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

TL;DR

This paper analyzes the branch cut structure and provides an all-order epsilon expansion of the massless off-shell scalar box integral, crucial for higher-order perturbative calculations in quantum field theory.

Contribution

It introduces a method to eliminate superficial branch cuts and presents an all-orders epsilon expansion in terms of single-valued polylogarithms, extending previous finite-order results.

Findings

All-order epsilon expansion of the scalar box integral

Explicit real and imaginary parts in all kinematic regions

Elimination of superficial branch cuts in representations

Abstract

We investigate the single off-shell scalar box integral with massless internal lines in dimensional regularization. A special emphasis is given to higher orders in the dimensional regularization parameter epsilon, its branch cut structure, and kinematic limits. Common representations of the box integral introduce superficial branch cuts, which we eliminate to all orders in the epsilon expansion. In the literature so far a satisfactory solution for this issue only exists up to finite order in the epsilon expansion. However, for calculations at NNLO in perturbation theory, higher orders in epsilon of this integral are required. In this paper, we present results to all orders in epsilon in terms of single-valued polylogarithms and explicitly determine the real and imaginary part of the box integral in all kinematic regions.