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Functional equations for Feynman integrals

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Abstract

New types of equations for Feynman integrals are found. It is shown that the latter satisfy functional equations that relate integrals with different kinematics. A regular method for obtaining such relations is proposed. A derivation of the functional equations for one-loop two-, three-, and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that the functional equations can be used to analytically continue Feynman integrals to various kinematical domains.

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References

  1. O. V. Tarasov, Phys. Lett. B 670, 67 (2008), arXiv:0809.3028 [hep-ph].

    Article  MathSciNet  ADS  Google Scholar 

  2. B. A. Kniehl and O. V. Tarasov, Nucl. Phys. B 820, 178 (2009).

    Article  ADS  MATH  Google Scholar 

  3. B. Petersson, J. Math. Phys. 6, 1955 (1965); G.’ t Hooft and M. J. G. Veltman, Nucl. Phys. B 44, 189 (1972); F. V. Tkachov, Phys. Lett. B 100, 65 (1981); K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B 192, 159 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  4. O. V. Tarasov, Phys. Rev. D 54, 6479 (1996), arXiv:hep-th/9606018.

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Erdely et al., Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 1.

    Google Scholar 

  6. J. Fleischer, F. Jegerlehner, and O. V. Tarasov, Nucl. Phys. B 566, 423 (2000), arXiv:hep-ph/9907327.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. G. Bollini and J. J. Giambiagi, Phys. Lett. B 40, 566 (1972).

    Article  ADS  Google Scholar 

  8. E. E. Boos and A. I. Davydychev, Teor. Mat. Fiz. 89, 56 (1991) [Theor. Math. Phys. 89, 1052 (1991)].

    MathSciNet  Google Scholar 

  9. Z. Bern, L. J. Dixon, and D. A. Kosower, Nucl. Phys. B 412, 751 (1994), arXiv:hep-ph/9306240.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. A. I. Davydychev, Phys. Rev. D 61, 087701 (2000), arXiv:hep-ph/9910224.

    Article  MathSciNet  ADS  Google Scholar 

  11. P. Appell and J. de Feriet, Fonctions hypergeometriques et hypersperiques (Gauthier Villars, Paris, 1926).

    Google Scholar 

  12. O. V. Tarasov, Nucl. Phys. Proc. Suppl. 89, 237 (2000), arXiv:hep-ph/0102271.

    Article  ADS  Google Scholar 

  13. J. Fleischer, F. Jegerlehner, and O. V. Tarasov, Nucl. Phys. B 672, 303, arXiv:hep-ph/0307113.

  14. A. I. Davydychev, Nucl. Instrum. Methods Phys. Res. A 559, 293 (2006), arXiv:hep-th/0509233.

    Article  ADS  Google Scholar 

  15. P. O. M. Olsson, J. Math. Phys. 5, 420 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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  1. Joint Institute for Nuclear Research, Dubna, 141980, Russia

    O. V. Tarasov

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  1. O. V. Tarasov
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Correspondence to O. V. Tarasov.

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Tarasov, O.V. Functional equations for Feynman integrals. Phys. Part. Nuclei Lett. 8, 419–427 (2011). https://doi.org/10.1134/S1547477111050219

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