Multiple Mellin-Barnes integrals with straight contours

Abstract

We show how the conic hull method, recently developed for the analytic and non-iterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the $\epsilon$-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in $\epsilon$ of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the $\epsilon$-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and $D=4-2\epsilon$.

arXiv comment17 pages, 2 figures, code repository: https://github.com/SumitBanikGit/MBConicHulls

References in corpus (18)

• Automatized analytic continuation of Mellin-Barnes integrals
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• FIESTA5: numerical high-performance Feynman integral evaluation
• Numerical evaluation of loop integrals
• Yangian Bootstrap for Conformal Feynman Integrals
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• On convergent series representations of Mellin-Barnes integrals
• Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli
• The one-loop pentagon to higher orders in epsilon
• MBsums - a Mathematica package for the representation of Mellin-Barnes integrals by multiple sums
• Analytic result for the one-loop scalar pentagon integral with massless propagators
• The Double Box and Hexagon Conformal Feynman Integrals
• MultivariateResidues: a Mathematica package for computing multivariate residues
• MB Tools reloaded
• Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
• Method of Brackets and Feynman diagrams evaluation

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