LGT results and their interpretation within Hadron Resonance Gas Model

1
LGT results and their interpretation within
Hadron Resonance Gas Model

• Motivation phase boundary
• chemical freezeout
• LGT at large pion mass and HRG
• Recent LGT results and their relation
• with HRG fluctuations as probe of
• deconfinement and chiral dynamics
• 
  
• 
  Krzysztof Redlich, Trento 08

2
LGT phase boundary and chemical freezeout

• The critical curve and CEP obtained in LGT
  coincides with the chemical freeze-out
• However recent LGT results show that
• there is no unique value
• of at (Y.Aoki at.al)
• Critical temperature at
• can be as large as
• (M. Cheng et al.)

3
QCD Thermodynamics of confined phase
?

• Heavy Ion
• Phenomenology
• through

Lattice Gauge Theory at finite and

Based on common work with Bielefeld-Swansea LGT
Coll. C.R. Allton, M. Doring, S. Ejiri,
S.J. Hands, O. Kaczmarek, F. Karsch, E.
Laermann, K.R. S. Ejiri, F. Karsch B.
Stokic, B. Friman
4
The endpoint of QCD in T-miu_B plane
Fodor Katz
01, 04
renormalized physical operator

• Multiparameter reweighting

Lee-Yang zeroes
Finite volume V
If and
phase transition
crossover transition
5
QCD at non-vanishing chemical potential
Bielefeld-Swansea
approach
C.R. Allton, et al..
complex fermion determinant
Taylor expansion of
,
Also expansion in that allows to
get different mixed susceptibility
6
Statistical operator and mass spectrum
resonance dominance (R. Hagedorn)
approximate by
experimentally known mass spectrum
Breit-Wigner res.
Essential properties of HRG partitin function
No mixing of mesons and batyons
Factorization
7

factorization on the Lattice

Lattice confirmed that
HRG
8
Taylor expansion of resonance pressure
baryon mass spectrum
Factorization of the baryonic pressure

Compare with LGT results

Consequences
For fixed any ratio of
these observables is T-independent

the ratio of the O(2) and O(4) coefficients

9
QCD partition function from LGT and
Phenomenology
Taylor coefficients of
The LGT Taylor coefficients ratios consistent
with that expected in HRG
10
Ratio of as a probe of
deconfinement
S. Ejiri, F. Karsch, K.R.

• The peak in at also
• consistent with deconfinement
• HRG factorization of pressure
• consequently in HRG
• In QGP,
• Ratio of cumulants
• excellent probe of deconfinement

11
Isovector and electric charge fluctuations


0 for
related with space-like screening limit of the
retarded photon self-energy
In LGT obtained from
,however requires
independent Monte-Carlo calculations
12
Isovector susceptibility in LGT and
resonances gas

on the lattice
expanding cosh(x) one expects

LGT result supports decomposition of meson baryon
contribution in confined phase
13
quark condensate at finite density

Baryon contribution
Net baryon pressure
In 2-flavour LGT calculations
14
Hadron Mass Spectrum versus quark mass
chiral limit



quenched limit



extrapolate from LGT or model



15
Bag Model and Hadron Masses

• --------------------
• --------------------
• ---------------------
• ------- ---
  
• ----------------------
  
• ----------B-----------
  surface boundary
• 
  conditions
  
• Hadron Masses from
  
• for and

q
g
q
q
g

16
Hadron Mass Spectrum LGT and Bag model results
F. Karsch, A. Tawfik, K.R.
LGT results for pion mass dependence of and
their parity partners
2
QCDSF Coll., M. Göckeler, et al..
17
Isospin multiplets contribution to QCD
thermodynamics
Very good description of LGT Pressure by HRG
model!
Largest deviations in mesonic sector
Connected with LGT coefficient in the Taylor
expansion of susceptibilities
18
Deconfinement is density driven -
(percolation)
Hadron resonance gas partition function
LGT result shows strong dependence of on
and , however for
and for all

provides a good description of m and
depen. of deconfinement temperature
A. Peikert, et al..
condition for deconfinement

hadrons
hadrons
gluballs
H. Satz
percolation deconfinement
lines of constant energy density in HG
19
Quark number and isovector fluctuations in LGT
C. Allton et al.,
S. Ejiri, F. Karsch K.R.

• Smooth change of and peak
• in at expected from O(4)
  universality argument

• For fluctuations as
• expected in the Hadron Resonance Gas

20
Quark number and isovector fluctuations in LGT
C. Allton et al., (Bielefeld-Swansea)

• Smooth change of at
• as expected from O(4)
  universality argument
• No difference between and
• for
• the described by the HRG
  with LGT m-spectrum
• good description of
• within the quasiparticle model

Off-diagonal susceptibility For
the
Similar behaviour in LGT studies by S. Ejiri,
T. Hatsuda, et al., MILC coll., Gavai Gupta
21
Mixed susceptibilities

22
Hadron resonance gas model and LGT


thermodynamics
23
Quark mass dependence of the QCD
thermodynamics below
deconfinement
Linear dependence of on the quark
mass in LGT
24
LGT results in 21 flavor QCD with physical
mass spectrum
Different critical temperatures
Z. Fodor et al.
M. Cheng et al.
Different critical temperatures for different
observables Z. Fodor et al.
25
Taylor coefficients LGT in 21 flavor with and
HRG results calculated with
Strong deviations of HRG results from LGT if the
scale is fixed through the critical temperature
26
Strangeness and quark Susceptibility
21 flavor,
21 flavor,
HRG results would be consistent with quark
susceptibility if changing T_c !!!! However, this
change is not allowed
HRG results consistent with strangeness
susceptibility extrapolated to continuum limit
with Fodor
27
Kurtosis in 21 flavor QCD
F. Karsch et al.
Large pion mass Smooth change of
kurtosis between their hadronic and QGP
asymptotic values Small pion mass Increase
beyond HRG and peak at pseodocritcal temperature
28
Inverse compressibility per quark density
F. Karsch et al.
Smooth change at large quark mass, however deep
for physical quark mass !!!
29
Quark-meson model coupled to Polyakov loop

B.J. Schaefer, J. M. Pawlowski and J.Wambach,

• An effective quark potential under mean field
  approximation

In the low temperature phase leading contribution
coming from 3-quark states
statistical confinement
30
Chiral dynamics, Kurtosis and inverse
compressibility, model
calculations
A peek in kurtosis and deep in inverse
compressibility appear as remnant of chiral
dynamics and O(4) universality! The 21 flavor
QCD sensitive to O(4) dynamics expected in
2-flavor QCD
31
Conclusions

• HRG consistent with LGT results
• obtained in 2 flavor LGT with heavy quarks
• HRG inconsistent with recent results
• obtained in 21 flavor LGT with physical pion
  mass if

• Recent LGT results obtained in 21 flavor LGT
  with light pion mass show remnant of chiral
  dynamics expected in 2-flavor QCD

32
Inverse compressibility per quark density

Isothermal compressibility
should be large near CEP
For the HRG gives
Large density fluctuations at saturated by
fluctuations in HRG
Bulk properties due to flavor content gap of
medium constituents
33
Net-quark and isovector fluctuations at
Susceptibilities obtained via Taylor expansion
Allton et al. 05
F. Karsch et al. 07
An increase of fluctuations with
could be of non-critical nature through the
factor ?
34
Hadron resonance gas model and LGT


thermodynamics
?
?

• Critical structure due to QCD End-Point

How large the singular contribution could be in
the actual LGT calculations ?