HAL : in2p3-00610334, version 1
 arXiv : 1107.0328
 DOI : 10.1063/1.3679686
 On convergent series representations of Mellin-Barnes integralsFriot S., Greynat D.Journal of Mathematical Physics 53 (2011) 023508 - http://hal.in2p3.fr/in2p3-00610334
 Physique/Physique des Hautes Energies - Phénoménologie Physique/Physique des Hautes Energies - Théorie Physique/Physique mathématique Mathématiques/Physique mathématique
On convergent series representations of Mellin-Barnes integrals
S. Friot1, D. Greynat
 1 : IPNO - Institut de Physique Nucléaire d'Orsay http://ipnweb.in2p3.fr CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud IPN - 15, rue Georges Clemenceau - 91406 ORSAY CEDEX France
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple series in powers and logarithms of the parameters involved in the problem under consideration. However, in most of the cases, several series representations exist for a given integral. They converge in different regions of values of the parameters, and it is not obvious to obtain them. For twofold integrals we present a method which allows to derive straightforwardly and systematically: (a) different sets of poles which correspond to different convergent double series representations of a given integral, (b) the regions of convergence of all these series (without an a priori full knowledge of their general term), and (c) the general term of each series (this may be performed, if necessary, once the relevant domain of convergence has been found). This systematic procedure is illustrated with some integrals which appear, among others, in the calculation of the two-loop hexagon Wilson loop in N = 4 SYM theory. Mellin-Barnes integrals of higher dimension are also considered.

Articles dans des revues avec comité de lecture
2011
 Journal of Mathematical Physics (J. Math. Phys.) Publisher American Institute of Physics (AIP) ISSN 0022-2488
53
023508

49 pages, 16 figures
 Lien vers le texte intégral : http://fr.arXiv.org/abs/1107.0328
 in2p3-00610334, version 1 http://hal.in2p3.fr/in2p3-00610334 oai:hal.in2p3.fr:in2p3-00610334 Contributeur : Sophie Heurteau <> Soumis le : Vendredi 22 Juillet 2011, 14:59:37 Dernière modification le : Vendredi 25 Mai 2012, 15:12:32