B Hadronic matter Quark- Gluon Plasma Chiral symmetry broken x Exploring QCD Phase Diagram in Heavy Ion Collisions Krzysztof Redlich University of Wroclaw and EMMI/GS 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
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Exploring QCD Phase Diagram in Heavy Ion Collisions
Exploring QCD Phase Diagram in Heavy Ion Collisions. Krzysztof Redlich University of Wroclaw and EMMI/GSI. AA collisions. QCD phase boundary and freezeout in HIC Cumulants and probability distributions of conserved charges as Probe for the Chiral phase transition: - PowerPoint PPT Presentation
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B
Hadronic matter
Quark-Gluon Plasma
Chiral symmetrybroken
x
Exploring QCD Phase Diagram in Heavy Ion Collisions
Krzysztof Redlich University of Wroclaw and EMMI/GSI
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 field, i.e. variation of one of its external control parameters:
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
Pm
11/
/ ,( )sf z z tmm
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
12
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 TcT
( ) (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
qV
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
Including quantum fluctuations: FRG approach
FRG flow equation (C. Wetterich 93)J. Berges, D. Litim, B. Friman, J. Pawlowski, B. J. Schafer, J. Wambach, ….
start at classical action and includequantum fluctuations successively by lowering k
Regulator function suppressesparticle propagation with momentum Lower than k
0lim(( ) ), ( /) k kk
T T VV
k k kk R
k-dependentfull propagator
B. Stokic, V. Skokov, B. Friman, K.R.
FRG for quark-meson model
•LO derivative expansion (J. Berges, D. Jungnicket, C. Wetterich) (η small) •Optimized regulators (D. Litim, J.P. Blaizot et al., B. Stokic, V. Skokov et al.)
•Thermodynamic potential: B.J. Schaefer, J. Wambach, B. Friman et al.
,
11 2 1 2( , : ) [3 4 ]q a qk k o k f c
q
n nn nT N NE E E
Non-linearity through self-consistent determination of disp. rel. 2 2
i iE k M with ' ' ''2 2 2 2
0, 0,2 2k k kk q kM M M g
and 2k k h 0,
'/ |
kk k with
Employed Taylor expansion around minim
Get Potential Ignore flow of mesonic field get Mean Field result
Essential to include fermionic vacuum fluctuations:
Solving the flow equation with approximations:
0( ), ,) (kT T
E. Nakano et al.
Deviations of the ratios of odd and even order cumulants from their asymptotic, low T-value: are increasing with and the cumulant order Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations !
4 2 3 1/ / 9c c c c /T
4,2 4 2/R c cRatios of cumulants at finite density: PQM +FRG
HRG
B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694
HRGHRG
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 pHRG 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)
Deviations of the ratios from their asymptotic, low T-value, are increasing with the order of the cumulant
Ratio of higher order cumulants in PQM model B. Friman, V. Skokov &K.R. Phys.Rev. C83 (2011) 054904
Negative ratio!
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 of the net conserved charges
Obtained as susceptibilities from Pressure
or since they are expressed as polynomials in the central moment N N N
4( / ) / ( / )nn B
nTc P T
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:
)( ()N
C T
GC
Z NZ
P 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)
Probability distribution of net proton number STAR Coll. data at RHIC
STAR data
Do we also see the O(4) critical structure in these probability distributions ?
Thanks to Nu Xu and Xiofeng Luo
Influence of O(4) criticality on P(N)
Consider Landau model:
Scaling properties:
Mean Field 0
O(4) scaling 0.21
2 2 41 12 4bg t
21 | ( , ) |4
t T ( )t T
sin3 gnn c
( , )t T
Contribution of a sigular part to P(N)(
(,
), ) N
C T
GC
Z N T VZ
P eN
Get numerically from:
For MF broadening of P(N) For O(4) narrower P(N)
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
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.
Ratios at central collisions show properties expected near O(4) chiral pseudocritical line
For less central collisions the critical structure is lost
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
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 in QCD phase diagram