Abstract
The main steps of the process of obtaining the result [1] in terms of elliptic polylogarithms for a two-loop sunrise integral with two different internal masses with pseudothreshold kinematics for all orders of the dimensional regulator are shown.
Similar content being viewed by others
REFERENCES
L. G. J. Campert, F. Moriello, and A. Kotikov, “Sunrise integrals with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms,” J. High Energy Phys. 09, 072 (2021). arXiv: 2011.01904.
J. L. Bourjaily et al., “Functions beyond multiple polylogarithms for precision collider physics,” in 2022 Snowmass Summer Study (2022). arXiv:2203.07088.
M. Yu. Kalmykov and B. A. Kniehl, “Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters,” Nucl. Phys. B 809, 365—405 (2009). arXiv:0807.0567 [hep-th].
B. A. Kniehl, A. V. Kotikov, A. Onishchenko, and O. Veretin, “Two-loop sunset diagrams with three massive lines,” Nucl. Phys. B 738, 306–316 (2006). arXiv: hep-ph/0510235.
B. A. Kniehl, A. V. Kotikov, A. I. Onishchenko, and O. L. Veretin, “Two-loop diagrams in non-relativistic QCD with elliptics,” Nucl. Phys. B 948, 114780 (2019). arXiv: 1907.04638.
A. V. Kotikov, “Differential equations method: new technique for massive Feynman diagrams calculation,” Phys. Lett. B 254, 158—164 (2019).
A. V. Kotikov, “Differential equations method: the calculation of vertex type Feynman diagrams,” Phys. Lett. B 259, 314—322 (1991).
A. V. Kotikov, “Differential equation method: the calculation of N point Feynman diagrams,” Phys. Lett. B 267, 123—127 (1991);
Erratum: Phys. Lett. B 295, 409 (1992).
Z. Bern, L. J. Dixon, and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412, 751—816 (1994); arXiv:hep-ph/9306240.
E. Remiddi, “Differential equations for Feynman graph amplitudes,” Nuovo Cimento A 110, 1435–1452 (1997). arXiv:hep-th/9711188.
A. V. Kotikov, “New method of massive Feynman diagrams calculation,” Mod. Phys. Lett. A 6, 677–692 (1991).
B. A. Kniehl and A. V. Kotikov, “Counting master integrals: integration-by parts procedure with effective mass,” Phys. Lett. A 712, 233—234 (2012). arXiv: 1202.2242 [hep-ph].
A. V. Kotikov, “About calculation of massless and massive Feynman integrals,” Particles 3, 394–443 (2020). arXiv:2004.06625.
A. V. Kotikov, “Differential equations and Feynman integrals,” (2021). arXiv:2102.07424.
O. V. Tarasov, “Hypergeometric representation of the two-loop equal mass sunrise diagram,” Phys. Lett. B 638, 195–201. arXiv:hep-ph/0603227.
L. Adams and S. Weinzierl, “Feynman integrals and iterated integrals of modular forms,” Commun. Num. Theor. Phys. 12, 193–251 (2018). arXiv:1704.08895.
M. A. Bezuglov, A. I. Onishchenko, and O. L. Veretin, “Massive kite diagrams with elliptics,” Nucl. Phys. B 963, 115302 (2021). arXiv:2011.13337.
M. A. Bezuglov and A. I. Onishchenko, “Non-planar elliptic vertex,” J. High Energy Phys. 04, 045 (2022). arXiv:2112.05096.
M. A. Bezuglov, A. V. Kotikov, and A. I. Onishchenko, “On series and integral representations of some NRQCD master integrals,” JETP Lett. 116, 61–69 (2022). arXiv:2205.14115.
J. Broedel, C. Duhr, F. Dulat, and L. Tancredi, “Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: General formalism,” J. High Energy Phys. 05, 093 (2018). arXiv:1712.07089.
ACKNOWLEDGMENTS
Author thanks the Organizing Committee of the International Conference on Quantum Field Theory, High-Energy Physics, and Cosmology for the invitation.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
Rights and permissions
About this article
Cite this article
Kotikov, A.V. Sunrise Integral in Non-Relativistic QCD with Elliptics. Phys. Part. Nuclei Lett. 20, 246–249 (2023). https://doi.org/10.1134/S154747712303041X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S154747712303041X