Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions

Kniehl BA, Kondrashuk I, Notte-Cuello EA, Parra Ferrada I, Rojas-Medar M (2013)
Nuclear Physics B 876(1): 322-333.

Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
; ; ; ;
Abstract / Bemerkung
In our previous paper (Allendes et al., 2013 [10]), we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms. The MB transforms were written there as polynomials of logarithms of ratios of squares of the external momenta with certain coefficients. We also showed that these coefficients have a combinatoric origin. In this paper, we present an explicit formula for these coefficients. The procedure of recovering the coefficients is based on taking the double-uniform limit in certain series of smooth functions of two variables which is constructed according to a pre-determined iterative way. The result is obtained by using basic methods of mathematical analysis. We observe that the finiteness of the limit of this iterative chain of smooth functions should reflect itself in other mathematical constructions, too, since it is not related in any way to the explicit form of the MB transforms. This finite double-uniform limit is represented in terms of a differential operator with respect to an auxiliary parameter which acts on the integrand of a certain two-fold MB integral. To demonstrate that our result is compatible with original representations of UD functions, we reproduce the integrands of these original integral representations by applying this differential operator to the integrand of the simple integral representation of the scalar triangle four-dimensional integral J(1,1, 1 - epsilon). (C) 2013 Elsevier B.V. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
Nuclear Physics B
Band
876
Zeitschriftennummer
1
Seite
322-333
ISSN
PUB-ID

Zitieren

Kniehl BA, Kondrashuk I, Notte-Cuello EA, Parra Ferrada I, Rojas-Medar M. Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions. Nuclear Physics B. 2013;876(1):322-333.
Kniehl, B. A., Kondrashuk, I., Notte-Cuello, E. A., Parra Ferrada, I., & Rojas-Medar, M. (2013). Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions. Nuclear Physics B, 876(1), 322-333. doi:10.1016/j.nuclphysb.2013.08.002
Kniehl, B. A., Kondrashuk, I., Notte-Cuello, E. A., Parra Ferrada, I., and Rojas-Medar, M. (2013). Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions. Nuclear Physics B 876, 322-333.
Kniehl, B.A., et al., 2013. Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions. Nuclear Physics B, 876(1), p 322-333.
B.A. Kniehl, et al., “Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions”, Nuclear Physics B, vol. 876, 2013, pp. 322-333.
Kniehl, B.A., Kondrashuk, I., Notte-Cuello, E.A., Parra Ferrada, I., Rojas-Medar, M.: Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions. Nuclear Physics B. 876, 322-333 (2013).
Kniehl, Bernd A., Kondrashuk, Igor, Notte-Cuello, Eduardo A., Parra Ferrada, Ivan, and Rojas-Medar, Marko. “Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions”. Nuclear Physics B 876.1 (2013): 322-333.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Quellen

arXiv: 1304.3004

Inspire: 1227833

Suchen in

Google Scholar