Double Heavy baryons and Corrections to Heavy Quark-Diquark Symmetry Prediction for Hyperfine Splitting

TL;DR

This paper investigates the corrections to the heavy quark-diquark symmetry predictions for hyperfine splittings in doubly heavy baryons, quantifying perturbative and nonperturbative effects within NRQCD.

Contribution

It provides a detailed analysis of perturbative and nonperturbative corrections to hyperfine splittings, extending the heavy quark-diquark symmetry framework with quantitative estimates.

Findings

Perturbative corrections are a few percent or smaller for doubly charm or bottom baryons.

Nonperturbative corrections are about 10% for doubly charm baryons and 1% or less for doubly bottom baryons.

Heavy quark-diquark symmetry remains a good approximation with small corrections.

Abstract

In the $m_Q\rightarrow\infty$ limit, the hyperfine splittings in the ground state doubly heavy baryons $\left(QQq\right)$ and single heavy antimesons $(\bar{Q}q)$ are related by heavy quark-diquark symmetry (HQDQ) as the light degrees of freedom in both the hadrons are expected to have identical configurations. In this article, working within the framework of nonrelativistic QCD (NRQCD), we study the perturbative and nonperturbative corrections to the HQDQ symmetry hyperfine splitting relation that scale as ${\cal O}\left(\alpha_s^2\right)$ and $\Lambda_{\rm QCD}^2/m_Q^2$ respectively. In the extreme heavy quark limit, the perturbative corrections to hyperfine splitting of doubly charm or bottom baryons are a few percent or smaller. The nonperturbative corrections to hyperfine splitting are of order $10\%$ in the case of doubly charm baryons and $1\%$ or smaller in doubly bottom baryons.