Transcript Confronting fluctuations of conserved charges in heavy ion
Confronting fluctuations of conserved charges in HIC at the LHC with lattice QCD
T c
T ^ A-A collisions fixed
s
Quark-Gluon Plasma Fluctuations of conserved charges at the LHC and LQCD results P. Braun-Munzinger, A. Kalweit and J. Stachel The influence of critical fluctuations on the probability distribution of net baryon number B. Friman & K. Morita Hadronic matte r Chiral symmetry restored Chiral symmetry x broken B 1 st , ,
T
T q
principle calculations:
T QCD QCD
: : : perturbation theory pQCD > LGT >
Deconfinement and chiral symmetry restoration in QCD
L H C
T c
Critical region Pisarski & Wilczek; The QCD chiral transition is crossover Y.Aoki, et al Nature (2006) and appears in the O(4) critical region O. Kaczmarek et.al. Phys.Rev. D83, 014504 (2011) TCP CP Asakawa-Yazaki Rajagopal, Schuryak Stephanov; Hatta, et al.
Chiral transition temperature
T c
T . Bhattacharya et.al. Phys. Rev. Lett. 113, 082001 (2014) See also: Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz,
et al.
JHEP, 0906 (2009) Deconfinement of quarks sets in at the chiral crossover A.Bazavov, Phys.Rev. D85 (2012) 05450 3
T c
(
B
)
T c
(
B
/
T c
) 2 ] Ch. Schmidt Phys.Rev. D83 (2011) 014504
Excellent data of ALICE Collaboration for particle yields
ALICE Collaboration A. Kalweit ALICE Time Projection Chamber (TPC), Time of Flight Detector (TOF), High Momentum Particle Identification Detector (HMPID) together with the Transition Radiation Detector (TRD) and the Inner Tracking System (ITS) provide information on the flavour composition of the collision fireball, vector meson resonances, as well as charm and beauty production through the measurement of leptonic observables.
Consider fluctuations and correlations of conserved charges
They are quantified by susceptibilities: If denotes pressure, then
B Q S
N T
2 2 (
N
) 2
NM T
2 2
N
M N
N q
N
q
,
P
Susceptibility is connected with variance 1 2 2
N
(
N
N
)
T
2
VT
3
N
N n
N N n
4
Consider special case:
P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R.
Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48)
N q
N q
=> Charge and anti-charge uncorrelated and Poisson distributed, then the Skellam distribution
N q N
q
N
/2
I N
(2
N
q N q N
q
N q
)] Then the susceptibility
N
1
T
2
VT
3 (
N q N
q
)
Consider special case: particles carrying
q
P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R.
Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48) The probability distribution
S
q
S
q q
Fluctuations Correlations
Variance at 200 GeV AA central coll. at RHIC
P. Braun-Munzinger, et al. Nucl. Phys. A880 (2012) 48) STAR Collaboration Consistent with Skellam distribution 2
p
1 3 The maxima of have a very 2
p
p
p
p
p p
i n i n
0.4
0.0
p t p t
0.8
G e V
similar values at RHIC and LHC thus
RHIC N p
N p
const., indeed 2 Momentum integrated:
p
LHC
2
p
Probing O(4) chiral criticality with charge fluctuations
Due to expected O(4) scaling in QCD the free energy:
P
P R q I
)
b
1
P S
(
b
(2 ) 1
t b h
) Generalized susceptibilities of net baryon number
c B
n
(
B
4 )
n
c R
c S
with
c
s
c
s | 0 | 0
d h
(2
n
/2)/
d h
(2
n
)/
f
f
0 0
c c B n n n
6 3
c c S
(
z
)
c B n
2
B
/
T
2 Generalized susceptibilities of the net baryon number never critical with respect to ch. sym. 8
Constructing net charge fluctuations and correlation from ALICE data
B T
2 1
VT
3 (
p
N
Net baryon number susceptibility 0
par
) Net strangeness
S T
2 1
VT
3 (
K
K S
0 0
K
K
K
0
S
K
0
L
) ) 4 4 9
par
Q S T
2 Charge-strangeness correlation 1
VT
3 (
K
3
K
K
)
par K
0 *
K
K
0 *
K
)
K
0 * )
B S
,
QS
constructed
from ALICE particle yields
Net baryon fluctuations Net strangeness fluctuations Charge-Strangeness corr. Ratios is volume independent
B S
and
B
QS
s
25
GeV
B
2
T
1
VT
3
S T
2 1
VT
3
QS T
2 1
VT
3
Compare the ratio with LQCD data:
A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, E. Laermann, Y. Maezawa and S. Mukherjee Phys.Rev.Lett. 113 (2014) and HotQCD Coll. A. Bazavov et al. Phys.Rev. D86 (2012) 034509 Is there a temperature where calculated ratios from ALICE data agree with LQCD?
Baryon number strangeness and Q-S correlations
Compare at chiral crossover There is a very good agreement, within systematic uncertainties, between extracted susceptibilities from ALICE data and LQCD at the chiral crossover How unique is the determination of the temperature at which such agreement holds?
Consider T-dependent LQCD ratios and compare with ALICE data
The LQCD susceptibilities ratios are weakly T-dependent for
T
0.15
GeV T
T c
described by the hadronic degrees of freedom
Extract the volume by comparing data with LQCD
Since thus (
N
/
T
2 )
LQCD
(
N
2
N
3 2 )
LH C V
B
(
T
)
T
3 (
B
/
T
2 )
LQCD V
S
(
T
)
T
3 (
B
/
T
2 )
LQCD V
QS
T
3 (
B
/
T
2 )
LQCD
All volumes, should be equal at a given temperature if originating from the same source
Particle density and percolation theory
Density of particles at a given volume exp
N total
Total number of particles in HIC at LHC, ALICE Percolation theory: 3-dim system of objects of volume
V
0 4 / 3
R
0 3
n c
1.22
V
0
R
0
n c
0.57
[
fm
3 ] P. Castorina, H. Satz &K.R. Eur.Phys.J. C59 (200 9
)
T c p
154 [
MeV
]
Constraining the volume from HBT and percolation theory
Some limitation on volume from Hanbury-Brown –Twiss: HBT volume Take ALICE data from pion interferometry
V HBT
fm
3 If the system would decouple at the chiral crossover, then
V
V HBT
From these results : variance extracted from LHC data consistent with LQCD 4500
fm
3
Excellent description of the QCD Equation of States by Hadron Resonance Gas
A. Bazavov et al. HotQCD Coll. July 2014 F. Karsch et al. HotQCD Coll.
2
B
2 4 ) |
B
0 “Uncorrelated” Hadron Gas provides an excellent description of the QCD equation of states in confined phase “Uncorrelated” Hadron Gas provides also an excellent description of net baryon number fluctuations
Thermal origin of particle yields with respect to HRG
Rolf Hagedorn => the Hadron Resonace Gas (HRG): “uncorrelated” gas of hadrons and resonances
N i
V
[
n i th
)
K
K
i n i th
A. Andronic, Peter Braun-Munzinger, & Johanna Stachel, et al. )] Particle yields with no resonance decay contributions: 2
j
1 1
dN dy
V
(
m
2
K
2 (
m
Measured yields are reproduced with HRG at
T
156 MeV
What is the influence of O(4) criticality on P(N)?
For the net baryon number use the Skellam distribution (HRG baseline)
P
B
N
/ 2
I N
(2
B B B B
as the reference for the non-critical )] behavior Calculate P(N) in an effective chiral model which exhibits O(4) scaling and compare to the Skellam distribtuion
The influence of O(4) criticality on P(N) for
0
P FRG
Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different
pc
K. Morita, B. Friman &K.R. (PQM model within renormalization group FRG) 0 Ratios less than unity near the chiral crossover, indicating the contribution of the O(4) criticality to the thermodynamic pressure
Conclusions:
From a direct comparison of fluctuations constructed with ALICE data to LQCD: there is thermalization in heavy ion collisions at the LHC and the 2nd order charge fluctuations and correlations are saturated at the chiral crossover temperature Skellam distribution, and its generalization, is a good approximation of the net charge probability distribution P(N) for small N. The chiral criticality sets in at larger N and results in the shrinking of P(N) relative to the Skellam function .
Moments obtained from probability distributions
Moments obtained from probability distribution
N k
N N k
Probability quantified by all cumulants
P
1 2 2 0
dy
exp [
i yN
(
iy
) ] Cumulants generating function: ) In statistical physics
N P
(
N
)
Z C Z
(
N GC
)
e T
) ]
k
k y k
The influence of O(4) criticality on P(N) for
0
P FRG
Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different
pc
K. Morita, B. Friman &K.R. (QM model within renormalization group FRG) 0 Ratio < 1 at larger |N| if c 6 /c 2 < 1
Modelling O(4) transtion: effective Lagrangian and FRG
Effective potential is obtained by solving
the exact flow equation
(Wetterich eq.) with the approximations resulting in the O(4) critical exponents B.J. Schaefer & J. Wambach,; B. Stokic, B. Friman & K.R. q q G L = S classical Full propagators with k < q < L Integrating from k = L to k = 0 gives a full quantum effective potential Put W k =0 ( s min ) into the integral formula for P(N)
Higher moments of baryon number fluctuations
B. Friman, K. Morita, V. Skokov & K.R.
If freeze-out in heavy ion collisions occurs from a thermalized system close to the chiral crossover temperature, this will lead to a negative sixth and eighth order moments of net baryon number fluctuations.
These properties are universal and should be observed in HIC experiments at LHC and RHIC Figures: results of the PNJL model obtained within the Functional Renormalisation Group method 25
The influence of O(4) criticality on P(N) for
0
P FRG
Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different
pc
K. Morita, B. Friman &K.R. (QM model within renormalization group FRG) 0 Ratios less than unity near the chiral crossover, indicating the contribution of the O(4) criticality to the thermodynamic pressure
The influence of O(4) criticality on P(N) at
0 distribution with the same Mean and Variance near
T pc
K. Morita, B. Friman et al.
0 Asymmetric P(N)
T
than unity for
N
N
0