Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities

A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, “Integrals and Series”, Vol. 2, Gordon and Breach, New York, 1990

1990

Earlier work this paper cites.

N.I. Usyukina and A.I. Davydychev, “An Approach to the evaluation of three and four point ladder diagrams,” Phys. Lett. B298

1993

Earlier work this paper cites.

I.S. Gradshteyn and I.M. Ryzhik, “Tables of integrals, series, and products”, Academic Press, 1994

1994

Earlier work this paper cites.

Z. Bern, L.J. Dixon, D.A. Kosower and S. Weinzierl, “One loop amplitudes for e + ​ e − → q ¯ ​ q ​ Q ¯ ​ Q e^{+}e^{-}\to\bar{q}q\bar{Q}Q ,” Nucl. Phys. B489

1997

Earlier work this paper cites.

S. Groote, J.G. Körner and A.A. Pivovarov, “A New technique for computing the spectral density of sunset type diagrams: Integral transformation in configuration space,” Phys. Lett. B443

1998

Earlier work this paper cites.

S. Groote, J.G. Körner and A.A. Pivovarov, “On the evaluation of sunset-type Feynman diagrams,” Nucl. Phys. B542

1999

Earlier work this paper cites.

S. Groote, J.G. Körner and A.A. Pivovarov, “Configuration space based recurrence relations for sunset-type diagrams,” Eur. Phys. J. C11

1999

Earlier work this paper cites.

S. Groote, J.G. Körner and A.A. Pivovarov, “Transcendental numbers and the topology of three loop bubbles,” Phys. Rev. D60

1999

Earlier work this paper cites.

S. Groote and A.A. Pivovarov, “Threshold expansion of Feynman diagrams within a configuration space technique,” Nucl. Phys. B580

2000

Earlier work this paper cites.

S. Groote, J.G. Körner and A.A. Pivovarov, “Laurent series expansion of sunrise type diagrams using configuration space techniques,” Eur. Phys. J. C36

2004

Cited alongside, same era.

S. Groote, J.G. Körner and A.A. Pivovarov, “On the evaluation of a certain class of Feynman diagrams in x x -space: Sunrise-type topologies at any loop order,” Annals Phys. 322

2007

Cited alongside, same era.

D.H. Bailey, J.M. Borwein, D. Broadhurst and M.L. Glasser, “Elliptic integral evaluations of Bessel moments,” J. Phys. A41

2008

Cited alongside, same era.

L. Adams, C. Bogner and S. Weinzierl, “The two-loop sunrise graph with arbitrary masses,” J. Math. Phys. 54

2013

Cited alongside, same era.

L. Adams, C. Bogner and S. Weinzierl, “The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms,” J. Math. Phys. 55

2014

E. Remiddi and L. Tancredi, “Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral,” Nucl. Phys. B907

2016

Later among the works it cites.

T. Luthe and Y. Schröder, J. Phys. Conf. Ser. 762

Original

2016

Later among the works it cites.

S.P. Martin and D.G. Robertson, “Evaluation of the general 3-loop vacuum Feynman integral,” Phys. Rev. D95

2017

Later among the works it cites.

A. Primo and L. Tancredi, “Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph,” Nucl. Phys. B921

2017

Later among the works it cites.

C. Bogner, A. Schweitzer and S. Weinzierl, “Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral,” Nucl. Phys. B922