$\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^+e^-\to 2(Q\bar Q)$

TL;DR

This paper introduces an $psilon$-regular basis method for evaluating complex multiloop integrals involving elliptic sectors, demonstrated through calculating the photon contribution to $e^+e^- o 2(Qar Q)$ cross section.

Contribution

It presents a novel $psilon$-regular basis approach that simplifies non-polylogarithmic multiloop integrals with elliptic sectors, enabling more manageable calculations.

Findings

Expressed results via iterated integrals with rational weights.

Calculated the photon contribution to the total cross section of $e^+e^- o 2(Qar Q)$.

Demonstrated the effectiveness of the $psilon$-regular basis method.

Abstract

We argue that in many physical calculations where the "eliptic" sectors are involved, one can express the results via iterated integrals with almost all weights being rational. Our method is based on the existence of $\epsilon$-regular basis, which is akin to the $\epsilon$-finite basis defined in Ref. [hep-ph/0601165]. As a demonstration of our technique, we calculate the photon contribution to the total cross section of the production of two $Q\bar Q$ pairs in the electron-positron collisions.