Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay

TL;DR

This paper calculates complex two-loop integrals for pseudo-scalar quarkonium and leptonium processes, providing analytic and numerical results that advance understanding of these quantum systems and their decay mechanisms.

Contribution

It introduces new analytic expressions for two-loop master integrals involving MPLs, eMPLs, and Eisenstein series, crucial for precise quantum calculations.

Findings

Analytic expressions for two-loop integrals in terms of MPLs, eMPLs, and Eisenstein series.

First analytic two-loop amplitude for para-positronium decay to two photons.

High-precision numerical results supporting the analytic formulas.

Abstract

We compute the master integrals relevant for the two-loop corrections to pseudo-scalar quarkonium and leptonium production and decay. We present both analytic and high-precision numerical results. The analytic expressions are given in terms of multiple polylogarithms (MPLs), elliptic multiple polylogarithms (eMPLs) and iterated integrals of Eisenstein series. As an application of our results, we obtain for the first time an analytic expression for the two-loop amplitude for para-positronium decay to two photons at two loops.