calculation of dielectric function of a quark-gluon plasma
DESCRIPTION
Calculation of Dielectric Function of a Quark-gluon Plasma. Jiang Bing-feng Li Jia-rong IOPP CCNU 2008.4. Outline Motivation Gluon self-energy and dielectric function of QGP calculated with the effective perturbative theory---the HTL resummation technique - PowerPoint PPT PresentationTRANSCRIPT
Calculation of Dielectric Function of a Quark-gluon
Plasma
Jiang Bing-feng Li Jia-rong
IOPP CCNU
2008.4
Outline
• Motivation• Gluon self-energy and dielectric function of Q
GP calculated with the effective perturbative theory---the HTL resummation technique
• Numerical curves of the dielectric function and discussion on the results
• Summary
Motivation
• The medium effects of hot and/or dense nuclear matter---hot topics in Heavy ion collision.
• The dielectric function is very important. The field in medium is different from that in vacu-um and the dielectric function reflects that differences.
• The dielectric function in the HTL approxi-mation is incomplete
• The formula for dielectric function
---longitudinal part of gluon self energy
In general, it is not possible to derive an analytic formula of the gluon self-energy, unless in the case of the HTL approximation. The gluon self-energy in the HTL approximation:
A brief Introduction to HTL resummation technique
• Hard momentum~T, soft momentum~gT
• Soft inner line---effective propagator
Hard inner line---bare propagator
• All legs of a vertex are soft---effective vertex, otherwise---bare vertex
Effective propagator
• Effective propagator is constructed with Dyson-schwinger equation
Calculation with HTL resummation technique
• Loop integrals seperated by two parts ---hard momentum and soft momentum
Braatten,Pisarski Phys.Rev.Lett 64.1138 Thoma hep-ph/0010164
our purpose: calculate the dielectric function excited by the hard gluon
• Hard contribution
External line and inner lines both are hard momentum, bare propagator and bare vertex are enough.
Hard contribution ~ the HTL gluon self energy at high temperature.
• Soft contribution
= +
• Effective propagator at finite temperature in the
real time formula in Coulomb gauge
• Gluon self-energy calculated with HTL resummation technique
= +
→
→
• Hard part
• Soft part
• Parameters:
g=0.1
T=500MeV
p=350MeV
Numerical curves and discuss on the dielectric function of QGP
• Real part of the dielectric function
Left picture: the HTL resummation result
Right picture: the HTL result
• The time-like region
• The singularity
• The space-like region
• Magnitude
• Solid curve: the HTL resummation result
dashed curve: the HTL result
The imaginary part of the dielectric function
• The positions of the inflexion and the maximum of the imaginary part are exactly the same as that of the maximum and the minimum of the real part
• Nonzero imaginary dielectric function related to some energy exchange phenomenon
• Exchange phenomenon in space-like region---Landau damping
• Nontrivial behavior of real dielectric function in space-like region related to Landau damping
• In the HTL approximation, dispersion relation is time-like, Landau damping is absent.
• In the case of the HTL resummation, although adopting time-like dispersion relation, we obtain the resonance absorbing structure of
the imaginary dielectric function, which comes from the nonlinear Landau damping.
• Because of non-Abelian and nonlinear interactions of eigenwaves, the time-like eigenwaves may produce space-like pulsations
the space-like pulsations interacting with plasma particles may cause nonlinear Landau damping.
Xiao-fei Zhang and Jia-rong Li Phys.Rev.C52.964
Xiao-ping Zheng and Jia-rong Li Phys.Lett.B409.45
• Rusummation : gluon self-polarization contains multi-waves processes which reflects non-Abelian and nonlinear interaction of QGP,which causes the Landau damping lost in the HTL approximation
Summary
• In space-like region, the dielectric function of QGP have two extrema,which reflects Landau damping mechanism.
• HTL approximation lost some imformation in the space-like region.
Thanks!