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Massive one-loop conformal Feynman integrals and quadratic transformations of multiple hypergeometric series

B. Ananthanarayan1,*, Sumit Banik1,†, Samuel Friot2,3,‡, and Shayan Ghosh4,§

  • 1Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, Karnataka, India
  • 2Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
  • 3Université Lyon, Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, F-69622 Villeurbanne, France
  • 4Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany

  • *anant@iisc.ac.in
  • †sumitbanik@iisc.ac.in
  • ‡samuel.friot@universite-paris-saclay.fr
  • §ghosh@hiskp.uni-bonn.de
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Phys. Rev. D 103, 096008 – Published 13 May, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.096008

Abstract

The computational technique of N-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal three-point Feynman integral in various configurations. This shows the great simplicity and efficiency of the method in nonresonant cases (generic propagator powers) as well as some of its subtleties in the resonant ones (for unit propagator powers). We confirm certain results in the physics and mathematics literature and provide many new results, some of them dealing with the more general massive one-loop conformal n-point case. In particular, we prove two recent conjectures that give the massive one-loop conformal n-point integral (for generic propagator powers) in terms of multiple hypergeometric series. We show how these conjectures, that were deduced from a Yangian bootstrap analysis, are related by a tower of new quadratic transformations in hypergeometric functions theory. Finally, we also use our MB method to identify spurious contributions that can arise in the Yangian approach.

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See Also

Multiple Series Representations of N-fold Mellin-Barnes Integrals

B. Ananthanarayan, Sumit Banik, Samuel Friot, and Shayan Ghosh
Phys. Rev. Lett. 127, 151601 (2021)

Article Text

References (18)

  1. B. Ananthanarayan, S. Banik, S. Friot, and S. Ghosh, arXiv:2012.15108.
  2. F. Loebbert, J. Miczajka, D. Müller, and H. Münkler, Phys. Rev. Lett. 125, 091602 (2020).
  3. F. Loebbert, J. Miczajka, D. Müller, and H. Münkler, arXiv:2010.08552.
  4. H. M. Srivastava, Rend. Circ. Mat. Palermo 16, 99 (1967).
  5. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian hypergeometric series, Halsted Press (Ellis Horwood Limited, Chichester) (John Wiley and Sons, New York, 1985).
  6. H. M. Srivastava, Mat. Vesnik 9, 101 (1972).
  7. F. Loebbert, D. Müller, and H. Münkler, Phys. Rev. D 101, 066006 (2020).
  8. B. Ananthanarayan, S. Banik, S. Friot, and S. Ghosh, Phys. Rev. D 102, 091901 (2020).
  9. H. M. Srivastava, Ganita 15, 97 (1964).
  10. B. Ananthanarayan, S. Friot, and S. Ghosh, Eur. Phys. J. C 80, 606 (2020).
  11. B. Ananthanarayan, S. Friot, and S. Ghosh, Phys. Rev. D 101, 116008 (2020).
  12. B. Ananthanarayan, S. Friot, S. Ghosh, and A. Hurier, arXiv:2005.07170.
  13. V. A. Smirnov, Analytic Tools for Feynman Integrals, Springer Tracts in Modern Physics Vol. 250 (2012), pp. 1–296, 10.1007/978-3-642-34886-0.
  14. O. Zhdanov and A. Tsikh, Dokl. Math. 57, 24 (1998).
  15. M. Passare, A. K. Tsikh, and A. A. Cheshel, Theor. Math. Phys. 109, 1544 (1996).
  16. O. Zhdanov and A. Tsikh, Siberian Math. J. 39, 245 (1998).
  17. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Bateman Project Vol. 1 (McGraw-Hill, New York, 1953).
  18. K. J. Larsen and R. Rietkerk, Comput. Phys. Commun. 222, 250 (2018).

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Phys. Rev. D 103, 096008– Published 13 May, 2021
  • Received 1 January 2021
  • Accepted 24 February 2021
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