Baryons and baryoniums in the perspective of QCD sum rules

TL;DR

The article provides a comprehensive overview of QCD sum rules as applied to baryons, baryon spectra, baryon semileptonic decays, and baryoniums, highlighting how the SVZ framework connects quark–gluon dynamics to hadronic observables through correlators, OPE, and dispersion relations. It details canonical two- and three-point sum rules, their extensions (FESR, Gaussian, and double ratios), and the crucial roles of the Borel window, continuum threshold, and condensates in stabilizing predictions. The review emphasizes recent experimental progress in hadron spectroscopy, notably BESIII, and discusses how baryoniums—including light and heavy baryon–antibaryon bound states and compact triquark–antitriquark configurations—are studied within QCD sum rules, revealing both predictive successes and significant theoretical uncertainties. Collectively, the work underscores the continued relevance and limitations of QCD sum rules in elucidating hadron structure and decays, while advocating for integrated approaches with lattice QCD, LCSR, and phenomenology to advance the field.

Abstract

Following the experimental confirmation of tetraquark and pentaquark states, the search for hexaquark states has emerged as a new frontier in hadron physics. Recent experimental progress, particularly by the BESIII collaboration, has provided compelling evidence for the existence of near-threshold $p\bar{p}$ bound states. These baryon-antibaryon systems, commonly referred to as baryoniums, are regarded as promising hexaquark candidates. In this article, we provide a comprehensive review of the investigations into baryonium states and their constituents, i.e., baryons, within the framework of QCD sum rules. We delineate the fundamental calculation procedures of this method to facilitate its practical application and benchmark the theoretical predictions against alternative models as well as the latest experimental data.

Figures (20)

• Figure 1: Typical Feynman diagrams of the operator product expansion up to dimension 5.
• Figure 2: Feynman diagrams of the mesonic (left) and baryonic (right) semileptonic decays.
• Figure 3: Typical Feynman diagrams for baryonic semileptonic decays.
• Figure 4: The contour integration in the complex $s$-plane for finite energy sum rules Shankar:1977ap.
• Figure 5: The mass of $\Xi_{cc}$ and $\Omega_{cc}$ as a function of the Borel parameter $M_B^2$ in Ref. Tang:2011fv.