Communication Dans Un Congrès Année : 2024

Analytic Evaluation of Multiple Mellin-Barnes Integrals

Résumé

We summarize two geometrical approaches to analytically evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. The first method is based on intersections of conic hulls, while the second one, which is more recent, relies on triangulations of a set of points. We demonstrate that, once automatized, the triangulation approach is computationally more efficient than the conic hull approach. As an application of this triangulation approach, we describe how one can derive simpler hypergeometric solutions of the conformal off-shell massless two-loop double box and one-loop hexagon Feynman integrals than those previously obtained from the conic hull approach. Lastly, by applying the above techniques on the MB representation of multiple polylogarithms, we show how to obtain new convergent series representations for these functions. These new analytic expressions were numerically cross-checked with GINAC.

Dates et versions

hal-04669319 , version 1 (08-08-2024)

Identifiants

Citer

Sumit Banik, Samuel Friot. Analytic Evaluation of Multiple Mellin-Barnes Integrals. Loops and Legs in Quantum Field Theory, Apr 2024, Wittenberg, Germany. pp.039, ⟨10.22323/1.467.0039⟩. ⟨hal-04669319⟩
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