Two-loop Quarkonium Hamiltonian in Non-annihilation Channel

TL;DR

This paper computes the two-loop heavy quarkonium Hamiltonian in the non-annihilation channel using effective field theory, advancing towards higher-order precision in weak coupling regimes.

Contribution

It introduces a systematic calculation method employing the β expansion, differential equations, and a single-step matching, improving upon traditional approaches.

Findings

First non-trivial two-loop Hamiltonian in this context

Systematic handling of complex computations

Progress towards N$^4$LO Hamiltonian in weak coupling regime

Abstract

We calculate the two-loop heavy quarkonium Hamiltonian within potential-NRQCD effective field theory in the non-annihilation channel. This calculation represents the first non-trivial step towards determining the N$^4$LO Hamiltonian in the weak coupling regime. The large amount of computation is systematically handled by employing the $\beta$ expansion, differential equations for master integrals, and adopting a single-step matching procedure, in contrast to the conventional two-step approach.