=
d 2 pT dY
Z
+∞
+∞
Z
Z
e T (x), λ(x)] ,
d xT τ dτ dη Γ[E,
dNγth
1
=
2π pT dpT dY
2π
2
τ0
Z2π
dϕ
−∞
dNγth
,
d 2 pT dY
0
e = pµ uµ = γ⊥ pT cosh(Y − η) − vx cos ϕ − vy sin ϕ in (2+1)D.
with E
γ
Implementation:
At each τ step contributions from all transverse cells calculated
Very CPU intensive, takes much longer than solving hydro itself
Contribution from each cell can be calculated independently ⇒
embarrassingly parallel task
Calculation moved to GPU with NVIDIA CUDA ⇒ 20-30x speedup
over CPU, photons no longer bottleneck the simulation
15 / 23
Photon production rate
QGP emission described by AMY rate5
Applied at T > 155 MeV
Chemical non-equilibrium introduces λ
factors6
e T , λ) = λ Γ1 + λ2 (Γ − Γ1 )
LA: Γ(E,
e T , λ) = λ2 Γ2 + λ (Γ − Γ2 )
UA: Γ(E,
In our hydro calculations difference between
LA and UA turns out to be rather small
Additionally, at T < 155 MeV emission from hadronic stage considered.
This includes in-medium ρ-meson and ππ-bremsstrahlung7 ,
and assumes λ = 1
5 P.
Arnold, G. D. Moore, L. G. Yaffe, JHEP 12, 009 (2001).
to F.-M. Liu, S.-X. Liu, Phys. Rev. C 89, 034906 (2014).
7 M. Heffernan et al., PRC 91, 027902 (2015); S. Turbide et al., PRC 69, 014903 (2004).
6 Similar
16 / 23
Calculation results: Photon yield
Thermal + ’prompt’8 photons
Thermal photons
2
10
1/2
Pb+Pb, s
2
10
=2.76 TeV
*
*
*
-1
Solid: QGP-UA
10
Dashed: QGP-LA
20-40%
-2
T
10
-3
10
-4
10
T > 155 MeV
-5
10
cm
-6
*
0
10
*
= 0 fm/c
= 5 fm/c
'prompt' only
10
-2
10
-3
10
1
x 10 , 0-20%
-4
10
QGP-UA
0
x 10 , 20-40%
T > 155 MeV
-5
= 0
Y
(b)
cm
-6
10
= 1 fm/c
-1
10
Y
(a)
10
-2
= 5 fm/c
T
T
T
0
10
=2.76 TeV
1
= 1 fm/c
dN/(2 p dp dY) (GeV )
*
-2
dN/(2 p dp dY) (GeV )
x 10 , 0-20%
1/2
Pb+Pb, s
= 0 fm/c
1
1
10
= 0
10
0
2
4
p
6
T
(GeV/c)
8
10
0
2
4
p
6
T
8
10
(GeV/c)
Pure glue scenario has strong effect on high-pT thermal photons
High-pT thermal spectrum depends on choice of AMY non-equilibrium
rate
’Prompt’ photons dominate high pT of direct photon spectra, pure glue
effect is masked, much weaker dependence on details of modeling
8 pQCD pp yield scaled by N
coll , taken from
J. Adam et al. [ALICE Collaboration], Phys. Lett. B 754, 235 (2016).
17 / 23
Direct photon yield
d2N γ
dir
1
(GeV-2c 2)
2π N ev. p dp dy
Direct photon yield measured experimentally
2
10
1/2
Pb+Pb, s
=2.76 TeV
ALICE
ALICE 20-40%
1
T
T
Pb-Pb sNN = 2.76 TeV A exp(-p / T eff)
T
0-20% ALICE
0-20%
20-40% ALICE
20-40%
40-80% ALICE
102
T
10
*
= 0 fm/c
T
-2
dN/(2 p dp dY) (GeV )
0-20%
0
10
*
-1
10
*
= 1 fm/c
= 5 fm/c
10
1
x 102
'prompt' only
-2
−1
10
10
x 101
-3
10
10−2
1
x 10
-4
10
QGP-UA + Hadronic
10−3
0
x 10
T > 125 MeV
-5
10
Y
(b)
cm
-6
= 0
10−4
10
0
2
4
p
6
T
(GeV/c)
8
10
10−5
0.5
Paquet et al.
arXiv:1509.06738
Linnyk et al.
arXiv:1504.05699
v. Hees et al.
NPA 933(2015) 256
1
1.5
2
x 100
Chatterjee et al.
PRC 85(2012) 064910
+ JHEP 1305(2013) 030
2.5
3
3.5
4
p (GeV/c )
T
Fair description of data and generally consistent with other models
Underestimation of low pT yield in most central collisions
Present data does not conclusively discriminate between different
scenarios/models
18 / 23
Photon elliptic flow
0.10
v2γ = hcos 2ϕi
0.08
0.06
=0 fm/c
p
Strong enhance of thermal v2
*
=1 fm/c
Consequence of initial
suppression of production
*
0.04
=5 fm/c
*
0.02
1/2
0-20% Pb+Pb, s
Effect masked by ’prompt’
photons
=2.76 TeV
0.00
0.1
2
4
6
8
10
12
(fm/c)
0-40% Pb+Pb, s
0.20
Y
cm
1/2
=2.76 TeV
(a)
1.0
ALICE preliminary
= 0
*
0.15
*
0.10
0.8
= 1 fm/c
= 5 fm/c
=0 fm/c
0.6
v2
*
= 0 fm/c
*
=1 fm/c
*
0.05
0.4
=5 fm/c
*
0.00
QGP-UA
Thin: thermal
-0.05
0.2
T > 155 MeV
Thick: direct
0.0
0
1
2
3
p
T
(GeV/c)
4
5
6
0.1
2
4
6
8
10
12
(fm/c)
19 / 23
Photon elliptic flow
Effect of slow quark equilibration was studied before, in particular at RHIC
Thermal photon v2 in hydro
Direct photon v2 in PHSD
P. Moreau et al.
A. Monnai
Suppression of yield and enhancement of v2 of photons was obtained
in hydro
A. Monnai, Phys. Rev. C 90, 021901 (2014).
F.-M. Liu, S.-X. Liu, Phys. Rev. C 89, 034906 (2014).
and microscopic
PHSD model, P. Moreau et al., Phys. Rev. C 93, 044916 (2016).
BAMPS, M. Greif et al., in preparation.
models.
20 / 23
Thermal dileptons
Thermal dilepton q q̄ → e+ e− production rate in undersaturated QGP9
Qu
dN
2
= Cq λ exp −
d 4 xd 4 Q
T
with Q = p+ + p− = (M⊥ cosh Y , Q⊥ , M⊥ sinh Y ).
-1
10
2
-2
dN/(dM dY) (GeV )
-2
Pb+Pb, s
10
1/2
=2.76 TeV
0-20%
20-40%
-3
10
-4
*
-5
*
10
10
-6
10
*
= 0 fm/c
= 1 fm/c
= 5 fm/c
-7
10
-8
10
-9
10
Y
Thermal dileptons
cm
= 0
T>155 MeV
-10
10
(a)
(b)
-11
10
0
2
4
6
2
M (GeV/c )
8
0
2
4
6
8
10
2
M (GeV/c )
Thermal QGP dilepton yield clearly suppressed in PG initial state
scenario
Similar result for RHIC within same scenario reported within PHSD10
9 M.
10 P.
Strickland, PLB (1994); B. Kämpfer et al., PRC (1995).
Moreau et al., Phys. Rev. C 93, 044916 (2016).
21 / 23
Thermal dileptons
v2dp = hcos 2ϕi
where ϕ is angle between Q⊥ and x-axis.
0.08
Pb+Pb, s
Y
cm
1/2
=2.76 TeV
0-20%
20-40%
= 0
0.06
T > 155 MeV
vdp
2
*
0.04
*
*
= 0 fm/c
= 1 fm/c
= 5 fm/c
0.02
(b)
(a)
0
0
1
2
3
4
2
M (GeV/c )
5
0
1
2
3
4
5
6
2
M (GeV/c )
Momentum anisotropy of thermal dileptons is clearly enhanced
Dileptons appear to be potentially more sensitive
22 / 23
Summary
1
Lattice-based equation of state for chemically non-equilibrium QCD is
constructed by linear interpolation of two limiting cases.
2
Evolution of chemically non-equilibrium QGP is modeled by ideal
hydrodynamics with time-dependent equation of state.
3
About 25% of total entropy is generated during the ideal hydro
evolution of initially pure glue system.
4
Photon and dilepton yields are suppressed in pure glue scenario while
their momentum anisotropies are enhanced. Dileptons appear to be
more sensitive.
Outlook
More consistent treatment of hadron observables in chemical
non-equilibrium case.
Lower energies and/or smaller systems.
23 / 23
Summary
1
Lattice-based equation of state for chemically non-equilibrium QCD is
constructed by linear interpolation of two limiting cases.
2
Evolution of chemically non-equilibrium QGP is modeled by ideal
hydrodynamics with time-dependent equation of state.
3
About 25% of total entropy is generated during the ideal hydro
evolution of initially pure glue system.
4
Photon and dilepton yields are suppressed in pure glue scenario while
their momentum anisotropies are enhanced. Dileptons appear to be
more sensitive.
Outlook
More consistent treatment of hadron observables in chemical
non-equilibrium case.
Lower energies and/or smaller systems.
Thanks for your attention!
23 / 23
Backup slides
23 / 23
Photon elliptic flow
0.16
Pb+Pb, s
0.14
Y
cm
= 0
1/2
=2.76 TeV
(a)
Thin: thermal
v2
20-40%
0-20%
T > 155 MeV
0.12
Thick: direct
0.10
(b)
QGP-UA
*
*
= 0 fm/c
= 1 fm/c
0.08
*
= 5 fm/c
0.06
0.04
0.02
0.00
0
1
2
3
p
T
(GeV/c)
4
5
0
1
2
3
p
T
4
5
6
(GeV/c)
23 / 23