qcd phase diagram and its verification in hic
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QCD Phase diagram and its verification in HIC. Krzysztof Redlich University of Wroclaw. Chiral transition and O(4) pseudo-critical line in LGT Probing O(4) criticality with Charge fluctuations theoretical expectations and STAR data - PowerPoint PPT PresentationTRANSCRIPT
T
B
Hadronic matter
Quark-Gluon Plasma
Chiral symmetrybroken
Chiral symmetryrestored
LH
C
A-A collisions fixed s
x
1st principle calculations: perturbation theory pQCD LGT
, :QCDT , :QCDT
:q T
QCD Phase diagram and its verification in HICKrzysztof Redlich University of Wroclaw
Collaboration: P. Braun-Munzinger, B. Friman , F. Karsch, K. Morita, C. Sasaki & V. Skokov
Chiral transition and O(4)
pseudo-critical line in LGT Probing O(4) criticality with Charge
fluctuations
theoretical expectations and
STAR data Deconfinement in SU(N) pure gauge
theory and in QCD from LGT
Collaboration: B. Friman, O. Kaczmarek,, F. Karsch, K. Morita, Pok. Man Lo, C. Sasaki & V. Skokov
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
Is there 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
The phase diagram at finite quark masses
Can the QCD crossover line appear in the O(4) critical region?
YES, It has been confirmed in LQCD calculations
TCP
CP
LQCD results: BNL-Bielefeld
Critical region
Phys. Rev. D83, 014504 (2011)Phys. Rev. D80, 094505 (2009)
O(4) scaling and magnetic equation of state
Phase transition encoded in
the magnetic equation
of state
Pqq
m
11/
/( ) ,sf z tz m
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)/O(2)
11 (2 ) /( , , ) ( , )Sq IRP T b b t bPP h
6
Due to expected O(4) scaling in QCD the free energy:
Consider generalized susceptibilities of net-quark number
Since for , are well described by the
search for deviations (in particular for larger n) from HRG
to quantify the contributions of , i.e. the O(4) criticality F. Karsch & K. R. Phys.Lett. B695 (2011) 136
B. Friman, et al. . Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48
11 (2 ) /( , , ) ( ( ), )q IR SP T b b t bP hP
Quark fluctuations and O(4) universality class
4( ) ( / )
( / )
n
nB
nB
P Tc
T
(2 /2)/ ( )( )s 0 (| )n nn d h fc z
pcT T
with
( )nRc HRG
( )nSc
( )( )nR
nSc c
( )s 0
(2 )/ ( )| ( )nn ndc h f z
7
Only 3-parameters needed to fix all particle yields
Tests of equlibration of 1st “moments”: particle yields
resonance dominance: Rolf Hagedorn, Hadron Resonance
Gas (HRG) 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
Thermal yields and parameters and their energy dependence in HIC
Thermal origin of particle yields in HIC is well justified
A. Andronic, P. Braun-Munzinger & J. Stachel, Nucl. Phys. (06)
Phys.Rev. C73 (2006) 034905 J. Cleymans et al.
P. Braun-Munzinger et al.QM^12
Particle yields and their ratio, as well as LGT results
(F. Karsch, A. Tawfik, S. Ejiri & K.R.) well described by the HRG . A. Andronic et al., Nucl.Phys.A837:65-86,2010.
Budapest-Wuppertal
Chemical freezeout defines a lower bound for the QCD phase boundary
HotQCD Coll.
Quark-meson model w/ FRG approach
Effective potential is obtained by solving the exact flow equation (Wetterich eq.) with the approximations resulting in the O(4) critical exponents
Full propagators with k < q <
q q
Integrating from k= to k= gives a full quantum effective potential
Put k=0(min) into the integral formula for P(N)
B. Stokic, B. Friman & K.R.
S classical
B.J. Schaefer & J. Wambach,;
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
0/ pcT T T
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
STAR DATA Phys. Rev. Lett in print
Deviations of the ratios from their asymptotic, HRG values, are increasing with the order of the cumulants
Ratio of higher order cumulants in PQM modelB. Friman, V. Skokov &K.R. Phys. Rev. C83 (2011) 054904
Negative ratio!
4 2/B B 6 2/B B
6 2/B B
HRG
Theoretical predictions and STAR data 14
Deviation from HRG if freeze-out curve close toPhase Boundary/Cross over line
Lattice QCDPolyakov loop extendedQuark Meson Model
STAR Data
STAR Preliminary
L. Chen, QM 12
Strong deviatins of data from the HRG model (regular part ofQCD partition function) results: Remnant of O(4) criticality ?
Polyakov loop on the lattice needs renormalization Introduce Polyakov loop:
Renormalized ultraviolet
divergence
Usually one takes
as an order parameter
151/ V
c
c
0 deconfined T T
0 confined T<T
renren| | qFL e
NL c L 2 / ( )i k NNc e Z N
HotQCD Coll.
To probe deconfinement : consider fluctuations
Fluctuations of modulus of
the Polyakov loop
However, the Polyakov loop
Thus, one can consider fluctuations of the real and the imaginary part of the Polyakov loop.
SU(3) pure gauge: LGT data
R IL L Li
R
I
HotQCD Coll.
Compare different Susceptibilities:
Systematic differences/simi-larities of the Polyakov lopp susceptibilities
Consider their ratios!
Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement
In the deconfined phase
Indeed, in the real sector of Z(3)
Expand modulus
and find:
2 2 2| | | | ( )RL L L
Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) 1AR
0 0withR R RL L L L L
0 0with 0, thusI II IL L L L
2 2( ) , ( )L LR R I IV L V L
Expand the modulus,2
2 20 2
0 0
( )| | (1 )
2R I
R I
L LL L L L
L L
get in the leading order
thus A R
LA
A LR
R
Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement
In the confined phase
Indeed, in the Z(3) symmetric phase,
the probability distribution is Gaussian
to the first approximation,
with the partition function
consequently
Expand modulus
and find:
Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) 0.43AR
In the SU(2) case
is in agreement with MC results
Thus and
LA
A LR
R
3 2 2[ ( )( )]R IVT T L LR IZ dL dL e
3 3
1 1,
2 2R IT T
3
1(2 ),
2 2A T
(3) (2 ) 0.4292
SUAR
(2) 2(2 ) 0.363SU
AR
Ratio Imaginary/Real of Polyakov loop fluctuations
In the confined phase for any symmetry breaking operator its average vanishes, thus
and
thus
2 2 0LL L L
LL R I R I
In deconfined phase the ratio of and its value is model dependent
/ 0I R
Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013)
LILR
Ratio Imaginary/Real and gluon screening In the confined phase
WHOT QCD Coll. (Y. Maezawa et al.)
and WHOT-coll. identified as the magnetic and electric mass:
Since
,(2
,( ) ) (4 )RR I Idr r C r
2 21/ , 1/RE MI m m
LILR
,( ) ,( ) ,( )( ) ( ) (0)R I R IR cIC L r Lr
,( )
,( ),( ) ( )( )R I
I
m
Ir RR
reC
rTr T
( )R Im
2 2M RE Im m
Phys. Rev. D81 091501 (2010)
316 4 / 0.6PS Vm m
WHOT QCD Coll:
2-flavors of improved Wilson quarks
String tension from the PL susceptibilities
Common mass scale for
In confined phase a natural choose for M
c I RT T
,(2
,( ) ) (4 )RR I Idr r C r
,( ) ( )4R I
rMe
rC
Tr
,( ) ( )R IC r
/M Tbstring tension
2 2 3 1(
/2, )( ) / ( / ) ( )Ic c RT T Tb T T
Pok Man Lo, et al. ( in preparation)
O. Kaczmarek, et al. 99
Polyakov loop and fluctuations in QCD
Smooth behavior for the Polyakov loop and fluctuations
difficult to determine where is “deconfinement”
The inflection point at 0.22decT GeV
HOT QCD Coll
The influence of fermions on the Polyakov loop susceptibility ratio
Z(3) symmetry broken, however ratios still showing deconfinement
Dynamical quarks imply smoothening of the susceptibilities ratio, between the limiting values as in the SU(3) pure gauge theory
Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.
LA
A LR
R
Change of the slope in the
narrow temperature range signals color deconfinement
/ pcT T
this work
Probing deconfinement in QCD
Kurtosis measures the squared of the baryon
number carried by leading
particles in a medium S. Ejiri, F. Karsch & K.R. (06)
2
2
2 4
1
1
9
PC
BPC
B T T
T TB
Pok Man Lo, B. Friman, (013)O. Kaczmarek, C. Sasaki & K.R.
S. Ejiri, F. Karsch & K.R. (06)
316 4 lattice with p4 fermion action
0.77GeV, =0Bm
S. Ejiri, F. Karsch & K.R. (06) ( , ) ( ) cosh( / )Bq BP T F BT T
HRG factorization of pressure:
4
2
B
B
200 MeVpcT
2 770fN m MeV
Kurtosis of net quark number density in PQM modelV. Skokov, B. Friman &K.R.
For
the assymptotic value
2
24 2
( ) 2 3 3cosh
3qq f q q
c
qP T N m
KT T T
m
N T
due to „confinement” properties
Smooth change with a very weak dependence on the pion mass
cT T9
4 2/ 9c c
For cT T
4
P T
T
4 22/ 6 /c c
4 2/c c
4 2 2
2
1 1 7[ ]2 6 180f cN N
T T
Probing deconfinement in QCD
The change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value
In the presence of quarks
there is “remnant” of Z(N)
symmetry in the
ratio, indicating deconfi-
nement of quarks
Pok Man Lo, B. Friman, (013)O. Kaczmarek, C. Sasaki & K.R.
S. Ejiri, F. Karsch & K.R. (06)
316 4 lattice with p4 fermion action
0.77GeV, =0Bm /L LA R
/L LA R
/L LA R
4
2
B
B
200 MeVpcT
Probing deconfinement in QCD
Change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value In the presence of quarks
there is “remnant” of Z(N)
symmetry in the
ratio, indicating deconfi-
nement
Still the lattice finite size effects need to be studied
Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.
S. Ejiri, F. Karsch & K.R. (06)
0.77GeV, =0Bm /L L
A R
/L LA R
/L LA R
4
2
B
B
Ch. Schmidt
This paper
150 200 T[MeV]
Polyakov loop susceptibility ratios still away from the continuum limit:
The renormalization of the Polyakov loop susceptibilities is still not well described:
Still strong dependence on in the presence of quarks.
N
Ch. Schmidt et al.
Conclusions:
Chiral transition in QCD belong to the O(4) universality class Ratios the Net-charge susceptibilities are excellent probes of the
O(4) chiral crossover in QCD Systematics of the net-proton number fluctuations and their
probability distributions measured by STAR are qualitatively consistent with the expectation, that they are influenced by the O(4) criticality.
Ratios of different Polyakov loop susceptibilities are excellent and novel probe of deconfinement in QCD
There is a coincident between deconfinement and O(4) chiral crossover in QCD at small baryon density