1. DILEPTONS FROM A CHEMICALLY EQUILIBRATING QGP AT FINITE BARYON DENSITY
Guan-Nana
OUTLINE
PART Ⅰ Background & Motivation
PART Ⅱ Evolution of the system
PART Ⅲ Dilepton production
PART Ⅳ Summary
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2. Background & Motivation
Dilepton production is considered to be a good probe to detect the new state of matter-QGP, because
Finite interaction with the plasma is only electromagnetic interaction.
Electromagnetic interaction has been studied very well .
Therefore, the dileptons are expected to retain the initial information of the QGP system.
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3. Jüttner distribution function of partons:
The system we study:
Chemical non-equilibrium
Finite baryon density
Jüttner distribution function of partons:
for quarks or antiquarks
for gluons
Fugacity are used to characterize the
nonequilibrium of the system .
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4. Evolution of the system
Expanding over chemical potential , get ＆
Combining:
Equation of energy-momentum conservation
Equation of baryon number conservation
Master equations of reactions:
Assuming that elastic parton scattering is rapid enough to maitain local thermal equilib- rium, the evolution of the parton densities can be given by the master equations .
Take the approximation
A set of coupled relaxation equations describing evolutions of temperature and quark chemical potential and fugacities .
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5. The evolution of QGP for initial values
with initial quark chemical potential
(a) the fugacity of quark(anti-quark) and gluon;
(b) quark chemical potential and temperature.
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6. The relation of quark chemical potential and the temperature at the same time.
Initial values:
The quark phase life-time increases with the initial quark chemical potencial going higher.
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7. Quark-antiquark annihilation:
Dilepton production
Dilepton production processes :
Quark-antiquark annihilation:
Compton-like scattering:
Bremsstrahlung of a quark and annihilation with scattering:
(i denotes a quark, an antiquark or a gluon).
Gluon fusion:
Quark-antiquark annihilation:
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8. Dileptons from annihilation -reaction (0):
Dileptons from annihilation –reaction (1) and Compton-like processes (2)and (3) :
Inserting the Jüttner distribution functions of partons and the squared matrix elements for reaction processes into the equation, integrate over
θ: the step function,
s, t and u : the Mandelstam variables.
to get the rate.
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9. Landau-Pomeranchuk-Migdal resummation for dilepton production from bremsstrahlung of a quark:
(Multiple scattering plays an important role in the process.)
They developed a simple method to compute the imaginary part of the retarded current-current correlator.
P. Aurenche, G. D. Moore, JHEP12 (2002) 006.
We further integrate these rates over the space-time volume of the reaction.:
We consider central collisions of
, so the final dilepton spectra is:
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10. The calculated dilepton spectra from various processes.
Curves 0-7 represent :
(7) Total of 0-6
Initial values:
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11. The calculated total dilepton yields for differentinitial quark chemical potential, curves 1- 4 represent the total spectra for:
0.001
0.284 q
GeV m =
0.569
0.852 q
GeV m =
We can see from the figure that the dilepton production goes up with the increasing initial quark chemical potential.
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12. Summary
In this work, based on the chemically equilibrating QGP model, at finite baryon density, we studied the evolution of the temperature and quark chemical potential, as well as the fugacity of quarks and gluons of the system;
Then we calculated the dilepton productions from different processes, and found that the contributions from leading-order quark-antiquark annihilation is dominant, and contributions from bremsstrahlung at low invariant mass and reactions at relatively higher invariant mass, cannot be ignored but half an order of magnitude lower;
At last we studied the effect of initial quark chemical potential on the total production of dileptons, and found that the initial quark chemical potential heighten the dilepton spectra.
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