The massless non-adjacent double off-shell scalar box integral -- branch cut structure and all-order epsilon expansion

Abstract

We generalize the result of our recent paper on the massless single off-shell scalar box integral to the case of two non-adjacent end points off the light cone. An analytic result in $d=4-2\epsilon$ dimensions is established in terms of four Gauss hypergeometric ${}_2{\mathrm{F}}_1$ functions respectively their single-valued counterparts. This allows for an explicit splitting of real and imaginary parts, as well as an all-order $\epsilon$-expansion in terms of single-valued polylogarithms.

arXiv comment8 pages, 1 figure, updated to match version published in JHEP

References in corpus (11)

• Differential Equations for Two-Loop Four-Point Functions
• Dimensionally Regulated Pentagon Integrals
• Scalar one-loop integrals for QCD
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• TikZ-Feynman: Feynman diagrams with TikZ
• A New Hypergeometric Representation of One-Loop Scalar Integrals in $d$ Dimensions
• Application of the negative-dimension approach to massless scalar box integrals
• Dimensionally regulated one-loop box scalar integrals with massless internal lines
• New ideas for handling of loop and angular integrals in D-dimensions in QCD
• Functional reduction of one-loop Feynman integrals with arbitrary masses
• The massless single off-shell scalar box integral -- branch cut structure and all-order epsilon expansion

Cited by in corpus (1)

• Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order