177 Β© Published by College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad. This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License Ola Z Ridha1* and Ahmed M Shweikh2 1,2Department of Physics, College of Education for Pure Science (Ibn-Al-Haitham), University of Baghdad, Baghdad,Iraq. *Corresponding Author. Received:6 June 2023 Accepted:9 July 2023 Published:20 July 2024 doi.org/10.30526/37.3.3574 Abstract In this paper, a theoretical model has been presented to calculate the rate of photon emission. The photonic yield has been calculated for the interaction of heavy charm quarks with gluon from Bremsstrahlung processes. The rate of photon emission was evaluated for the interaction of the charm quarks with the gluons for𝑐𝑔 β†’ d𝛾 system based on quantum chromodynamics theory. The calculation is due to essential parameters, including the quantum flavor number Nf =6 the chromodynamics constant, thermal energy in range 185MeV ≀ T ≀305MeV, and critical temperature TC=0.1311479288GeV, 0.1748639051 GeV, 0.2040078893GeV. It was considered the energy of photons in the range 1GeV ≀ E ≀ 3.5GeV. Furthermore, the values of the fugacity of quark Χ’ 𝑄 =0.068 and gluon Χ’ 𝐺 =1. We found that the photonic yield at TC= 0.2040078893GeV was greater than the photonic yield at TC=0.1311479288 and 0.1748639051 GeV. The rate of photon emission increases with increases in both the critical temperature and thermal energy and decreases with chromodynamic constant, and it decreases with increases in the energy of photons. Keywords: Charm-gluon interaction, photon emission, chromodynamics, bremsstrahlung. 1. Introduction The picture of the basic components of matter and the interactions between them that has emerged in recent years is very amazing [1]. All matter appears to consist of quarks and leptons, which are assumed to be point-like (no structure), spin 1/2 particles [2]. Quarks are hypothetical particles hypothesized by the two scientists George Zweig and Gell-Mann [3]. The six flavors of quarks are divided into three generations (up, down), (strange, charm), and(top, bottom) [4]. Each particle that consists of a quark is known as a hadron, which is classified into mesons and baryons [5]. Baryon is made of three quarks, and Meson is made of quarks and antiquarks [6]. Quarks have many intrinsic properties, like mass, spin, charge, symmetry, etc. All these properties are called quantum numbers and must be conserved [7]. They are subject to electromagnetic interactions as they carry the electric charge [8]. Furthermore, they have a second type of charge, which is the color charge (red, blue, or green), which makes them also subject to strong interactions by gluon exchanging [9,10]. Calculation of the Photons Emission Rate by Interaction of Charm Quark with Gluon https://creativecommons.org/licenses/by/4.0/ https://www.researchgate.net/scientific-contributions/Saba-Mustafa-Hussein-2190849612 https://orcid.org/0000-0002-4656-1941 mailto:ula.Reda2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0002-4656-1941 mailto: ahmad.mosa@ihcoedu.uobaghdad.edu.iq IHJPAS. 2024, 37( 3 ) 178 Charm (C) is a quark flavor that was invented to explain the big narrowness of the huge resonances (ψ) during observation of the meson J/ψ resonance produced by electron and antielectron annihilation [11]. The theory that depicts strong interactions is quantum chromodynamics theory [12]. Photons are produced in heavy ion collisions by establishing the quark-gluon matter system and exploring the state of matter in decoupled quarks and gluons. The two phenomena that predict the behavior of quarks at high temperatures and high densities are confinement and deconfinement [13] and [14]. In the Large Hadron Collider, there are many processes for photon production, such as Compton scattering, bremsstrahlung, and annihilation processes [15,16]. In the present paper, the photonic yield rate for the 𝑐𝑔 β†’ d𝛾 system is calculated and discussed for bremsstrahlung processes. 2. Materials and Methods The photon emission rate from the interaction of quark and gluon is given [17]. Rqg H (E, P)= - FG(E) (2Ο€)3 Im∏ i f (E, P) (1) Where FG(E) is the distribution function of gluons, Im∏ i f (E,P) is the propagation of self-energy for photon emission, which is given in [18]. Im∏ i f (E, P) = ( N Ο€4 Cca) gE 2 gC 2 T EΞ³ 2 ∫ |Itl ∞ 0 | [Fa(P) βˆ’ F q(E + P)][P2 + (P + E)2]dp (2) Cca is Casmir factor given by[19]. Cca = Nc 2βˆ’1 2Nc (3) Where Nc is the quarks number Nc = 3, then Cca = 4/3, and N is the degeneracy factor N β‰ˆ 3, with introducing the total electric charge of the quarks βˆ‘ ( eq e )2 q into the system, Equation (2) is reduced to: Im∏ i f (E,P) = ( 4 Ο€4) gE 2 gC 2 T EΞ³ 2 βˆ‘ ( eq e )2 q ∫ |Itl ∞ 0 | [Fa (P) βˆ’ Fq (E + P)][P2 + P2 + 2EP + E2 ] dp (4) Integration of self-energy [20] |Itl|= |It-Il| (5) Where It and Il are dimensionless constants, and by inserting Equation (5) into Equation (4), it is reduced to: Im∏ i f (E,P) = ( 4 Ο€4) gE 2 gC 2 T EΞ³ 2 βˆ‘ ( eq e )2 q |It-Il|∫ [Fa (P) βˆ’ Fq (E + P)] ∞ 0 [2P2 + 2PE + E2] dp.(6) The juttner distribution function for quarks is [21] Fa(P) = Ξ»Q e P T+Ξ»Q (7) And Fq (E + P) = Ξ»Q e (P+E) T +Ξ»Q (8) Where Ξ»Q is the fugacity function of quark, and by inserting Equations (7) and (8) in Equation (6), it is reduced to: Im∏ i f (E,P) = ( 4 Ο€4) gE 2 gC 2 T EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il| ∫ Ξ»Q(2P2+ 2PE+E2) e P T+ Ξ»Q ∞ 0 dP - ∫ Ξ»Q(2P2+ 2PE+E2) e (P+E) T +Ξ»Q ∞ 0 dP (9) The solution to the integral term is: IHJPAS. 2024, 37( 3 ) 179 ∫ Ξ»Q(2P2+ 2PE+E2) e P T+ Ξ»Q ∞ 0 dP -∫ Ξ»Q(2P2+ 2PE+E2) e (P+E) T +Ξ»Q ∞ 0 dP = Ξ»QT(1 βˆ’ eβˆ’ EΞ³ T )[2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1)] (10) Inserting equation (10) into equation (9), it is reduced to Im∏ i f (E,P) = ( 4 Ο€4) gE 2 gC 2 T EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il| [Ξ»Q T(1βˆ’eβˆ’ EΞ³ T ) ( 2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1))] (11) The strength of electrodynamics is [22] gE 2 = 4παE (12) The quantum chromodynamics coupling is [23] gC 2 = 4παC (13) Inserting the Equations (12) and (13) in Equation (11), Equation (11) is reduced to: Im∏ i f (E,P) = ( 64 Ο€2) Ξ±EΞ±C T2 EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il| [Ξ»Q (1βˆ’eβˆ’ EΞ³ T )( 2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1))] (14) Substituting Equation (14) in Equation (1), it is reduced to: Rqg H (E, P)=- FG(E) (2Ο€)3 ( 64 Ο€2) Ξ±EΞ±C T2 EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il|[Ξ»Q (1βˆ’eβˆ’ EΞ³ T )( 2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1))] (15) The distribution of gluons FG(E) for EΞ³ ≫ T is [24]. FG(E) = Ξ»G e EΞ³ T βˆ’Ξ»G = 1 e EΞ³/T Ξ»G βˆ’1 Χ’ β‰ˆ G eβˆ’ EΞ³ T (16) Where Ξ»G is the fugacity of gluons and by inserting Equation (16) in Equation (15), Equation (15) reduced to: Rqg H (E, P)= 8 Ο€5 Ξ±EΞ±C T2 EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il| Ξ»QΞ»Geβˆ’ EΞ³ T (eβˆ’ EΞ³ T βˆ’ 1)( 2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1)) (17) For EΞ³ β‰₯ T, then eβˆ’ EΞ³ T βˆ’ 1 β‰ˆ eβˆ’ EΞ³ T (18) Inserting Equation (18) in Equation (17), it is reduced to Rqg H (E, P)= 8 Ο€5 Ξ±EΞ±C T2 EΞ³ 2 βˆ‘ ( eq e )2 q |It βˆ’ Il| Ξ»QΞ»Geβˆ’ 2EΞ³ T ( 2T2Ξ“(3) + 2ET Ξ“(2) + E2Ξ“(1)) (19) The critical temperature is [25] TC = [ 90B Ο€2(NSΓ—NC)+ 7 4 (ncΓ—nsΓ—nf) ] ΒΌ (20) Where TC is the critical temperature, B1/4 is the Bag constant, NS, NC is the number of spin and gluon color, and nc, ns, nf is the number of quark color, spin, and flavor number. The coupling strength is given by [26] Ξ±c = 6Ο€ (33βˆ’2Nf) ln 8T TC (21) Where T is the temperature of the system. IHJPAS. 2024, 37( 3 ) 180 3. Results The rate of photons emitted from the interaction of heavy charm quarks with gluons was studied and evaluated theoretically. We estimated the critical temperature according to the bag constant in Eq (20) with B 1 4⁄ = 225, 300, and 350MeV [27], and the degrees of freedom for gluon are NS=2, NC=8 and the degrees of freedom for quarks are 𝑛𝑐 =3, ns = 2, nf = 6. The result of the critical temperature calculation can be shown in Table 1. Table 1. Critical temperature calculation result for 𝑐𝑔 β†’ d𝛾 system The chromodynamics constant between charm quarks and gluon was calculated using Eq (21) with the critical temperature in Table1, and the system temperature in the limit (185-305MeV) and Nf=6.The result of strength coupling is listed in Table 2. Table 2. Critical result of strength coupling for 𝑐𝑔 β†’ d𝛾 system. T (GeV) Chromodynamics constant 𝛂𝐂 π“πœ=0.1311479288 π“πœ=0.1748639051 π“πœ=0.2040078893 0.185 0.3703769235 0.4202651765 0.4529573937 0.205 0.3553259183 0.4009919782 0.4306486485 0.225 0.3426971623 0.3849816976 0.4122369774 0.245 0.3319059992 0.3714159636 0.3967211497 0.265 0.3225468018 0.359735121 0.3834229094 0.285 0.3143284738 0.3495424097 0.3718652301 0.305 0.307036152 0.3405480378 0.3617020613 The rate of photon emission was calculated by summation of the electric charge βˆ‘ ( eq e )2 q for 𝑐𝑔 β†’ d𝛾 system with ec= +3/2e and ed= -1/3e and the results was 5/9e. The flavor number Nf=6 for the system as it was calculated from the summation of Nfi = βˆ‘ Nfi 6 i=1 for charm and down quarks with inserting ∝E = 1/137 and the self-integral constant It=4.45,Il=-4.26 [28], supposing that the fugacity Ξ»Q=0.068, Ξ»G=1[29]. In addition to the system temperature in the range (185–305MeV), photon energy (1–3.5GeV) [30] and the values of chromodynamics constant are stated from Table 2. The emission rate of photons is calculated by substituting all the above values into Eq (19) and using MATLAB software. The photon emission rate result for the system 𝑐𝑔 β†’ d𝛾 is shown in Table 3 to Table 5 and Figure 1 to Figure 3. 𝐁 𝟏 πŸ’β„ (GeV) Critical temperature π“πœ(GeV) 0.225 0.1311479288 0.300 0.1748639051 0.350 0.2040078893 IHJPAS. 2024, 37( 3 ) 181 Table 3. Rate of emission photons Rqg H (E, P) at 𝑇𝑐= 0.1311479288GeV for 𝑐𝑔 β†’ d𝛾 system with Nf =6 and Χ’ Q Χ’ ,0.068= g = 1 𝐄𝛄 π†πžπ• 𝐑πͺ𝐠 𝐇 (𝐄, 𝐏) 𝟏 π†πžπ•πŸπŸπ¦πŸ’ T=185 MeV T=205 MeV T=225MeV T=245MeV T=265MeV T=285MeV T=305MeV 𝛂𝐂 = 𝟎. πŸ‘πŸ•πŸŽπŸ’ 𝛂𝐂 = 𝟎. πŸ‘πŸ“πŸ“πŸ‘ 𝛂𝐂 = 𝟎. πŸ‘πŸ’πŸπŸ• 𝛂𝐂 = 𝟎. πŸ‘πŸ‘πŸπŸ— 𝛂𝐂 = 𝟎. πŸ‘πŸπŸπŸ“ 𝛂𝐂 = 𝟎. πŸ‘πŸπŸ’πŸ‘ 𝛂𝐂 = 𝟎. πŸ‘πŸŽπŸ•πŸŽ 1 2.4203E-11 8.5728E-11 2.4825E-10 6.1664E-10 1.3588E-09 2.7218E-09 5.0461E-09 1.25 1.4895E-12 6.8040E-12 2.4251E-11 7.1575E-11 1.8238E-10 4.1351E-10 8.5300E-10 1.5 9.4340E-14 5.5742E-13 2.4523E-12 8.6236E-12 2.5477E-11 6.5543E-11 1.5079E-10 1.75 6.0746E-15 4.6509E-14 2.5299E-13 1.0618E-12 3.6428E-12 1.0651E-11 2.7371E-11 2 3.9518E-16 3.9251E-15 2.6429E-14 1.3253E-13 5.2860E-13 1.7584E-12 5.0526E-12 2.25 2.5884E-17 3.3377E-16 2.7841E-15 1.6693E-14 7.7462E-14 2.9337E-13 9.4327E-13 2.5 1.7034E-18 2.8532E-17 2.9499E-16 2.1161E-15 1.1430E-14 4.9312E-14 1.7750E-13 2.75 1.1249E-19 2.4484E-18 3.1388E-17 2.6947E-16 1.6950E-15 8.3333E-15 3.3595E-14 3 7.4471E-21 2.1070E-19 3.3502E-18 3.4434E-17 2.5229E-16 1.4139E-15 6.3859E-15 3.25 4.9399E-22 1.8171E-20 3.5846E-19 4.4117E-18 3.7660E-17 2.4065E-16 1.2179E-15 3.5 3.2818E-23 1.5698E-21 3.8425E-20 5.6639E-19 5.6342E-18 4.1057E-17 2.3287E-16 Figure 1. Rate of emission photons Rqg H (E, P) as function of EΞ³at 𝑇𝑐= 0.1311479288GeV for 𝑐𝑔 β†’ d𝛾 system. 1 1.5 2 2.5 3 3.5 10 -24 10 -22 10 -20 10 -18 10 -16 10 -14 10 -12 10 -10 10 -8 E (GeV) lo g (R H q g ) (G e V 2 ) T =185 MeV T =205 MeV T =225 MeV T =245 MeV T =265 MeV T =285 MeV T =305 MeV IHJPAS. 2024, 37( 3 ) 182 Table 4. Rate of emission photons Rqg H (E, P) at 𝑇𝑐= 0.1748639051GeV for 𝑐𝑔 β†’ d𝛾 system with Nf =6 and Χ’ Q Χ’ ,0.068= g = 1. 𝐄𝛄 π†πžπ• 𝐑πͺ𝐠 𝐇 (𝐄, 𝐏) 𝟏 π†πžπ•πŸπŸπ¦πŸ’ T=185 MeV T=205 MeV T=225MeV T=245MeV T=265MeV T=285MeV T=305MeV 𝛂π‘ͺ = 𝟎. πŸ’πŸπŸŽπŸ‘ 𝛂π‘ͺ = 𝟎. πŸ’πŸŽπŸπŸŽ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ–πŸ“πŸŽ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ•πŸπŸ’ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ“πŸ—πŸ• 𝛂π‘ͺ = 𝟎. πŸ‘πŸ’πŸ—πŸ“ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ’πŸŽπŸ“ 1 2.7463E-11 9.6746E-11 2.7889E-10 6.9005E-10 1.5155E-09 3.0267E-09 5.5969E-09 1.25 1.6901E-12 7.6784E-12 2.7243E-11 8.0095E-11 2.0341E-10 4.5983E-10 9.4610E-10 1.5 1.0705E-13 6.2906E-13 2.7549E-12 9.6502E-12 2.8414E-11 7.2886E-11 1.6725E-10 1.75 6.8928E-15 5.2486E-14 2.8421E-13 1.1882E-12 4.0628E-12 1.1844E-11 3.0359E-11 2 4.4841E-16 4.4295E-15 2.9690E-14 1.4831E-13 5.8954E-13 1.9554E-12 5.6041E-12 2.25 2.9370E-17 3.7666E-16 3.1276E-15 1.8681E-14 8.6393E-14 3.2624E-13 1.0462E-12 2.5 1.9329E-18 3.2199E-17 3.3139E-16 2.3680E-15 1.2748E-14 5.4836E-14 1.9688E-13 2.75 1.2764E-19 2.7631E-18 3.5261E-17 3.0155E-16 1.8904E-15 9.2669E-15 3.7262E-14 3 8.4502E-21 2.3778E-19 3.7636E-18 3.8533E-17 2.8138E-16 1.5723E-15 7.0829E-15 3.25 5.6053E-22 2.0507E-20 4.0269E-19 4.9369E-18 4.2002E-17 2.6761E-16 1.3508E-15 3.5 3.7238E-23 1.7716E-21 4.3166E-20 6.3381E-19 6.2838E-18 4.5657E-17 2.5829E-16 Figure 2. Rate of emission photons Rqg H (E, P) as function of EΞ³at 𝑇𝑐=0.1748639051GeV for 𝑐𝑔 β†’ d𝛾 system. 1 1.5 2 2.5 3 3.5 10 -24 10 -22 10 -20 10 -18 10 -16 10 -14 10 -12 10 -10 10 -8 E (GeV) lo g (R H q g ) (G e V 2 ) T =185 MeV T =205 MeV T =225 MeV T =245 MeV T =265 MeV T =285 MeV T =305 MeV IHJPAS. 2024, 37( 3 ) 183 Table 5. Rate of emission photons Rqg H (E, P) at 𝑇𝑐= 0.2040078893GeV for 𝑐𝑔 β†’ d𝛾 system with Nf =6 and Χ’ Q Χ’ ,0.068= g = 1. 𝐄𝛄 π†πžπ• 𝐑πͺ𝐠 𝐇 (𝐄, 𝐏) 𝟏 π†πžπ•πŸπŸπ¦πŸ’ T=185 MeV T=205 MeV T=225MeV T=245MeV T=265MeV T=285MeV T=305MeV 𝛂π‘ͺ = 𝟎. πŸ’πŸ“πŸ‘πŸŽ 𝛂π‘ͺ = 𝟎. πŸ’πŸ‘πŸŽπŸ” 𝛂π‘ͺ = 𝟎. πŸ’πŸπŸπŸ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ—πŸ”πŸ• 𝛂π‘ͺ = 𝟎. πŸ‘πŸ–πŸ‘πŸ’ 𝛂π‘ͺ = 𝟎. πŸ‘πŸ•πŸπŸ— 𝛂π‘ͺ = 𝟎. πŸ‘πŸ”πŸπŸ• 1 2.9600E-11 1.0390E-10 2.9863E-10 7.3706E-10 1.6153E-09 3.2200E-09 5.9445E-09 1.25 1.8216E-12 8.2463E-12 2.9172E-11 8.5552E-11 2.1681E-10 4.8920E-10 1.0049E-09 1.5 1.1537E-13 6.7559E-13 2.9499E-12 1.0308E-11 3.0285E-11 7.7540E-11 1.7764E-10 1.75 7.4290E-15 5.6368E-14 3.0433E-13 1.2691E-12 4.3303E-12 1.2601E-11 3.2245E-11 2 4.8329E-16 4.7571E-15 3.1792E-14 1.5841E-13 6.2836E-13 2.0802E-12 5.9522E-12 2.25 3.1655E-17 4.0452E-16 3.3490E-15 1.9953E-14 9.2082E-14 3.4707E-13 1.1112E-12 2.5 2.0832E-18 3.4580E-17 3.5485E-16 2.5293E-15 1.3587E-14 5.8338E-14 2.0911E-13 2.75 1.3757E-19 2.9674E-18 3.7757E-17 3.2210E-16 2.0149E-15 9.8587E-15 3.9577E-14 3 9.1075E-21 2.5536E-19 4.0301E-18 4.1159E-17 2.9991E-16 1.6728E-15 7.5229E-15 3.25 6.0413E-22 2.2023E-20 4.3119E-19 5.2732E-18 4.4768E-17 2.8470E-16 1.4347E-15 3.5 4.0135E-23 1.9026E-21 4.6222E-20 6.7700E-19 6.6975E-18 4.8572E-17 2.7433E-16 Figure 3. Rate of emission photons Rqg H (E, P) as function of EΞ³at 𝑇𝑐=0.2040078893GeV for 𝑐𝑔 β†’ d𝛾 system. 4. Discussion The rate of photon emission was calculated to understand the behavior of quarks. It is related to the energy of photons and chromodynamics constant which is affected by the critical temperature, thermal energy, and flavor number for 𝑐𝑔 β†’ d𝛾 system. The chromodynamics constant was calculated with the Nf=6 and different values of the critical temperature and thermal energy in Eq (21). It can be found that the chromodynamics constant decreases with increases of the thermal energy from 185MeV to 305MeV as we note from the results in Table 2, chromodynamics constant at T=185MeV is𝛼𝑐=0.3703769235, 0.4202651765, 0.4529573937 for 𝑇𝑐=0.1311479288, 0.1748639051, 0.2040078893 GeV respectively. It decreases with the increase 1 1.5 2 2.5 3 3.5 10 -24 10 -22 10 -20 10 -18 10 -16 10 -14 10 -12 10 -10 10 -8 E (GeV) lo g (R H q g ) (G e V 2 ) T =185 MeV T =205 MeV T =225 MeV T =245 MeV T =265 MeV T =285 MeV T =305 MeV IHJPAS. 2024, 37( 3 ) 184 of the system temperature, where it reaches at T=305MeV to 𝛼𝑐=0.307036152, 0.3405480378, 0.3617020613. On the other side, the chromodynamics constant increases with the increase of the critical temperature as we can note for T=185MeV that 𝛼𝑐=0.3703769235 at 𝑇𝑐= 0.1311479288GeV and 𝛼𝑐= 0.4529573937at 𝑇𝑐= 0.2040078893GeV. The rate of photon emission Rqg H (E, P) was calculated using Eq (19) with the thermal energy in the range of (185MeV≀ T ≀ 305MeV) and the energy of photons (1GeV≀ EΞ³ ≀ 3.5GeV). The critical temperature was calculated using Eq (20). We can observe that the maximum value of photons rate at T= 305MeV and EΞ³ =1GeV where Rqg H (E, P)=5.9445E-09 1 GeV2fm4at 𝛼𝑐 = 0.3617 and 𝑇𝑐=0.2040078893 GeV. On the other hand the minimum value of photon emission rate at T= 185MeV and EΞ³=3.5GeV where Rqg H (E, P) = 3.2818E-23 1 GeV2fm4 at 𝛼𝑐= 0.3704 and 𝑇𝑐=0.1311479288GeV. If a comparison can be made between the calculation values of Table 3, Table 4, and Table 5, one can find that the rate of photon emission for three tables is Rqg H (E, P) =2.4203E-11, 2.7463E-11, 2.9600E- 11 1 GeV2fm4, respectively at T=185MeV and it increases with the increasing of the system temperature as it reaches to Rqg H (E, P) =5.0461E-09, 5.5969E-09, 5.9445E-09 1 GeV2fm4 at T=305MeV. In contrast, the above result of the photon emission rate shows that the photon is yield at 𝑇𝑐=0.1311479288GeV is less than the rate of photons yield at 𝑇𝑐= 0.2040078893GeV which mean the rate of photon emission increases with increasing the critical temperature. Figure 1, Figure 2 and Figure 3 demonstrate the relationship between the rate of photon emission Rqg H (E, P) and the energy of photons EΞ³. We can note from figures that the photons rate decreases with the increasing of the energy of photons from 1GeV to 3.5GeV at various values of the critical temperatures and thermal energy, and the production of photons emitted at EΞ³ = 1GeV is faster compared to EΞ³= 3.5GeV. 5. Conclusion In conclusion, the emission rate of photons from the bremsstrahlung processes for a system 𝑐𝑔 β†’ d𝛾 system is calculated based on the quantum chromodynamics (QCD) theory using a flavor number, chromodynamics constant, critical temperature, system temperature, fugacity of quark and gluon and photon energy for the charm-gluon reaction. It was found that chromodynamics constant decreases with increases in system temperature from 185MeV to 305MeV and this affects the photon emission rate, which increases with decreases in chromodynamics constant as a result of deconfinement phenomena. On the other hand, the photon emission rate decreases with the increase in photon energy from 1GeV to 3.5GeV. 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