Abstract
In this paper the class ofN loop massive scalar self-energy diagrams withN+1 propagators is studied in an arbitrary number of dimensions. As it is known these integrals cannot be expressed in terms of polylogarithms. Here it is shown, however, that they can be described by generalized hypergeometric functions of several variables, namely Laricella functions. These results represent previous small and large momentum expansions in closed form. Numerical comparisons for the finite part in four dimensions with a two-dimensional integral representation show good agreement.
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References
A.I. Davydychev, J.B. Tausk: Nucl. Phys. B 397 (1993) 123
A.I. Davydychev, V.A. Smirnov, J.B. Tausk. Nucl. Phys. B. 410 (1993) 325
D. Kreimer: Phys. Lett. B 273 (1991) 277
F.A. Berends, J.B. Tausk: Nucl. Phys. B, to appear
E. Mendels: Nuovo Cimento 45A (1978) 87
E.E. Boos, A.I. Davydychev: Teor. Mat. Fiz. 89 (1991) 56, Theor. Math. Phys. 89 (1991) 1052
D.J. Broadhurst, J. Fleischer, O.V. Tarasov: Z. Phys. C 60 (1993) 287
G. Weiglein, R. Scharf, M. Böhm: Nucl. Phys. B, 416 (1994) 606
A.P. Prudnikov, Yu. A. Brychkov, O.I. Marichev: Integrals and series. New York: Gordon and Breach: 1986
G. Lauricella: Sulle funzioni ipergeometriche a piu variabili, Rendiconti del Circolo Matematico di Palermo (1893), 7, 111–3
H. Exton: Multiple hypergeometric functions and applications. Chicester: Ellis Horwood 1976
P. Appell, J. Kampé de Fériet: Fonctions hypergéométriques. Paris: Gauthier-Villars, 1926
H.M. Srivastava, P.W. Karlson: Multiple Gaussian hypergeometric series. New York: Halstead Press, John Wiley, 1985
R.J. Sasiela, J.D. Shelton: J. Math. Phys. 34 (1993) 2572
J.B. Tausk: Thesis Leiden (1993)
F.A. Lunev: Moscow State University preprint (1993)
D.J. Broadhurst: Z. Phys. C 47 (1990) 115
R. Scharf, J.B. Tausk: Nucl. Phys. B, 412 (1994) 523
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Work supported in part by the NATO Research Grant CRG 900136
Research supported by the Stichting FOM
Research supported by the DFG Grant Bo 542/7-1
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Berends, F.A., Böhm, M., Buza, M. et al. Closed expressions for specific massive multiloop self-energy integrals. Z. Phys. C - Particles and Fields 63, 227–234 (1994). https://doi.org/10.1007/BF01411014
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DOI: https://doi.org/10.1007/BF01411014