Simple Scenario of Photons Emission from Anti Charm–Gluon Interaction using QCD Theory

 




In this work, the chromodynamics (QCD) theory was used to investigate the photon rate which was produced in interactions of anti-charm with gluon. The simple quantum scenario theory was implemented to give the rate equation that describes the collision of quark and gluon at a chemical potential  .The photon emission rate was evaluated from the anti-charm-gluon interaction of the cg →  dγ  collision at the temperature of the system in the range of 180 -  360 MeV with different critical temperatures (e.g. 116.575, 139.891, 157.377 and 174.863 MeV) with photons energy  GeV under the assumption that fugacity of quark and gluon  are   =0.08 and =0.02 respectively . The photon rate increases with decreasing the coupling of quark and gluon according to a decrease in the temperature of the system from 360 MeV to 180 MeV. The photon emission spectrum was calculated and discussed using a photon energy of 1GeV to 10GeV with different critical temperatures. In terms of QCD theory, the quantitative accomplishment was made for a unique six-flavor number nf = 4 + 2 of photon emission. The photon rate reaches minimum with photon energy E=10 GeV, it reﬂects the less coupling for the cg →  dγ interaction.




 


INTRODUCTION
An elementary particle is one of the main important branches of physics. It considers describing the fundamental building blocks of materials from an unbreakable component of bit small particles [1]. In recent years, the quarkgluon interaction that occurred in the heavy-ion collisions (RHIC) and large hadron collider (LHC) experiments were introduced as a valuable probing for photon production [2]. Nevertheless, the quark-gluon produced in heavy-ion collisions introduces a good understanding of the behavior of nucleons in a hadron medium [3]. Gell-Mann and Zweig are introduced independently the quark model in 1964 for building nuclear matter. Quark is the basic building matter of protons and neutrons; they are held together according to the strong nuclear force [4]. However, the higher temperature is not been an extreme feature for the interaction of quark-gluon that's producing in the heavy ion collisions [5]. Different theories have been introduced to study the structure of matter and interaction of quarkgluon in a variety of scientific institutes across the world [6]. Most of the theoretical treatments of quark-gluon interaction try to describing the quantities relying on the loss energy of heavy quarks via different dynamics [7]. The charm hadrons are observable in heavy ion collision experiments and that is important to provide detailed knowledge about the strong coupling of quark gluon [8]. The photons are produced in various processes; decay photons come from hadron decays and direct photons. Moreover, the direct photons are divided to prompt photons and thermal photons are emitted from the quark-gluon medium [9]. The photons are produced through quark-gluon interaction and achieved in higher energy relativistic heavy-ion collisions to understand the equilibrium state of quark-gluon matter [10]. The standard model introduces a mathematical framework for describing the interactions of elementary particles; electromagnetism, weak, and strong interactions. Moreover, the standard model had succeeded in understanding new state of matter of quantum chromodynamics and quark-gluon interaction [11]. The main goal of this article is to theoretically calculate the photon emission rate form Interaction of anti-Charm quark with gluon using simple model based on quantum chromodynamic theory.

THEORY
The photon emission rate produces from hard interaction of quark-gluon with energy E and momentum P can be given by [12]. (1) where is the Bosonic distribution and is imaginary part of retarded self-energy polarization and given as follows [13]: where and are number of flavor and the Casimir operator, and are the quantum electrodynamics and quantum chromodunamic coupling, is Fermi distribution of quark, and are the dimensionless constant of self-integral [14], and is square electric charge for quarks. The Juttner function and as function of fugacity of quarks is as below [15]: where is chemical potential relative to fugacity of quarks and gluons by [16]. Inserting Eq. (3) and Eq.(4) in Eq.(2) with expand to given .
where and are integral parameters that's given by We reform integrals Eq.(6) and Eq.(7) in six term; The second integral is The third integral is The fourth terms is The five integral term The final integral term is The solutions of six term are given by .
On the other hand, we insert the , , and in Eq.(7) to result .
Where is flavor number, is temperature of system and is critical temperature of system, it can be given by [22].
where is the bag coefficient and degeneracy factors for gluons and quarks The is number of gluons degrees of freedom as function of gluons spin and color states and is number of quarks degrees of freedom.as function of color number , spin and flavour degrees ,the Eq. (28) become (29)

RESULTS
Firstly, the critical temperature to predict the photon emission rate was estimated . The critical temperature was evaluated according to the bag constant B in Eq.(29) using the degeneracy factor as function of spin state and for gluons and function to for anti-charm and anti-down quarks in system with using the Bag constant from table (1) with insert in Eq.(29), the results are presented in Table (1) for ̅ quark, gluon to produce ̅ quarks and emission . Next, we had evaluated the coupling between anti-charm quarks with gluon in Eq.
(27), we were inserted the critical temperature from table (1) and take into account the temperature of ̅ g → ̅ γ system from T=180 to 360 MeV and increases by 30 Mev with . The results can be shown in Table (2). A simple scenario to evaluate the photon rate need to compute the electric charge with flavour number of ̅ g → ̅ γ system , where one can evaluate the electric charge of anti-charm and anti -down quarks in the system with no electric charge for gluon. However, the electric charge of ̅ g → ̅ γ system uses summation ∑ , which was already applied on anticharm and anti-down quarks to extract of charge system, ,this results ii ⁄ of ̅ g → ̅ γ system where charge of anti-charm quark is ⁄ and anti-down is ⁄ ,and the favor of quarks system is for ̅ g → ̅ γ collision system .The photon rate produces from the anti-charm -gluon collision was calculated using Eq.(26) with insertion of the critical temperature from Table(1) and coupling  from Table(2), the self-integrals constant 4.26 and 4.45 [23] and takes and with uses the photon energy [24].Specifically ,we assume the fugacity =0.02 for quark , =0.08 for gluon [25] and take the chemical potential [26]. The Resulted data are given in Tables (3)

DISCUSSION
The photon rate theory in Eq.(26), is good tool to discuss the hard interaction between quark and gluon interaction depending on the QCD theory and strength coupling ,temperature of system , energy of photon , fugacity of quark and gluon , and critical temperature parameters. Coupling between quark and gluon is the main parameters that has impact on QCD parameters. It is influenced by the flavour number, temperature of system and critical temperature. In fact, the critical temperature has been implicitly affected by Bag constant and flavor number. However, we can see from to study the effect on the photons rate, we can perform the calculation with different critical temperatures. In fact, the critical temperature is the main parameter that influence the strong coupling and photon rate. The photons rate in tables (3) to (6) are different for different critical temperatures and the coupling of quark and gluon. In fact, we can find a large coupling at the higher critical temperature and low photon rate. The Coupling of quark and gluon in Table (2) was decreased with the increase of the temperature of the system from 180 MeV to 360 MeV, which was a significant influence on the rate. The coupling was decreased with the increase temperature of system in the range of 180 MeV to 360MeV for ̅ g → ̅ γ system. The approach expression in Eq.(27) shows that coupling proportional with critical temperature and temperature of ̅ g → ̅ γ system . The coupling of quark-gluon collisions at ̅ g → ̅ γ system varied at different critical temperature. As seen as from Table (2), the coupling increases with increaseing the critical temperature and increases temperature from 180 MeV to 360MeV. Figures (1) (2), (3) and (4) and Tables 3),(4), (5)and (6) (3),(4), (5) and (6) respectively . In Figures (1) to (4), we can notice the rate of photon spectra in ̅ g → ̅ γ collision. The rate of photon yields from the in ̅ g → ̅ γ system decreases with increasing the energy of photons E(GeV) from 1 to 10 GeV at critical temperatures from to MeV with six flavors number and various temperatures of system. The rate of photon yields from interaction of quark -gluon in ̅ g → ̅ γ system increases with increasing energy of the system and decreases the coupling with an increasing critical temperature. It can be seen from Table (6) and Figure (4) that the rate of photon was with large value at the critical temperature of = MeV when compared to the less rate at the = MeV. However, the photon rate was reached to maximum from ̅ g → ̅ γ system at the energy of photons in Tables from (3) to (6) and Figures from (1) to (4) compares to minimum for . In general, the theoretical model of photons spectrum shows that rate increases to the high values and effects by increases the temperature of the system and decreases the coupling between anti charm quark and gluon to produces anti down with photons emission at any critical temperature in all Tables from (3) to (6) for the ̅ g → ̅ γ system with .

CONCLUSION
A systematic discussion of a hard collision of quark-gluon to produce photon spectra at chemical potential is presented with emphasis on the influences of the coupling, temperature of the system, photon energy and critical temperature of quark flavors on photons spectrum. The rate of photon emission at various critical temperatures and coupling of quark and gluon calculated according to the expression of photon emission using a simple model for collisions for anti-charm quark interaction with gluon to produce anti-down and photons in the energy region. The models of the emission of photon rate was based on the QCD model that describes the collision in six flavour numbers. According to the implemented expression of the photon rate equation, we can conclude that there is a significant influence on the coupling, temperature of the system, photon energy and critical temperature on the contribution of the rate of photon behavior of the ̅ g → ̅ γ interaction. The coupling photon energy, critical temperature and temperature of the system have been an ingredient in the production of the photon rate. We discussed the feature of the QCD effect on the photon rate of the anti-charm -gluon interaction at a temperature of the system in the range of 180-360 MeV.
With regard to possible QCD features; coupling, the temperature of the system, critical temperature and photon energy to produce the photon was quantitatively achieved for a unique flavor number of = 4 + 2 of the photons spectrums. The interest of data in the case of flavour number =6 was the minimum of photon rate at E=10 GeV especially. It indicates the weak proportional of quarks and gluons which was already expected. Finally, the rate of photon will be producing in higher energy, it is a good tool to work with nucleons structure.