Study of Photon Emission at High Temperature of Quark Gluon Interaction

In this paper, the photons emission rate from the interaction of quark with gluon is calculated and studied based on quantum chromodynamics theory. The photonic rate is calculated for u g→d g γ system at bremsstrahlung processes with Bag constant B1/4=0.235GeV and B1/4=0.275GeV, system temperature (325-625) MeV and the value of fugacity of quark λQ=0.9 and gluon λG=0.02 to emit photons with energy 0.5 ≤ Eγ ≤ 5GeV in hadronic phase. The effect of system temperature on the photons emission rate was studied and discussed, it was found that it increases with increases of system temperature and decreases of coupling strength due to the deconfinement phenomena furthermore the photonic yield at B1/4=0.235GeV is less than the photonic yield at B1/4=0.275GeV.


Introduction
Elementary particle is one of the important branches of physics science [1].For several years, nuclear reaction models have a great importance to researchers to describe the nature of matter [2].The description of the nucleus structure depends on the nature of the elementary particles within it [3].According to the standard model, elementary particles are classified into fermions and bosons which the nuclear structure described through the interaction of fermions and bosons [4] [5].Quarks are fermions introduce by George Zweig and Gell-Mann [6].Each particle consists of a quark is known as a hadron, which is classified into mesons and baryons [7].Baryon is made of three quarks and meson is made of quark and antiquark [8] [9] There six flavors of quarks according to the increasing of quark mass, divided to three generations of quarks plus the antiquarks [10].and these quarks interacted with essential forces in addition to they are individually in interaction with the strong force [11] [12].Quarks have many intrinsic properties such as spin, charge, mass, isospin and parity called quantum numbers which must be conserved [13] [14].The strong interaction of quarks is descripted using quantum chromodynamics theory [15].The behavior of quarks in the strong interaction is explained by the color charge exchanging property through the gluons [16].There three type of color charge red, blue, and green and the principle that allows quarks to formation hadron is that they are color neutral [17] [18].Gluons are bosons or force carriers for strong interactions between elementary particles [19].There are eight gluons representing a pair of colors and anti-colors [20].Photon is a stable boson that does not carry a charge [21] which is emitted from the thermal equilibrium phase called the quark-gluon plasma phase [22] or the hot hadron phase, which follows the QGP in heavy ion collisions [23].In the Large Hadron Collider, there are many processes to photon production such as Compton scattering, bremsstrahlung, annihilation processes [24].In 2016, Hadi J.M. Al-agealy et al studied the photons emission rate for quark-gluon collisions emitted from Compton scattering using quantum chromodynamics theory [25].In 2016, Enas Jasim Mohsin and Hadi J.M. Al-agealy evaluated the photonic rate that emission from the interaction of quark-antiquark by annihilation processes [26].In 2023, Ola Z Ridha and Ahmed M Shwiekh calculated and studied the photons emission rate from charmgluon interaction by bremsstrahlung processes [27].In the present paper, the photonic yield rate for u g →d g γ system [28] is calculated and discussed for bremsstrahlung processes at high temperature.

Theory
The rate of photon emission from Bremsstrahlung processes for the quark-gluon interaction gives by [29].
Where F (E,T) is Bose -Einstein distribution function of gluon , I ∏ (E, λ ,T ) is the imaginary part of the self -energy at Bremsstrahlung process which is equal to [30].
Where N is the degeneracy factor, F is the factor of casimir S is the strength of electrodynamics, S is the strength of chromodynamics, ∑ e is the square charge of quark, F is the Jutiner distribution of quarks in the range of P and (E + P).
|K | is the integral of the self -energy which equal [31].

T B ………… 19
Where B is the Bag constant, N is the gluons spin states, N is the gluon color states, n is the freedom degree for quarks colors, n is the freedom degree for quarks spin and N is the flavor number.The strength coupling is given by [39] α ………….20 Where T is system temperature and N is the quantum flavor number and T is the critical temperature.

Results
The photons rate emitted from the interaction of up quark with gluon at high temperatures has been calculated and studied theoretically.The photons emission rate was presented for ug →dgγ system based on quantum chromodynamics theory (QCD) and quantum consideration.The quantum flavour number is the important parameter in limit (1 N 6) it is calculated by the summation of flavour number ∑ N , up quark has (N =1) [40] and down quark has (N 2) [41] and N for u g →d g γ system is N = (1+2) =3.The critical temperature is calculated using Eq (19) with B / =0.235, 0.275GeV [42], gluons spin states N 2 = , the gluon color states N = 8 [43], the degrees of freedom for quarks colors n =3, the freedom degrees for quarks spin n =2 [44].The result of critical temperature is shown in table1.The coupling strength is calculated by Eq (20) with critical temperatures values in table 1 and system temperature in limit (325-625) [45] MeV and N =3.The result of coupling strength list in table 2. The summation of square electric charge of the system of quark is compute from ∑ e with e = +2/3e [46] and e = -1/3e [47] then square electric charge for ug →dgγ system is 5/9e.the photons emission rate is calculated by Eq (18) and MATLAP program with coupling strength α from table 2, strength coupling constant for electromagnetic α =1/137 [48] , K = 4.45, K 4.26 [49] , fugacity of up quark λ =0.9 and fugacity of gluon λ =0.02 .The result of interaction of up quark with gluon is down quark and photons emission with energy of photon in rang (0.5-5 GeV) [50] .Result is shown in tables 3 and 4 and figures 1 and 2.

Discussion
The photons emission rate R E, P at bremsstrahlung processes was studied to understand the mechanism of the quark systems.The photons rate was calculated in Equation (18) as a function to flavor number, critical temperature, system temperature, coupling strength for up-gluon interaction.In table 1, the critical temperature T was calculated by Eq (19) with N =3 and B / =0.235, 0.275GeV.it can be found, the critical temperature increases with increases of the value of Bag constant.In table 2, the strength coupling calculated by Eq (20) and various value of critical temperatures and system temperature.It is noted that the strength coupling decrease with increases of system temperatures from 325MeV to 625MeV due to the confinement and deconfinement phenomena.In other side it is noted that the values of strength coupling at critical temperature T = 0.1820308439GeV is higher than the values of strength coupling at critical temperature T = 0.1555536302GeV.The photons emission rate R E, P was calculated for ug →dgγ system by Eq (18) with critical temperature T = 0.1820308439, 0.1555536302GeV, system temperature in rang (325-625MeV) and values of coupling strength from table2 to emit the photons with energy in rang (0.5-5 GeV) where the result of photonic rate R E, P can be seen in tables 3 and 4 with figure 1 and figure2.It is observed that the photons emission rate increase with increase the temperature of system and the maximum value of photonic rate at T = 0.1555536302GeV, T=625MeV and E = 0.5GeV is R E, P =2.5711E-06 1/GeV fm and the minimum value of photonic rate at T = 0.1555536302GeV, T=325MeV and E = 5GeV is R E, P =2.1641E-20 1/GeV fm .For T = 0.1820308439GeV, it can be observed that the photonic yield is higher than the photonic yield at previous critical temperature where the maximum value of photonic rate at T=625MeV and E = 0.5GeV is R E, P =2.6931E-061/GeV fm and the minimum value of photonic rate with T=325MeV and E = 5 GeV is R E, P =2.2921E-201/GeV fm .The calculation result of tables 1 and 2 show that the photons emission rate for ug →dgγ system increase with increase of system temperature and decrease of coupling strength and photonic yield at table 2 with B / =0.275GeV and T = 0.1820308439GeV is higher than the photonic yield at table 1 with B / =0.235GeV and T = 0.1555536302GeV.on other hand, the relationship between the photons emission rate and the photon energy.It is noted from figure1 and figure 2 that the photonic rate decreases with increase of photon energy from 0.5GeV to 5 GeV at varies values of the critical temperature and system temperatures.

Conclusion
In conclusion, the rate of photons emission from the interaction of up quark with gluon at bremsstrahlung processes was studied depending on quantum chromodynamics theory.The photons rate was calculated for ug →dgγ system with flavor number N =3 due to critical temperature, system temperature, strength coupling, the electric charge and quark-gluon fugacity to emit photons with energy in range (0.5-5GeV) by using MATLAP software.It was found that the rate of photons emission at high temperature for the system of ug →dgγ is inversely proportional to strength coupling and photon energy and directly proportional to bag constant, critical temperature and the temperature of system.

Table 1 .
The result of critical temperature calculation for ug →dgγ system.

Table 2 .
The coupling strength calculation results for ug →dgγ system.

Table 3 .
Rate of photon production at T = 0.1555536302 GeV, K