Post on 03-Feb-2016
description
B
Hadronic matter
Quark-Gluon Plasma
Chiral symmetrybroken
x
Exploring QCD Phase Diagram in Heavy Ion Collisions
Krzysztof Redlich University of Wroclaw
QCD phase boundary and freezeout in HIC
Cumulants and probability distributions of conserved charges as Probe for the Chiral phase transition:
theoretical expectations and
recent STAR data at RHIC
-CEP?
?
AA collisions
2
– probing the response of a thermal medium to an external fields, i.e. variation of one of its external control parameters:
(generalized) response functions == (generalized) susceptibilities
pressure:
thermal fluctuations density fluctuations condensate fluctuations
generalized susceptibilities:generalized susceptibilities:
energy density order parameter
Bulk thermodynamics and critical behaviour
, )i 4
1
( / )~ |
iii
NP T
Mean particle yields
3
Susceptibilities of net charge number
– The generalized susceptibilities probing fluctuations of net -charge number in a system and its critical properties
pressure:
particle number density quark number susceptibility 4th order cumulant
net-charge q susceptibilities
31 1
,q NVT
2 23
2 1( )q N N
VT 3
34 41
( ( ) 3 ( ) )q N NVT
q qN N N N N N expressed by and central moment
( )nq
(2)q
(4)q
4
Only 3-parameters needed to fix all particle yields
Tests of equlibration of 1st “moments”: particle yields
resonance dominance: Rolf Hagedorn partition function
22ln ( , ) ( ) ( , )
2
iQB WT
i ii hadrons
VT sZ T d e ds s K F m s
T
����������������������������
��������������
Breit-Wigner res.
Re .[ ( , ) ( , )]KB BK
ti
h si
thiiV T TnN n
particle yield thermal density BR thermal density of resonances
Chemical freezeout and the QCD chiral crossover
A. Andronic et al., Nucl.Phys.A837:65-86,2010. O(4) universality
2
00.0061 6c
c
T
T T
HRG model
Chiral
/ ( )T f s
crossover
Thermal origin of particle production: with respect to HRG partition function
A. Andronic et al., Nucl.Phys.A837:65-86,2010.
P. Braun-Munzinger et al. QM (2012)
Chemical freezeout and the QCD chiral crossover
A. Andronic et al., Nucl.Phys.A837:65-86,2010. O(4) universality
2
00.0061 6c
c
T
T T
HRG model
Chiral
/ ( )T f s
crossover
Is there a memory that the system has passed through a region of QCD chiral transition ?
What is the nature of this transition?
Chiral crosover Temperature from LGT
HotQCD Coll. (QM’12)
154 9cT MeV
Chemical Freezeout LHC (ALICE) P. Braun-Munzinger (QM’12)
(152,164)fT MeV
QCD phase diagram and the O(4) criticality
In QCD the quark masses are finite: the diagram has to be modified
Expected phase diagram in the chiral limit, for massless u and d quarks:
Pisarki & Wilczek conjecture
TCP: Rajagopal, Shuryak, Stephanov Y. Hatta & Y. Ikeda
TCP
The phase diagram at finite quark masses
The u,d quark masses are small
There is a remnant of the O(4) criticality at the QCD crossover line:
CPAsakawa-YazakiStephanov et al., Hatta & Ikeda
At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat
Critical region
Phys. Rev. D83, 014504 (2011)
Phys. Rev. D80, 094505 (2009)
LQCD results: BNL-Bielefeld group
9
singular
critical behavior controlled by two relevant fields: t, h
Close to the chiral limit, thermodynamics in the vicinity of the QCD transition(s) is controlled by a universal scaling function
K. G. Wilson,Nobel prize, 1982
Bulk Thermodynamics and Critical Behavior
non-universal scalescontrol parameter for amountof chiral symmetry breaking
regular
O(4) scaling and magnetic equation of state
Phase transition encoded in
the magnetic equation
of state
P
m
11/
/,( )sf z z tm
m
pseudo-critical line
1/m
F. Karsch et al
universal scaling function common forall models belonging to the O(4) universality class: known from spin modelsJ. Engels & F. Karsch (2012)
mz
QCD chiral crossover transition in the critical region of the O(4) 2nd order
O(4)
11
Find a HIC observable which is sensitive to the O(4) criticality
Consider generalized susceptibilities of net-quark number
Search for deviations from the
HRG results, which for
quantifies the regular part
1(21 /)( ),( , , ) SingularAnalytic q I bP T b hb tP P
0(4) : .2O
Quark fluctuations and O(4) universality class
To probe O(4) crossover consider fluctuations of net-baryon and electric charge: particularly their higher order cumulants with
F. Karsch & K. R. Phys.Lett. B695 (2011) 136
B. Friman, V. Skokov et al, P. Braun-Munzinger et al. Phys.Lett. B708 (2012) 179
Nucl.Phys. A880 (2012) 48
4( ) ( / )
( / )
n
nB
nB
P Tc
T
( ) (2 /2)/ ( /2) ( 0)nr
nnc d h f z and n even
( ) (2 )/ ( ) ( ) 0nn nrc d h f z
cT T( )nrc 6n
or compare HIC data directly to the LGT results, S. Mukheriee QM^12 for BNL lattice group
Effective chiral models Renormalisation Group Approach
coupling with meson fileds PQM chiral model FRG thermodynamics of PQM model:
Nambu-Jona-Lasinio model PNJL chiral model
1/3
0
i *4
nt ( , ),[ ](( ) )T
q
V
S d d x iq V U Lq q q LA q q
the SU(2)xSU(2) invariant quark interactions described through:
K. Fukushima; C. Ratti & W. Weise; B. Friman , C. Sasaki ., ….
B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov, ...
int ( , )V q q
*( , )U L L the invariant Polyakov loop potential (Get potential from YM theory, C. Sasaki &K.R. Phys.Rev. D86, (2012); Parametrized LGT data: Pok Man Lo, B. Friman, O. Kaczmarek &K.R.)
(3)Z
B. Friman, V. Skokov, B. Stokic & K.R.
fields
Deviations from low T HRG value: are increasing with and the cumulant order
/T
4,2 4 2/R c cRatios of cumulants at finite density: LGT and PQM with FRG
HRG
B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694
HRG valueHRGCh. Schmidt et al.S. Ejiri et al.
4,2 / 9R
STAR data on the first four moments of net baryon number
Deviations from the HRG
Data qualitatively consistent with the change of these ratios due to the contribution of the O(4) singular part to the free energy
4)2
(
(2)B
B
(3)
(2),B
B
S
HR
G
, 1| |p p
p p
HRG HRG
N N
N NS
Kurtosis saturates near the O(4) phase boundary
The energy dependence of measured kurtosis consistent with expectations due to contribution of the O(4) criticality. Can that be also seen in the higher moments?
B. Friman, et al. EPJC 71, (2011)
STAR DATA Presented at QM’12
Lizhu Chen for STAR Coll.
V. Skokov, B. Friman & K.R., F. Karsch et al.
The HRG reference predicts:
6 2/c c
HRG
6 2/ 1c c O(4) singular part contribution: strong deviations from HRG: negative structure already at vanishing baryon density
Moments obtained from probability distributions
Moments obtained from probability distribution
Probability quantified by all cumulants
In statistical physics
2
0
( ) (1
[ ]2
)expdy iP yNN iy
[ ( , ) ( , ]( ) ) k
kkV p T y p T yy
( )k k
N
N N P N
Cumulants generating function:
)(
()
NC T
GC
Z N
ZP eN
Probability distribution of the net baryon number
For the net baryon number P(N) is described as Skellam distribution
P(N) for net baryon number N entirely given by measured mean number of baryons and antibaryons
In Skellam distribution all cummulants expressed by the net mean
and variance
BB
/2
( ) (2 )exp[ ( )]N
NB
B BN B BB
P I
2 B B M B B
P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48)
Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different / pcT T
( )FRGP N
Ratios less than unity near the chiral critical point, indicating the contribution of the O(4) singular part to the thermodynamic pressure
0 K. Morita, B. Friman et al.
The influence of O(4) criticality on P(N) for 0
The influence of O(4) criticality on P(N) for Take the ratio of which contains O(4) dynamics to Skellam
distribution with the same Mean and Variance near ( )pcT ( )FRGP N
Asymmetric P(N) Near the ratios less
than unity for For sufficiently large
the
for
0 K. Morita, B. Friman et al.
0
( )pcT N N
( )( ) / 1FRG Skellam NP N P
N N
0
The influence of O(4) criticality on P(N) for
0
K. Morita, B. Friman & K.R.
0
In central collisions the probability behaves as being influenced by the chiral transition
For preliminary STAR dataQM 2012
Centrality dependence of probability ratio
O(4) critical
Non- criticalbehavior
For less central collisions, the freezeout appears away the pseudocritical line, resulting in an absence of the O(4) critical structure in the probability ratio.
STAR analysis of freezeout K. Morita et al.
Cleymans & Redlich
Andronic, Braun-Munzinger & Stachel
Conclusions: Hadron resonance gas provides reference for O(4)
critical behavior in HIC and LGT results Probability distributions and higher order cumulants are
excellent probes of O(4) criticality in HIC Observed deviations of the and
by STAR from the HRG qualitatively expected due to the O(4) criticality (check for the influence of : efficiency , volume fluctuations and baryon number conservation!!!)
Deviations of the P(N) from the HRG Skellam distribution follows expectations of the O(4) criticality
3 2/ , 4 2/ , 6 2/
Present STAR data are consistent with expectations, that in central collisions the chemical freezeout appears near the O(4) pseudocritical line on QCD phase diagram