# Photons as a Signal of Deconfinement in Hadronic Matter under Extreme Conditions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Gluon Conversion in the Confinement Phase

## 3. Gluon Conversion and Photon Production in the Deconfinement Phase

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The diagrams of process $gg\to \gamma $ via quark loop in the presence of homogeneous Abelian gauge field. p and k are momenta of gluons ${Q}^{b}$ and ${Q}^{a}$ respectively, q is the photon (${A}_{\rho}$) momentum. The closed arrows inside the triangle diagrams (

**I**,

**II**) indicate the direction of quark loop momentum. See text for more details.

**Figure 2.**Some form factors, such as the function of transverse gluon momenta, ${p}_{\perp}^{2}={k}_{\perp}^{2}$, for longitudinal momenta, ${p}_{\left|\right|}^{2}={k}_{\left|\right|}^{2}=1$. Dimensionless notations ${p}^{2}={p}^{2}/B$ and ${k}^{2}={k}^{2}/B$ are used, form factors ${F}_{l}(p,k)$ are dimensionless. See [15] for the detailed form of ${\mathcal{F}}_{\mu \nu \rho}^{l}(p,k)$ and ${F}_{l}(p,k)$.

**Figure 3.**The squared amplitude, $T(p,k)$ (6), as a function of gluon momenta for ${k}_{\perp}^{2}={p}_{\perp}^{2}$. The dashed line corresponds to the pure magnetic field, ${B}_{\mathrm{el}}$ [8], dotted and solid lines represent the case of a pure chromomagnetic field B with different strengths. The mass of the pion, ${m}_{\pi}$, is chosen as the scale. Dimensionless notation ${p}_{\perp}^{2}={p}_{\perp}^{2}/B$ is used. The quarks are considered massless.

**Figure 4.**The squared amplitude (6) taking into account all Landau levels for different quark masses ${m}_{f}$ [15] at gluon momenta ${k}_{\perp}^{2}={p}_{\perp}^{2}<3{m}_{f}^{2}/2$ and the case of massless quarks. The chromomagnetic field strength $B=4{m}_{\pi}^{2}$ and magnetic field ${B}_{el}=0$. Dimensionless notation ${p}_{\perp}^{2}={p}_{\perp}^{2}/B$ is used.

**Figure 5.**Differential energy distribution of the generated photons for a pure magnetic field ${B}_{\mathrm{el}}$ (dashed line) and pure chromomagnetic field B (the dotted and solid lines).

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**MDPI and ACS Style**

Nedelko, S.; Nikolskii, A.
Photons as a Signal of Deconfinement in Hadronic Matter under Extreme Conditions. *Physics* **2023**, *5*, 547-553.
https://doi.org/10.3390/physics5020039

**AMA Style**

Nedelko S, Nikolskii A.
Photons as a Signal of Deconfinement in Hadronic Matter under Extreme Conditions. *Physics*. 2023; 5(2):547-553.
https://doi.org/10.3390/physics5020039

**Chicago/Turabian Style**

Nedelko, Sergei, and Aleksei Nikolskii.
2023. "Photons as a Signal of Deconfinement in Hadronic Matter under Extreme Conditions" *Physics* 5, no. 2: 547-553.
https://doi.org/10.3390/physics5020039