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What does HTL lose?. Hui Liu Jinan University, China. HTL approximation. Hard thermal loop (HTL) Widely used approximation to self-energy Advantages Simple and convenient for further calculations Gauge invariant Restrictions Requires weak coupling - PowerPoint PPT Presentation
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What does HTL lose?What does HTL lose?What does HTL lose?What does HTL lose?
Hui Liu Hui Liu Jinan University, ChinaJinan University, China
Hui Liu, SQM2008 Beijing, October 6-10 2
HTL approximation
• Hard thermal loop (HTL)– Widely used approximation to self-energy
– Advantages• Simple and convenient for further calculations• Gauge invariant
– Restrictions• Requires weak coupling• Equivalent to high temperature approximation
Hui Liu, SQM2008 Beijing, October 6-10 3
Why not HTL• Some facts in RHIC experiment
Lattice result, hep-lat/0011006v1
• Strongly coupled? Does HTL still work?― What information does HTL approximation
lose compared to the complete loop?
ST
AR
collab
oratio
n, P
RL
89 (2002
) 132301
Hui Liu, SQM2008 Beijing, October 6-10 4
Dispersion Relations
• Dispersion relation– Fundamental property of a many-body system– Energy-momentum relation determined by the
pole of effective propagator.
ΠL: longitudinal component of self-energy
ΠT: transverse component
Equation of dispersion
Hui Liu, SQM2008 Beijing, October 6-10 5
Comparison
• Self-energy of toy model QED
– HTL
– Complete one loop (C1L)
Q
P
Hui Liu, SQM2008 Beijing, October 6-10 6
• Dispersion relations– Solve the equation of dispersion and find out t
he relation between ω and q
The main difference between the two curves is the appearance of a threshold frequency on the C1L curve.
HTL
C1L
Above the plasma frequency, q is real and qi=0. While below it, q is complex. We plot ω-qi relation in the left area.
q=iqi
Hui Liu, SQM2008 Beijing, October 6-10 7
Dynamical screening
• Dynamical screening regime– Below the plasma frequency, the modes are
complex, which can be signaled by the screening of external charges .
cω
Above , is consis- tent zero. While below it has values, which indicates an expectant change in physics pro-perties.
q=qr+iqi
Hui Liu, SQM2008 Beijing, October 6-10 8
Oscillatory potential
• Static limit– HTL: Purely imaginary modes
– C1L: Complex modes
• Static screening potential
where
— Debye screening— Oscillatory screening
~~~~~~~~~~~~~~
Hui Liu, SQM2008 Beijing, October 6-10 9
Radial Distribution Function
• RDF– Probability of finding two particles at a distance r– Density-density autocorrelation function
– Typical RDFs of different states of matter
solid liqui
d gas
Hui Liu, SQM2008 Beijing, October 6-10 10
RDF of a liquid?• Which potential can result in a liquid? • RDF and the potential of “mean force”
– Short range order
– Indicate a liquid state?
Gelman, Shuryak, and Zahed, PRC 74, 044908 (06)
Molecular dynamical simulation
Hui Liu, SQM2008 Beijing, October 6-10 11
Conclusion• Physics concealed in the C1L dispersion relation might
not be revealed by the HTL
• Comparing the dispersion relations we found the existence of a threshold frequency in the dynamical screening regime of the C1L
– Below the threshold frequency the modes contain both real and imaginary parts
– In the static limit, the complex mode leads to an oscillatory screening potential, which is contrast to the Debye-like potential in the HTL case
• The oscillatory potential could result in a liquid-like RDF, which might indicate the liquid QGP
Hui Liu, SQM2008 Beijing, October 6-10 12
RDF in hot QGP
• Gluon polarization
• RDF of QGP
– Short range order. Very similar to the typical shape of liquid. Footprint of liquid QGP!?
– Enhanced oscillations at lower temperatures
0.5GeVT0.40.3
Hui Liu, SQM2008 Beijing, October 6-10 13
Non-zero frequencies
• Frequency-dependent screening
• For HTL, the potential is always Debye-like in the whole range of frequencies below the plasma frequency.
• For C1L, the potential can be either Debye-like or oscillatory.
– Above the threshold frequency the screening potential is Debye-like
– below that frequency, the potential is oscillating.
Hui Liu, SQM2008 Beijing, October 6-10 14
Screening of a moving particle?
• Current-current correlation
• Static case – density correlation– Static screening potential
• Non-static case– Frequency dependent screening potential