Folie 1 - PowerPoint PPT Presentation

Loading...

PPT – Folie 1 PowerPoint presentation | free to download - id: 845ed4-ODJlY



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Folie 1

Description:

Modeling of the Parton-Hadron Phase Transition Villasimius 2010 Hot and dense matter and the phase transition in quark-hadron approaches OUTLINE – PowerPoint PPT presentation

Number of Views:18
Avg rating:3.0/5.0
Slides: 33
Provided by: Stefan326
Learn more at: http://fias.uni-frankfurt.de
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Folie 1


1
Modeling of the Parton-Hadron Phase Transition
Villasimius 2010
Hot and dense matter and the phase transition in
quark-hadron approaches
OUTLINE
  • basic hadronic SU(3) model
  • generating a critical end point in a hadronic
    model
  • revisited
  • including quark degrees of freedom
  • phase diagram the QH model
  • excluded volume corrections, phase transition

J. Steinheimer, V. Dexheimer, H. Stöcker,
SWS Goethe University, Frankfurt
2
hadronic model based on non-linear realization of
chiral symmetry
degrees of freedom
SU(3) multiplets
baryons (n,?, S, ?) scalars (?, ?, ?0)
vectors (?, ?, f) , pseudoscalars, glueball
field ?
A) SU(3) interaction Tr B, M ? B
, ( Tr B B ) Tr M B) meson interactions
V(M) lt?gt ?0 ? 0
lt?gt ? 0 ? 0 C) chiral symmetry ? m?
mK 0 explicit breaking
Tr c ? (? mq q q ) ? light
pseudoscalars, breaking of SU(3)
_
_
_
_
_
_
_
? ltu u d dgt lt ? lts sgt ?0 lt u u -
d dgt
_
3
fit parameters to hadron masses
?
mesons
?
?
?
?
?
?
? ?
?
?
K
p,n
?
? ?
?
Model can reproduce hadron spectra via dynamical
mass generation
?
K
?
4
Lagrangian (in mean-field approximation)
L LBS LBV LV LS LSB
baryon-scalars
_
LBS - ? Bi (gi? ? gi? ? gi? ? ) Bi
baryon-vectors
_
LBV - ? Bi (gi? ? gi? ? gi? ? ) Bi
/
/
/
meson interactions
I
LBS k1 (?2 ?2 ?2 )2 k2/2
(?4 2 ?4 ?4 6 ?2 ?2 ) k3 ? ?2 ?
- k4 ?4 - ?4 ln ?/?0 ? ?4 ln (?2 - ?2) ?/
(?02?0)
I
LV g4 (?4 ?4 ?4 ß ?2?2)
explicit symmetry breaking LSB c1
? c2 ?
5
important reality check
nuclear matter properties at saturation density
asymmetry energy E/A (?p- ?n)
equation of state E/A (?)
binding energy E/A -15.2 MeV
saturation (?B)0 .16/fm3
compressibility 223 MeV
asymmetry energy 31.9 MeV
phenomenology 200 - 250 MeV
30 - 35 MeV
good description of finite nuclei / hypernuclei
SWS, Phys. Rev. C66, 064310
6
Task self-consistent relativistic
mean-field calculation coupled 7 meson/photon
fields equations for nucleons in 1 to 3
dimensions
parameter fit to known nuclear binding energies
and hadron masses
2d calculation of all measured ( 800) even-even
nuclei
error in energy ? (A ? 50) 0.21 (NL3
0.25 ) ? (A ? 100)
0.14 (NL3 0.16 )
relativistic nuclear structure models
good charge radii ?rch 0.5 ( LS
splittings)
correct binding energies of hypernuclei
SWS, Phys. Rev. C66, 064310 (2002)
7
phase transition compared to lattice simulations
heavy states/resonance spectrum is effectively
described by single (degenerate) resonance with
adjustable couplings
Tc 180 MeV µc 110 MeV
reproduction of LQCD phase diagram, especially
Tc, µc successful description of nuclear
matter saturation
phase transition becomes first-order for
degenerate baryon octet Nf 3 with Tc 185
MeV
D. Zschiesche et al. JPhysG 34, 1665 (2007)
8
Isentropes, UrQMD and hydro evolution
lines of constant entropy per baryon, i.e.
perfect fluid expansion E/A 5, 10, 40, 100,
160 GeV E/A 160 GeV goes through endpoint
J. Steinheimer et al. PRC77, 034901 (2008)
9
Including higher resonances explicitly
Add resonances up to 2.2 GeV. Couple them like
the lowest-lying baryons
P. Rau, J. Steinheimer, SWS, in preparation
10
connect hadronic and quark degrees of freedom
order parameter of the phase transition
confined phase
deconfined phase
effective potential for Polyakov loop, fit to
lattice data
U ½ a(T) FF b(T) ln1 6 FF 4 (FF)3
3 (FF)2 a(T) a0T4 a1 µ4
a2 µ2T2
baryonic and quark mass shift d mB f(F)
d mq f(1-F)
q
q
quarks couple to mean fields via gs, g?
V. Dexheimer, SWS, PRC 81 045201 (2010) Ratti et
al. PRD 73 014019 (2006) Fukushima, PLB 591, 277
(2004)
minimize grand canonical potential
11
Phase Diagram for HQM model
µc 360 MeV Tc 166 MeV
µc. 1370 MeV ?c 4 ?o
hybrid hadron-quark model critical endpoint
tuned to lattice results
V. Dexheimer, SWS, PRC 81 045201 (2010)
12
Mass-radius relation using Maxwell/Gibbs
construction
Gibbs construction allows for quarks in the
neutron star mixed phase in the inner 2 km core
of the star
V. Dexheimer, SWS, PRC 81 045201 (2010) R.
Negreiros, V. Dexheimer, SWS, PRC,
astro-ph1006.0380 
13
isentropic expansion overlap initial
conditions Elab 5, 10, 40, 100, 160 AGeV
averaged Cs significantly higher than 0.2
Csph ¼ Cs,ideal
14
Temperature distribution from UrQMD simulation as
initial state for (3d1) hydro calculation
initial temperature distribution
Speed of sound - (weighted) average over
space-time evolution
dip in cs is smeared out
15
different approach hadrons, quarks, Polyakov
loop and excluded volume
Include modified distribution functions for
quarks/antiquarks


Following the parametrization used in PNJL
calculations
U - ½ a(T) FF b(T) ln1 6 FF 4 (FF)3
3 (FF)2 a(T) a0T4 a1 T0T3 a2 T02T2
, b(T) b3 T03 T ? ?o (1 - FF /2)
The switch between the degrees of freedom is
triggered by excluded volume corrections
thermodynamically consistent -
Vq 0 Vh v Vm v / 8



e e / (1 S vi ?i )
µi µ i vi P
D. H. Rischke et al., Z. Phys. C 51, 485
(1991) J. Cleymans et al., Phys. Scripta 84, 277
(1993)
Steinheimer,SWS,Stöcker hep-ph/0909.4421
16
quark, meson, baryon densities at µ 0
densities of baryon, mesons and quarks
natural mixed phase, quarks dominate beyond 1.5
Tc
?
Energy density and pressure compared to lattice
simulations
17
Temperature dependence of chiral condensate and
Polaykov loop at µ 0
Interaction measure e 3p
lattice data taken from Bazavov et al. PRD 80,
014504 (2009)
speed of sound shows a pronounced dip around Tc !
18
subtracted condensate and polyakov loop
different lattice groups and actions
From Borsanyi et al., arxiv10053508 hep-lat
19
Lattice comparison of expansion coefficients as
function of T
expansion coefficients
lattice results
lattice data from Cheng et al., PRD 79, 074505
(2009)
Steinheimer,SWS,Stöcker hep-ph/0909.4421
suppression factor peaks
20
Dependence of chiral condensate on µ, T
Lines mark maximum in T derivative
F
s
Separate transitions in scalar field and Polyakov
loop variable
21
Dependence of Polyakov loop on µ, T
Lines mark maximum in T derivative
F
s
Separate transitions in scalar field and Polyakov
loop variable
22
Susceptibilitiy c2 in PNJL and QHM for
different quark vector interactions
QH
At least for µ 0 small quark vector repulsion
PNJL
gq? 0
gq? gn? /3
Steinheimer,SWS, hepph/1005.1176
23

s
F
24
UrQMD/Hydro hybrid simulation of a Pb-Pb
collision at 40 GeV/A
red regions show the areas dominated by quarks
25
simple time evolution including p, K
evaporation (E/A 40 GeV)
with evaporation
C. Greiner et al., PRD38, 2797 (1988)
E/A-mN
300
If you want it exotic
g2 0
g2 2
200
additional coupling g2 of hyperons to strange
scalar field
g2 4
100
follow star calcs by J. Schaffner et al., PRL89,
171101 (2002)
g2 6
0
0 0.5 1 1.5
barrier at fs 0.4 0.6
fs
26
SUMMARY
  • general hadronic model as starting point
  • works well with basic vacuum properties,
    nuclear matter, nuclei,
  • phase diagram with critical end point via
    resonances
  • implement EOS in combined molecular dynamics/
    hydro simulations
  • quarks included using effective deconfinement
    field
  • realistic phase transition line
  • implementing excluded volume term, natural
    switch of d.o.f.

If you want to see hadronization, grab your
Iphone -gt Physics to Go! Part 3
27
Hypernuclei - ? single-particle energies
Nuclear matter
Model and experiment agree well
28
Evolution of the collision system
Elab 5-10 AGeV sufficient to overshoot phase
border, 100-160 AGeV around endpoint
29
amount of volume scanning the critical endpoint
(lattice)
30
Comparison of gross properties of initial
conditions
Overlap of projectile and target
31
time integrated volume around the critical end
point
32
effective volume sampling the critical end point
window T Tc 10 MeV µ µc 10 MeV
maximum shifts in time
About PowerShow.com