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Landau–Khalatnikov–Fradkin Transformation and Even \(\zeta\) Functions

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Abstract

An exact formula that relates standard \(\zeta\) functions and so-called hatted \(\zeta\) (\(\hat{\zeta}\)) functions in all orders of perturbation theory is presented. This formula is based on the Landau–Khalatnikov–Fradkin transformation.

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Notes

  1. We note that the results in [3] also contain multiple \(\zeta\) functions (multi-zeta values), but their analysis is beyond the scope of the present article.

REFERENCES

  1. P. A. Baikov and K. G. Chetyrkin, PoS (LL2018), 008 (2018).

  2. D. J. Broadhurst, hep-th/9909185; P. A. Baikov and K. G. Chetyrkin, Nucl. Phys. B 837, 186 (2010).

    Article  ADS  Google Scholar 

  3. A. Georgoudis, V. Goncalves, E. Panzer, and R. Pereira, arXiv: 1802.00803 [hep-th]; P. A. Baikov and K. G. Chetyrkin, J. High Energy Phys. 1806, 141 (2018); 1910, 190 (2019).

  4. A. V. Kotikov and S. Teber, Phys. Rev. D 100, 105017 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  5. A. V. Kotikov and S. Teber, arXiv: 1912.10957 [hep-th].

  6. L. D. Landau and I. M. Khalatnikov, Sov. Phys. JETP 2, 69 (1956);

    Google Scholar 

  7. E. S. Fradkin, Sov. Phys. JETP 2, 361 (1956).

    Google Scholar 

  8. A. Bashir and A. Raya, Phys. Rev. D 66, 105005 (2002);

    Article  ADS  Google Scholar 

  9. S. Jia and M. R. Pennington, Phys. Rev. D 95, 076007 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ahmad, J. J. Cobos-Martínez, Y. Concha-Sánchez, and A. Raya, Phys. Rev. D 93, 094035 (2016);

    Article  ADS  Google Scholar 

  11. A. James, A. V. Kotikov, and S. Teber, Phys. Rev. D 101, 045011 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  12. T. De Meerleer, D. Dudal, S. P. Sorella, P. Dall’Olio, and A. Bashir, Phys. Rev. D 97, 074017 (2018); 101, 085005 (2020).

  13. K. G. Chetyrkin, A. L. Kataev, and F. V. Tkachov, Nucl. Phys. B 174, 345 (1980).

    Article  ADS  Google Scholar 

  14. A. V. Kotikov and L. N. Lipatov, Nucl. Phys. B 582, 19 (2000);

    Article  ADS  Google Scholar 

  15. 661, 19 (2003);

  16. 769, 217 (2007);

  17. A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, and V. N. Velizhanin, Phys. Lett. B 595, 521 (2004);

    Article  ADS  MathSciNet  Google Scholar 

  18. L. Bianchi, V. Forini, and A. V. Kotikov, Phys. Lett. B 725, 394 (2013).

    Article  ADS  MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

A.V. Kotikov is grateful to the Organizing Committee of the Session-Conference of Nuclear Physics Section at the Department of Physical Sciences, Russian Academy of Sciences, for the invitation.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia

    A. V. Kotikov

  2. Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Energies, LPTHE, F-75005, Paris, France

    S. Teber

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  1. A. V. Kotikov
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  2. S. Teber
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Correspondence to A. V. Kotikov.

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Kotikov, A.V., Teber, S. Landau–Khalatnikov–Fradkin Transformation and Even \(\zeta\) Functions. Phys. Atom. Nuclei 84, 105–107 (2021). https://doi.org/10.1134/S1063778820060198

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  • DOI: https://doi.org/10.1134/S1063778820060198

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