Abstract
In this work the \(e^{+}e^{-}\rightarrow l^{+}l^{-}\) scattering process is investigated. The cross-section is calculated considering three different effects: temperature, external magnetic field and chemical potential. The effect due to an external field is inserted into the problem through a redefinition of the fermionic field operator. Effects due to temperature and chemical potential are introduced using the Thermo Field Dynamics formalism.
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References
Y. Gabellini, T. Grandou, D. Poizat, Electron-positron annihilation in thermal QCD. Ann. Phys. 202, 436 (1990). https://doi.org/10.1016/0003-4916(90)90231-C
D.J. Schwarz, M. Stuke, Lepton asymmetry and cosmic QCD transition. J. Cosmol. Astropart. Phys. 2009, 025 (2009). https://doi.org/10.1088/1475-7516/2009/11/025
K. Bhattacharya, “Elementary Particle Interactions In A Background Magnetic Field,” arXiv:hep-ph/0407099v1
F.C. Khanna, A.P.C. Malbouisson, J.M.C. Malbouisson, A.R. Santana, Thermal quantum field theory - Algebraic aspects and applications (World Scientific Publishing Company, USA, 2009)
A.E. Santana, F. Khanna, Lie groups and thermal field theory. Phys. Lett. A 203, 68 (1995). https://doi.org/10.1016/0375-9601(95)00394-I
H. Gies, QED effective action at finite temperature: Two-loop dominance. Phys. Rev. D 61, 085021 (2010). https://doi.org/10.1103/PhysRevD.61.085021
H.-H. Xu, C.-H. Xu, Compton scattering at finite temperature. Phys. Rev. D 52, 6116 (1995). https://doi.org/10.1103/PhysRevD.52.6116
D.S. Cabral, A.F. Santos, Compton scattering in TFD formalism. Eur. Phys. J. C 83, 25 (2023). https://doi.org/10.1140/epjc/s10052-023-11182-x
D.S. Cabral, A.F. Santos, F.C. Khanna, Violation of Lorentz symmetries and thermal effects in Compton scattering. Eur. Phys. J. Plus 138, 91 (2023). https://doi.org/10.1140/epjp/s13360-023-03707-w
A.F. Santos, F.C. Khanna, Quantized gravito electromagnetism theory at finite temperature. Int. J. Mod. Phys. A 31, 1650122 (2016). https://doi.org/10.1142/S0217751X16501220
P.R.A. Souza et al., On Lorentz violation in \(e^{-}+e^{+}\rightarrow \mu ^{-}+\mu ^{+}\) scattering at finite. Phys. Lett. B 791, 195 (2019). https://doi.org/10.1016/j.physletb.2019.02.033
A.F. Santos, F.C. Khanna, Lorentz violation in Bhabha scattering at finite temperature. Phys. Rev. D 95, 125012 (2017). https://doi.org/10.1103/PhysRevD.95.125012
M.H. Lee, Fermionic chemical potential. J. Math. Chem. 5, 83 (1990). https://doi.org/10.1007/BF01166422
D. Persson, V. Zeitlin, Note on QED with a magnetic field and chemical potential. Phys. Rev. D 51, 2026 (1995). https://doi.org/10.1103/PhysRevD.51.2026
D. Binosi, L. Theussl, JaxoDraw: A graphical user interface for drawing Feynman diagrams. Comput. Phys. Commun. 161, 76 (2004). https://doi.org/10.1016/j.cpc.2004.05.001
R. Mertig, M. Böhm, A. Denner, Feyn Calc-computer-algebraic calculation of Feynman amplitudes. Comput. Phys. Commun. 64, 345 (1991). https://doi.org/10.1016/0010-4655(91)90130-D
Y. Kazama, C.N. Yang, A.S. Goldhaber, Scattering of a Dirac particle with charge Z e by a fixed magnetic monopole. Phys. Rev. D 15, 2287 (1977). https://doi.org/10.1103/PhysRevD.15.2287
K. Bhattacharya, “Solution of the Dirac equation in presence of an uniform magnetic field,” arXiv:0705.4275v2
K. Bhattacharya and P.B. Pal, “Inverse beta-decay of arbitrarily polarized neutrons in a magnetic field,” arXiv:hep-ph/0209053
G. Cook, R.H. Dickerson, Understanding the chemical potential. Amer. J. Phys. 63, 737 (1995). https://doi.org/10.1119/1.17844
R. Iengo, Quantum field theory : an arcane setting for explaining the world (Morgan & Claypool Publishers, USA, 2018)
L.D. Landau, E.M. Lifshitz, Statistical Physics: Volume 5 (Elsevier, USA, 2013)
H.B. Callen, Thermodynamics and an introduction to thermostatistics (John Willey and Sons, NY, USA, 1985)
N.W. Ashcroft, N.D. Mermin, Solid state physics (Holt Rinehart and Winston, NY, USA, 1976)
M.P. Marder, Condensed Matter Physics (Willey, USA, 2010)
E.W. Kolb, M.S. Turner, The early universe (Addison-Wesley Publishing Company, USA, 1990)
P.A.M. Dirac, A theory of electrons and protons. Proc. Royal Soc. London, Series A Contain. Papers Math. Phys. Char. 126, 360–365 (1930)
N.A. Lemos, Analytical mechanics (Cambridge University Press, UK, 2018)
M.E. Peskin, D.V. Schroeder, An introduction of quantum field theory (Addison-Wesley Publishing Company, USA, 1995)
A. Tiwari, B. K. Patra, “Lowest-order electron-electron and electron-muon scattering in a strong magnetic field,” arXiv:1808.04236
M.H. Sis, B. Mirza, A.K.B. Sefidi, \(e^{-}e^{+}\rightarrow l^{-}l^{+}\) scattering in a strong magnetic field and LV background. Ann. Phys. 448, 169173 (2023). https://doi.org/10.1016/j.aop.2022.169173
N.P. Landsman, C.G. Van Weert, Real- and imaginary-time field theory at finite temperature and density. Phys. Rep. 145, 141 (1987). https://doi.org/10.1016/0370-1573(87)90121-9
Acknowledgements
This work by A. F. S. is partially supported by National Council for Scientific and Technological Development - CNPq project No. 313,400/2020–2. D. S. C. thanks CAPES for financial support.
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Cabral, D.S., Santos, A.F. \(e^{+}e^{-}\rightarrow l^{+}l^{-}\) scattering at finite temperature in the presence of a classical background magnetic field. Eur. Phys. J. Plus 139, 190 (2024). https://doi.org/10.1140/epjp/s13360-024-04975-w
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DOI: https://doi.org/10.1140/epjp/s13360-024-04975-w