S-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

TL;DR

This paper calculates the S-wave heavy quarkonium spectrum with unprecedented NNNLL accuracy using Potential NRQCD, providing precise mass predictions for spin-averaged states.

Contribution

It derives the Potential NRQCD Lagrangian at NNNLL accuracy and computes heavy quarkonium masses with this high precision, advancing theoretical understanding.

Findings

Mass predictions for spin-averaged S-wave states with NNNLL accuracy

Complete potential derivation up to a missing two-loop soft running contribution

Enhanced theoretical precision in heavy quarkonium spectroscopy

Abstract

We obtain the Potential NRQCD Lagrangian relevant for S-wave states with next-next-to-next-to-leading logarithmic (NNNLL) accuracy. We compute the heavy quarkonium mass of spin-averaged $l= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with NNNLL accuracy. These results are complete up to a missing contribution of the two-loop soft running.