Abstract
We compute the next-to-leading order (NLO) hard correction to the gluon self-energy tensor with arbitrary soft momenta in a hot and/or dense weakly coupled plasma in Quantum Chromodynamics. Our diagrammatic computations of the two-loop and power corrections are performed within the hard-thermal-loop (HTL) framework and in general covariant gauge, using the real-time formalism. We find that after renormalization our individual results are finite and gauge-dependent, and they reproduce previously computed results in Quantum Electrodynamics in the appropriate limit. Combining our results, we also recover a formerly known gauge-independent matching coefficient and associated screening mass in a specific kinematic limit. Our NLO results supersede leading-order HTL results from the 1980s and pave the way to an improved understanding of the bulk properties of deconfined matter, such as the equation of state.
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Acknowledgments
The authors would like to thank Andreas Ekstedt and Aleksi Vuorinen for enlightening discussions. We are also thankful to Andreas Ekstedt for sending some of his unpublished results for comparison. Lastly, we wish to thank the anonymous referee for their insightful comments which led to an improved discussion on gauge-invariance and the missing soft resummed contributions. This work is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Project ID 279384907–SFB 1245 and by the State of Hesse within the Research Cluster ELEMENTS (Project ID 500/10.006) (T.G.). R.P. and K.S. have been supported by the Academy of Finland grant no. 347499 and 353772 as well as by the European Research Council, grant no. 725369. S.S. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC 2094 – 390783311. In addition, K.S. gratefully acknowledges support from the Finnish Cultural Foundation.
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Gorda, T., Paatelainen, R., Säppi, S. et al. Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge. J. High Energ. Phys. 2023, 21 (2023). https://doi.org/10.1007/JHEP08(2023)021
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DOI: https://doi.org/10.1007/JHEP08(2023)021