Discussions on Stability of Diquarks

TL;DR

This paper investigates the stability of diquarks using QCD sum rules by calculating their mass spectra and proposing a stability criterion based on mass gaps, but finds the results inconclusive due to theoretical uncertainties.

Contribution

It introduces a quantitative criterion for diquark stability and completes the mass spectrum analysis for heavy-heavy diquarks using QCD sum rules.

Findings

Mass gaps for diquarks are small and similar across types.

Heavy-heavy diquarks show slightly smaller gaps, suggesting potential stability.

Theoretical uncertainties prevent definitive conclusions on diquark stability.

Abstract

Since the birth of the quark model, the diquark which is composed of two quarks has been considered as a substantial structure of color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks which are composed of two-light (L-L), one-light-one-heavy (H-L) and two-heavy quarks (H-H) respectively have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and $\sqrt{s_0}$ where $s_0$ is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the type H-H to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquaks are within a small range, especially the gap for the diquark with two heavy quarks which is believed to be a stable structure, is slightly smaller than that for other two types of diquarks, therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.