Analytical Result for Dimensionally Regularized Massless On-shell Double Box

TL;DR

This paper provides an explicit analytical evaluation of the massless on-shell double box Feynman diagram with arbitrary Mandelstam variables, expressed through polylogarithmic functions, advancing theoretical understanding in quantum field theory calculations.

Contribution

It presents a new analytical solution for the double box diagram in dimensional regularization, expressed in terms of polylogarithms and generalized polylogarithms for general s and t.

Findings

Explicit formulas in terms of polylogarithms and generalized polylogarithms.

Applicable for general Mandelstam variables s and t.

Enhances analytical techniques for Feynman diagram evaluations.

Abstract

The dimensionally regularized massless on-shell double box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t. An explicit result is expressed either in terms of polylogarithms Li_a(-t/s), up to a=4, and generalized polylogarithms S_{a,b}(-t/s), with a=1,2 and b=2, or in terms of these functions depending on the inverse ratio, s/t.