Thermodynamics of Quasi

Particles
Fernanda Steffens
Mackenzie
–
São Paulo
Collaboration with F. G. Gardim
Hadronic Matter
New State, dominated by degrees of freedom
of quarks and gluons
Lattice QCD: Phase transition at T
c
. Stephan

Boltzmann limit at very large T
Perturbative QCD: up to order g
s
6
ln(1/g
s
)
–
Kajantie et al. PRD67:105008, 2003
Series is weakly convergent
Valid only for T ~ 10
5
T
c
Resum:
Hard Thermal Loops effective action
Andersen,Strickland, Annals Phys. 317: 281, 2005
2

loop
F
derivable approximation
Blaizot, Iancu, Rebhan, Phys. Rev. D63:065003, 2001
Region close to T
c
: quasi

particles?
Quasi

Particles: modified dispersion relations
Quark and gluon masses dependent on the
temperature T and/or the chemical potential
m
What is the thermodynamics of quasi

particles?
Originally: Gorenstein and Yang
–
PRD 52 (1995) 5206
Follow up: Peshier, Cassing, Kampfer, Blaizot, Rebhan, Weise, Bluhm, etc
Peshier et al. PRD 54 (1996) 2399
Goal: To calculate thermodynamics functions that reproduce the data
from lattice QCD and the results from perturbative QCD at large
T and/or
m
What about finite chemical potential?
Peshier et al., PRC 61 (2000) 045203
Thaler, Schneider, Weise, PRC 69 (2004) 035210
Bluhm et al., PRC 76 (2007) 034901
Thermodynamics in a grand canonical ensemble
If the mass is independent of
T and
m
, then
F
f
:
the grand potential
Partition Function
F
=

T
ln
Z
(m
;
V; T
)
However, in general:
Not zero if H depends
on T and on
m
The extra terms lead to an inconsistency in the
thermodynamics relations
Generalization
Extra term forces
a consistent formulation
With
What is the meaning of B?
Quantum interpretation
Density Operator
The internal energy:
Zero point energy
For T=0, we subtract the zero point energy
For finite T (and
m
), the dispersion relation depends on T
So does the zero point energy
It can not be subtracted
is the energy of the system in the absence of quasi

particles
The lowest energy of the system
The thermodynamics functions of the system are then
From all possible solutions, which ones are physically relevant?
g
= 0
Entropy unchanged
Originally developed for
m
=0
Solution of the type Gorenstein
–
Yang
Extension to finite
m
: Peshier, Cashing, etc
GY1 Solution
Set
a
=
l
,
h = g = 0
Entropy unchanged
Internal energy unchanged
Simpler
Smaller number of constants
Other solutions of the kind Gorenstein
–
Yang?
Yes
GY2 Solution
This solution allows us to write explicit expressions for the thermodynamics
functions
Reduced entropy: s’(T,
m
)
–
s’(T,0)
HTL mass was used
Number density
Pressure
Comparison to lattice QCD
Unpublished
HTL = Hard Thermal Loop
–
loops dominated by k~T
What about perturbative QCD at T >> T
c
? (HTL mass)
GY1 Solution
GY2 Solution
QCD
Both solutions fail!!
FG,FMS, NP A825: 222, 2009
Is there a solution that reproduces both, lattice QCD and
perturbative QCD?
YES
Solution with
a
=
㴠0
=
Doing the integrals
...
And similar for the entropy density, energy density and number density...
Lattice data:
FG,FMS, NP A825: 222, 2009
HTL mass in NLO was used, and
Factor of 1/2!
Disagreement:
Hard Thermal Loop (HTL) masses were used
Redefinition of the mass:
And agreement is found with
both
pQCD and Lattice QCD...
Main points:
•
General formulation of thermodynamics consistency for a system whose
masses depend on both T and
m
•
Multiple ways to obtain consistency
•
First explicit calculation of the thermodynamics functions
•
Good agreement with lattice QCD with a smaller number of free
parameters
•
Possible agreement with perturbative QCD and lattice QCD for finite T
and
m
for a particular solution
•
The usual quasi

particle approach (Gorenstein

Yang) does not reproduce
perturbative QCD and lattice QCD at finite chemical potential
•
Single framework to study a large portion of the T
m
plane
Feliz aniversário, Tony!
E obrigada pela sua amizade e por todo o resto!!!!
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