1 debye screened qgp qcd : confined chiral condensate quark potential deconfinement and chiral...
TRANSCRIPT
1
Debye screened
QGP
QCD :
confined
rrV )(
Chiral Condensate
0qq
Quark Potential
r
rrV D )exp(
~)(
0qq
Deconfinement and
Chiral Symmetry restoration
expected within QCD
( , , , )c c cf f fL q q A m(3) (2)c fSU SU
m m 0 symmetry )3(Z Chiral
symmetry )2()2( RL SUSU
HG
Global symmetries
111QSB UUU
2
Phases of QCD and charge fluctuations
quark-gluon plasma
hadron gas color
superconductor
B
Effective Chiral Models and QCD phase diagram: Charge fluctuations - probe of chiral phase transition : how to possibly search for TCP in heavy ion collisions?
T
K. Redlich
m=0O(4) 2nd order
TCP Z(2), 2nd order
1st order
Crossover m=0
(B. Friman, Ch. Sasaki &K.R)
3
Chiral Transformations of QCD-Langrangian
ˆ | , | ,s p p h h p h
qqqq LR )1(2
1)1(
2
155
( )quarq
k a aQCDL q i m qgA q q
L R R Lqq q q q q
L L R Rq D q q D q q D q
Chiral transformations:
Decompose:
Li
LRi
R qeqqeq LR 2/2/
(2) (2)R LSU SUBreaks chiral symmetry: invariant under
(2) ( )RV LSU In QCD vacuum chiral symm. spontaneously broken
33qq fm
L Rq q q
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Order parameter of chiral symmetry restoration
Consider chiral susceptibility:
to determine the position of
the chiral phase transition:
qq { csymmetry0 restored T >Tchiral
c symmet0 brokry T<n Techiral
2
2
q
q
P T m
m
Measures dynamically generated „constituent” quark mass: T=0 quarks „dress” with gluons
in hot medium dressing „melts”
effective quark mass shift
2 2( )qq qq
5
Extendet PNJL model and its mean field dynamics
2 2 25
2
( )
(3
4
)
( ) [( ) ( ) ] ( )
( ) ( [ ], [ ], )
1( exp[ ( , )])
SNJL
c
V
q I
S
VV
L q i m q qq qi q q q
q q q q q q U A A T
Tr P i d A x
G
NiA
G
D
G
D
Thermodynamic potential: mean-field approximation
, ,S VS V VG G G : Strength of quarks interactions in scalar and vector sector
Polyakov loop
( , )( , , , , , )u d q IT M dynamical (u,d)-quark masses, shifted chemical , :u dM qq
ipotentials and thermal averages of Polyakov loops
obtained from the stationary conditions:
( , ) / 0iT x x
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Chiral Symmetry Restoration – Order Parameterd
isco
nti
nu
ity
Divergence of the chiral susceptibility at the 2nd order transition and at the TCP
Discontinuity of the chiral susceptibility: at the 1st order transition
dis
con
tin
uit
y
discontinuity
Fixed q
Different Slopes
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Generic Phase diagram for effective chiral Lagrangians
Generic structure of the
phase diagram as expected
in different chiral models:
see eg. Y. Hatta & T. Ikeda;
M. Stephanov, K. Rajagopal, Fuji,.. Quantitative properties of the
phase diagram and the position of
TCP are strongly model dependent
Large no TCP at finite
temperature !VG
TCP
2nd order transition
1st order transition
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Effective Thermodynamic Potentials
Flattening of the potential at TCP: indeed expanding thermodynamic near
0M
62 4
26
4( , , ) ( , ) ( , ) ( , )aT TM M Ma MT a T
at TCP
Landau – Ginzburgpotential
finds: 42
42
( , ) 0 ( , ) 0
( , ) 0 ( , ) 0
c c c c
c c c c
a
a
T T
T T
a
a
2nd order TCP
2nd order
1st order
cT T
cT T
cT TTCPT T
cT T
cT T
cT T
6 0a
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Susceptibilities of conserved charges
Net quark-number ,isovector
and electric charge
fluctuations
21 1 1
36 4 6Q q Iq I
P
2
2II
P
2
2qq
P
I
2 2A A A
No mixing of isospin density with thesigma field due to isospin conservation Hatta & Stephanov
300q MeV
305TCPq MeV
310q MeV
TCP
1st order
2nd order
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Critical structure of the quark susceptibility
Quark number susceptibility at
Divergence of quark susc. at TCP is
directly related with the flattening ( ) of the thermodynamic potential
2(
(0
0
)0)
( )
1
( )2
2VS
q q SS sG
G
qS
m
Scalar susceptibility
qVS
vector-scalar susc.
0VG
42 4 6
2 6M aaa M M 4 0a
(0)4
(0
2
)
1 2
S
S S
V
MG a
M
4
1q a
{= finite at 2nd order
at TCP
Change of the universality class
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The universality class and T-dependence of M
Criticality of
directly related with the scalling of and with
(0) 2(0)
(
2
0) 2
( )2
1 2VS
q q SS s
GG
M
m
1 2 20 2
2 1/ ( )|M cmD M a T T
2M { at TCP
2M 2m ( )cT T
at 2nd1( )cT T
| |TCPT T
The critical exponents of determined
by the slope of the order parameter
as a function of near
qM
TcT
| |cT T
1| |cT T
2 42 ( ) ( )a T M O M
TCP
2nd
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Critical exponents near TCP
1 1
2 | |TCPT T
The strength of singularity at TCP depends on direction in plane( , )BT
1( )Cq T PT T along 1st order line
any direction not parallel
along 2nd order line 11
( )2 Tq CPT T
1/ 2( )Tq CPT T
Ising Model 1.25
Going beyond mean field:B.-J. Schaefer & J. Wambach
| |q TCPT T
Z(2) univer. class
1| |TCPT T
11| |
2 TCPT T
1/ 2| |TCPT T
(2 ) 0| |ndcT T
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Free energy: expected 2-order transition in 3-d, O(4)
universality class:
1( )1 2( , , ) ( )Analitic q SiI ngularF b tF F T b
2 ,( ) ~ 0F t t and small 2
| |: q
c c
cTTscaling field c
T Tt
Net Quark
Fluctuations
2( )qN
1 0
0 0
0
q
qt for vanishes t
t for cusp structure t
4( )qN (2 )
0
0 0
0
q
qt
t fo
for vanishes t
r diverges t
2 (( 2) 2)q diverges at Z nd order p tN oin
(2)Z
(4)O
1st order
T
Quark fluctuation and O(4) universality
/q T fix
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How to search for TCP
2/q T
2
2
2(1 )
3 qfN
T
( ) /q TMe
LGT-Bielefeld
An increase of is only necessary but not sufficient condition to verify the existence of TCP
2/q T
PNJL model, Sasaki et al..0qm
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Quark and isovector fluctuations along critical line
sensitive probes of TCP( , ( ))q c c cT T Non-singular behavior at TCP of ( , ( ))I c c cT T
Non-monotonic behavior of the net quark susceptibility in the vicinity to TCP
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Critical region near TCP
The critical window near TCP is elongated on the critical line
This window is quite
narrow in the direction
of fixed T and corresponds to
In heavy ion collisions
the
corresponds to change in
3q MeV
30T MeV
1s GeV
T
20q MeV
Sfix
B
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Finite quark mass and QCD phase diagram
0qm
surface of 1st order transitions
line of end pointCEP
TCP
0qm
T
q
qm
crossover line 2nd
T
0qm
0qm
acts as an external magnetic field and destroys the 2nd order transition preserving the 1st order below CEP
0qm
0qm
changes the effective thermodynamic potential 2 4 6
2 4 6( , , , )q qT M m a M a MM M ma
consequently the modification of the critical properties is to be expected:
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Conclusions
The effective chiral Lagrangians provide a powerful tool (due to universality) to study the critical consequences of chiral symmetry restoration in QCD, however
The quantitative verification of the phase diagram and the existence of the CEP/TCP in QCD requires the first principle LGT calculations and CBM experiment
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Phase boundary of the fixed energy density versus chemical freezeout
30.6c
GeV
fm
Splitting of the chemical freeze-out and the phase boundary surface appears when the densities of mesons and baryons are comparable?
particles production processes
0.77m GeV 0.14m GeV
LGT (Allton et al..)
1meson
baryon
MesonDominated
BaryonDominated
(6 8)NNs GeV
Z. Fodor et al..
: QGP hadronization
(6 8)NNs GeV : Hadronic rescattering
R. Gavai, S. Gupta