Post on 21-Dec-2015
Phase Fluctuations near the Chiral Critical Point
Joe Kapusta
University of Minnesota
Winter Workshop on Nuclear Dynamics Ocho Rios, Jamaica, January 2010
Phase Structure of QCD:Chiral Symmetry and Deconfinement
• If the up and down quark masses are zero and the strange quark mass is not, the transition may be first or second order at zero baryon chemical potential.
• If the up and down quark masses are small enough there may exist a phase transition for large enough chemical potential. This chiral phase transition would be in the same universality class as liquid-gas phase transitions and the 3D Ising model.
Phase Structure of QCD: Diverse Studies Suggest a Critical Point
• Nambu Jona-Lasinio model
• composite operator model
• random matrix model
• linear sigma model
• effective potential model
• hadronic bootstrap model
• lattice QCD
Goal: To understand the equation of state of QCD near the chiral critical point and its implications for high energy heavy ion collisions.
Requirements: Incorporate critical exponents and amplitudes and to match on to lattice QCD at µ = 0 and to nuclear matter at T = 0.
Model: Parameterize the Helmholtz free energy density as a function of temperature and baryon density to incorporate the above requirements.
1// 20
20 TT
latticeQCD
nuclear matter
400
2202
40
222
44 TBTTBATATAP
Coefficients are adjusted to:(i) free gas of 2.5 flavors of massless quarks(ii) lattice results near the crossover when µ=0
(iii) pressure = constant along critical curve.
Cold Dense Nuclear Matter
1219
2)()(
19
2)()( :II Model
13118
)()(
118
)()( :I Model
0000
2
0000
0000
2
0000
n
n
n
nKnEmn
n
nKnEnE
n
n
n
nKnEmn
n
nKnEnE
N
N
MeV 30250 MeV 3.16)( fm 153.0 003
0 KnEn
Stiff
Soft
MeV 1501230)4( 0 n
Parameterize the Helmhotz free energy density to incorporatecritical exponents and amplitudes and to match on to latticeQCD at µ = 0 and to nuclear matter at T = 0.
)()()()(),( 2
210 tftftftftf
cccc TTTtnnn /)(and/)(
0tif)(
0tif)()()(
20
20
0
tatf
tatftf
22
0
2
01 )1(1)( tT
Tntf cc
Parameterize the Helmhotz free energy density to incorporatecritical exponents and amplitudes and to match on to latticeQCD at µ = 0 and to nuclear matter at T = 0.
)()()()(),( 2
210 tftftftftf
cccc TTTtnnn /)(and/)(
0tif)(
0tif)()()(
2
22
tbtf
tbtftf
curve critical along MeV/fm 5125 3 cPf
isotherm critical along )(sign|~|
curve ecoexistenc along )(~
0n t whe
0 when )(),(
0n t whe
0 when )(),(
1
2
c
gl
TB
V
PP
t
t
tt
n
TnPn
n
tc
ttc
T
TnsTc
Critical exponents and amplitudes
815.424.1325.011.0
1 hasenergy freein || term
universal are 5.0/ and 5/
)1( and 22 :related are exponents
cc
phasecoexistence
spinodal
24.1
11.0
VffnfTT c ][ ||)(),();,( 2210
Expansion away from equilibrium states using Landau theory
Vnf c0 0 along coexistence curve
The relative probability to be at a density other than the equilibrium one is
Vff
TP
P
ll
l
||||
/exp)(
)(
222
Volume = 400 fm3
Volume = 400 fm3
Future Work• A more accurate parameterization of the equation of
state for a wider range of T and µ. • Incorporate these results into a dynamical simulation
of high energy heavy ion collisions.• What is the appropriate way to describe the
transition in a small dynamically evolving system? Spinodal decomposition? Nucleation?
• What are the best experimental observables and can they be measured at RHIC, FAIR or somewhere else?
Supported by the U.S. Department of Energy under Grant No. DE-FG02-87ER40328.