Theoretical Study of the Photons Production Kinetic In Hot Quark-Gluon Plasma Matter

In this paper, we study flow of photons rate production in a quark-gluon QG plasma. General theory of this study is based on the field theory for hard interaction. The kinetic of photons production from hard interaction in charm with anti-top to production photons with gluon ct̅ → γgdue to plasma phase at high temperatures (150, 200,250,300 and 350 MeV) .It has been investigated and studied using the postulate of quantum chromodynamic theory QCD .The photons production rate of hard photons with(E 1GeV) are insensitive to strength coupling and depend mainly on the temperature of system T . Despite the different critical temperature (150 and 190MeV) comes, we find that same order of flow rate photons magnitude in both cases. In both cases, the flow rate of photons production in the QG plasmais increased with increased temperature of system and photons energy and decreases with increases the strength coupling strength. Key Word: Photons Production, Kinetic, Hot Quark-Gluon Plasma


Introduction
The photons are important valuable tools to probing hot matter in relativistic heavy-ion collisions RHIC at BNL and Larger Hadronic Collision LHC at CERN [1][2]. The photons have been emitted from the different mechanism such that prompt photons, thermal photons and jet-medium photons .Photons are emited during the quark gluon plasma phase QGP and hadron gas Phase (HG) due to jets, and by decay of long-lived resonances into real photons [3]. Recently, the interaction of quark-gluon plasma has been achieved to understand the equilibrium state. Hard photons emission in both Compton and annihilation processes with having an energy large the temperature T of system [4]. The production of photons is observable in higher energy relativistic heavy-ion collisions. The interaction of quark-gluon plasma in hot media has radiated thermal photons due to transverse momenta [5]. Hard photons are a important tool to investigate and study the characteristic and properties of quark matter in ultrarelativistic heavy-ion collision. It could be probing the dense system during interaction of quark-gluon plasma for a short time [6]. In this paper,we can find the relation between the photons rate and properties in ̅ → quark system in plasma media according to the quantum chromodynamic postulate theory using MATLAP program .

2.Theory
The production of gamma photons from plasma quark gluon interaction has been related to the retarded polarization of the gamma photon using field theory the number of photons emitted from quarks gluon plasma interaction per unit time and per unit volume is [7][8].
where E is the energy of system ,q is momentum of quarks ,∏ , is the retarded selfenergy for photons emitted at temperature T and F E is the Bose-Einstein distribution function for gluon and given by [9].

F E
Where is the fugacity of gluon .Substituting Eq.(2) in Eq.(1) to produce: The retarded propagators self-energy term related to photons emission according to spectral density , by relation [10].
Where is square charge of quark , is soft momentum of quark propagator, is the hard momentum of quark propagator , is the energy of system , , and * , are the spectral function and conjugate spectral function of quark, and , , , , are the propagation and conjugate function of quarks system On the other hand, the and are Fermi Dirac representation for quark and anti-quark respectively. The quark and anti-quark distribution are given by the Juttner distribution functions [8]. Since the trace of system can be reformation using [12].
The Eq.(6) can simply be using the integral Dirac function [11].
Then Eq. (7) with Eq.(8) may be written as Then Eq.(3-46)simply due to solve the trace using identity of spectral functions to obtained [12].
Since the quark -gluon plasma system has interested with large photon energy case have, ́ ≫ , that's can use an approximation to given.
The Eq.(12) reformulated using to However the recursion relation of integral [11]. * , 1 * , Then Eq.(13 ) with Eq .(14) lead to: The second term in integral (3-59) refers to the correction term and is given by [ Where is the electro strength constant , is the strength coupling , is the square of electric charge of quarks system , is the fugacity of gluons , is the fugacity of quark , ́ is the fugacity of anti-quark , is the square of temperature of system and is the photons energy . The strength coupling is (25) Where is the flavor quantum number, is the momentum of photons system and the critical temperature .

3.Results
Table (1) shows strength coupling spectra of interaction ̅ → system in plasma that is calculated according to quantum flavor number, critical temperature and temperature of system. To obtain the strength coupling, the momentum spectra of system were taken from experimental date Pc =1,2,3,4 and 5 GeV [14] and elected the critical temperature Tc =150 MeV and Tc= 190MeV.It should be mentioned at this point that quantum flavor number was calculated using the summation ∑ 6 and estimation the total electric charge of quark  MeV. Figures (1) and (2) show the flow of photons rate plotted verse photons energy.

Discussion
We discuss behavior of photons flow rateproduction in quark anti quark interaction processes from a non-equilibrated QG plasma at finite potential with effect of coupling strength constant. The results indicate important information concerning photon produced as a signature of QG plasma. The photons flow rateof QG interaction with quantum quark flavor number 10 are discussed as follows. Figure (1 MeV. It has been taken the T = 0.350 GeV to find large effect of flow photons rate contribution due to increase the photons energy (1, 1.5, 2, 2.5, 3, 3.5 and 4 GeV). The strength coupling value also effect on contribute of the flow production rate and the rate is increased due to decreased the strength coupling and it has a larger flow rate produced at very higher temperature T=0.350 GeV and low strength coupling.  (1), the flow photons rate shows better outcome. This implies that critical temperature has more effect beside the strength coupling .In figure (2) ,we can show the less increases in contributions to the flow rate of photon at the same order of quantum flavor number as results of different in the strength coupling of QG plasma process. The flow rate increases with the effect of decreases strength coupling but decreases as temperature decreases. It is found that low temperature T=150 MeV produces less flow rate of photons in comparison to the large temperature T=350 MeV during the QG plasma. This shows that the flow rate produced by QG plasma process is low in high strength coupling in comparison to the low strength coupling in same processes. The results in both tables (1) and (2) and figures (1) and (2) do not show any huge of flow rate of photons in QG plasma process due to contributed by fugacities of quarks and gluon . In ̅ → system, the flow rate contribution from Tc=150MeV is less than flow rate contribution from Tc=190MeV over QG plasma process. Overall results are less effective in the case of critical temperature whith compared with photons energy and strength coupling .Finally, in both figures (1) and (2) , we consider the QG plasma interaction has large effect with photons energy and strength coupling and less effect with critical temperature . It is found that the flow rate of photons due to Tc=190 MeV is large in comparison to the Tc=150 MeV. Also, it is found a large flow photons rate due to same fugacity.

5.Conclusion
In conclusion the flow rate of photons yield is evaluated by integrated the flow rate over plasma phase. The calculation of flow rate of photons production as a function of photons energy corporating with strength coupling and critical temperature .So, the flow rate of photons emission from a QG plasma system play an important role in the investigation of photon emission from higher energy collision . It is found that large increase of flow photons production rate with decreased strength coupling and with increasing the temperature T and critical temperature at QG plasma system. Therefore, the flow photon rate is important for giving the information to create quark-gluon plasma media and supply more knowledge for the study and understanding of QGP interaction.