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Solving recurrence relations for multi-loop Feynman integrals. (English) Zbl 1058.81606

Summary: We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, i.e., the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by P. A. Baikov [Phys. Lett. B 385, 404–410 (1996), see also hep-ph/9611449, Nucl. Instrum. Methods A 389, 347-349 (1997)] can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential.

MSC:

81T18 Feynman diagrams
65D30 Numerical integration
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References:

[1] Baikov, P. A., Nucl. Instrum. Methods A, 389, 347 (1997)
[2] Smirnov, V. A., Nucl. Phys. B (Proc. Suppl.), 116, 417 (2003)
[3] Chetyrkin, K. G.; Tkachov, F. V., Nucl. Phys. B, 192, 159 (1981)
[4] Bollini, C. G.; Giambiagi, J. J., Nuovo Cimento, 12B, 20 (1972)
[5] Smirnov, V. A., Applied Asymptotic Expansions in Momenta and Masses (2001), Springer: Springer Berlin · Zbl 1025.81002
[6] Tarasov, O. V., Nucl. Phys. B (Proc. Suppl.), 89, 237 (2000)
[7] Laporta, S., Int. J. Mod. Phys. A, 15, 5087 (2000)
[8] Kotikov, A. V., Phys. Lett. B, 267, 123 (1991)
[9] Gehrmann, T.; Remiddi, E., Nucl. Phys. B, 601, 287 (2001)
[10] Baikov, P. A.; Smirnov, V. A., Phys. Lett. B, 477, 367 (2000)
[11] Baikov, P. A.; Steinhauser, M., Comput. Phys. Commun., 115, 161 (1998)
[12] Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H., Phys. Lett. B, 559, 245 (2003)
[13] Peter, M., Nucl. Phys. B, 501, 471 (1997)
[14] Schröder, Y., Phys. Lett. B, 447, 321 (1999)
[15] Y. Schröder, Ph.D. thesis, Hamburg, 1999, DESY-THESIS-1999-021; Y. Schröder, Ph.D. thesis, Hamburg, 1999, DESY-THESIS-1999-021
[16] Kniehl, B. A.; Penin, A. A.; Smirnov, V. A.; Steinhauser, M., Phys. Rev. D, 65, 091503 (2002)
[17] Kniehl, B. A.; Penin, A. A.; Smirnov, V. A.; Steinhauser, M., Nucl. Phys. B, 635, 357 (2002)
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