Irrational constants in positronium decays

TL;DR

This paper identifies new irrational constants contributing to positronium decay rates at specific orders, revealing constants not related to known mathematical sums like Euler-Zagier or multiple zeta values.

Contribution

It introduces a novel class of irrational constants affecting positronium lifetime calculations at higher orders, expanding the understanding of the mathematical structure involved.

Findings

New irrational constants identified at O(α) and O(α^2) orders.

Constants are distinct from Euler-Zagier sums and multiple zeta values.

Enhances theoretical understanding of positronium decay mechanisms.

Abstract

We establish irrational constants, that contribute to the positronium lifetime at $O(\alpha)$ and $O(\alpha^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $\zeta$ values.