The ultrafine splitting of heavy quarkonium with next-to-next-to-next-to-next-to-leading-order accuracy

TL;DR

This paper calculates the hyperfine splitting of P-wave heavy quarkonium states with very high precision, including resummation of logarithms, and applies the results to various systems like bottomonium, charmonium, and exotic atoms.

Contribution

It provides the first next-to-next-to-next-to-next-to-leading-order calculation of hyperfine splitting with logarithmic resummation for heavy quarkonium.

Findings

Accurate hyperfine splitting values for bottomonium, charmonium, and Bc systems.

Resummation of logarithms improves theoretical precision.

Application of results to positronium, muonium, and hydrogen-like systems.

Abstract

We compute the hyperfine splitting of P-wave heavy quarkonium states with next-to-next-to-next-to-next-to-leading-order accuracy. The resummation of logarithms with next-to-next-to-next-to-next-to-leading-logarithmic accuracy is also addressed. A phenomenological analysis of these results is performed for bottomonium, charmonium and the $B_c$ system. We also apply these results to positronium, muonium, hydrogen and muonic hydrogen.