Two-particle Distribution and Correlation in Hot QGP
-
Upload
hilliard-schwarz -
Category
Documents
-
view
45 -
download
1
description
Transcript of Two-particle Distribution and Correlation in Hot QGP
Two-particle Distribution and Two-particle Distribution and Correlation in Hot QGP Correlation in Hot QGP
Hui Liu (刘绘)Phys. Dep., JiNan University
Jiarong Li (李家荣)IOPP, CCNU
Outline:• Brief review on distribution functions
• Dispersion relations of HTL and complete one loop
• Oscillatory potential in complete one loop
• Radial distribution function and static structure function of hot QGP
USTC 0807 Hui Liu 2
Distribution Functions (review)Distribution Functions (review) Distribution functionDistribution function
Probability of occurrence of a particular arrangement of particles
Radial distribution function (RDF)Radial distribution function (RDF)
Probability of finding two particles at a distance r from each other
ji
δN
rgρ )rrr(1
)( ji0
What can RDF tell us?What can RDF tell us? Spacial configuration of many-body system
Length of order
)r,,r,r( N21)( Nn
USTC 0807 Hui Liu 3
Solid: long-range order Gas: completely randomLiquid: short-range order
Static structure function Fourier transformation
Can be measured by experiment
Basic quantity in atomic liquid theory, related to various observables
USTC 0807 Hui Liu 4
How to obtain the RDFHow to obtain the RDF
From theory
Potential of mean force
From experiment
In atomic liquid, the structure function can be
measured by scattering experiment
Liquid Cl2from Egelstaff 1985
Contains both effects of dynamical interactions and thermal statistics
Incident beams sample
Scattered beams
kk 0
0kkq
USTC 0807 Hui Liu 5
General form of static potentialGeneral form of static potential
Diagrammatic description
Analytic expression
General form with pole contribution
PotentialPotential
Effective propagator
obtained by resumming all possible irreducible diagrams
USTC 0807 Hui Liu 6
QED one-loop polarizationQED one-loop polarization
Oscillatory potentialOscillatory potential
Find out the poles numerically and then
plot the static potential
Obvious damping oscillation of the static
potential in the completely one-loop
calculation, qualitatively different with
Debye form
HTL approximation, Debye screening
Complete one loop, q-dependent
USTC 0807 Hui Liu 7
Dispersion RelationsDispersion Relations Dispersion relationDispersion relation
Energy-moment relation defined by the ze
ros of full propagator, which depends on t
he polarization patterns (dynamics) and th
ermodynamical environment
Vacuum (T= 0) , qr= qi= 0
free particle
HTL (high T limit), qr= 0
Debye screening
HTL
one loop
free particle
Complete one loopComplete one loop
Lower plasma frequency
Threshold frequency
Damping oscillatory screening
USTC 0807 Hui Liu 8
RDF in hot QGPRDF in hot QGP Gluon polarizationGluon polarization
RDF at complete one loopRDF at complete one loop
Short range order. Very similar to the
typical shape of liquid. Footprint of
liquid QGP!?
Enhanced peaks at lower temperatures.
0.5GeVT 0.40.3
USTC 0807 Hui Liu 9
Structure FunctionStructure Function Fourier transformation of auto correlation functionFourier transformation of auto correlation function
Auto correlation function
Fourier transformation
Structure functionStructure function Prominent peak in momentum space
Space-time correlationSpace-time correlation Spectral representation of structure function
Sensitive spectrum regions, quasi-particle?
),(),0(),()0()( qωStρtrρρrρ
USTC 0807 Hui Liu 10
SummarySummary Distribution function is describing the spacial configuration of a many-
body system which can be obtained via both theory and experiment.
We compared the dispersion relations of HTL and complete one loop,
pointing out an important discrepancy in the dynamical screening
regime which is responsible for the different static screening picture .
The RDF of hot QGP appears an obvious damping oscillation which
implies the QGP might be in a liquid state.
Static structure functions, which is the Fourier transformation of auto-
correlation function, can be measured by experiment. We hope in this
way the picture in our calculation can be tested by the experiments.
Any comments or suggestions are warmly welcome!
USTC 0807 Hui Liu 11
Back up slidesBack up slides
USTC 0807 Hui Liu 12
HTL approximationHTL approximation
The pole is purely imaginary
Soft modes of external line in HTL.
(high temperature limit)
All modes involved in complete
one-loop calculation.
Pole can be only chosen from the soft
modes in HTL approximation but from
all modes in complete one-loop
calculation.
USTC 0807 Hui Liu 13
One loopOne loop Static polarization tensor of QCDStatic polarization tensor of QCD
α
rq
iq Pole evolution with coupling Pole evolution with coupling
constantconstant T:1~2Tc α: 0.2~0.5