Unquenched Charmonium and Beyond

TL;DR

This review argues that unquenched hadronic spectroscopy, driven by coupled-channel effects and hadronic loops, is essential to understand the charmonium-like XYZ spectrum and its extension to bottomonium and light-vector sectors. It emphasizes the rho-pi puzzle, large non-DDbar decays, and Y-state proliferation as manifestations of long-distance dynamics beyond quenched models, and presents mechanisms such as hadronic loops, ISPE/ISChE, and S-D mixing as unifying tools. By applying unquenched frameworks to X(3872), X(3915)/Z(3930), Y(4220), Z_c/Z_b structures, and higher bottomonia, the authors demonstrate coherent explanations for masses, widths, and decay patterns, with predictions testable by BESIII, Belle II, LHCb, CMS, and lattice QCD. They further argue for universality of these effects across flavors, proposing a paradigm shift toward high-precision, unquenched spectroscopy with strong ties to lattice results. The work advocates systematic development of unquenched models to disentangle genuine resonances from threshold effects and interference in a data-rich era of hadron spectroscopy.

Abstract

The year 2024 marked the 50th anniversary of the discovery of the $J/ψ$ particle, which unveiled the charm quark and the charmonium spectrum, instigating the "November Revolution" in particle physics. This discovery catalyzed the development of quenched potential models, most notably the Cornell model, which provided a foundational quantitative description of the hadronic spectrum. However, the landscape of hadron spectroscopy has been profoundly transformed since the turn of the 21st century with the observation of numerous charmonium-like states, such as $X(3872)$, which exhibit properties starkly at odds with quenched model predictions. These discrepancies, exemplified by the "$X(3872)$ low-mass puzzle" and the "$Y$ problem" associated with vector states like $Y(4260)$, underscore the critical limitations of the quenched approximation and signal the necessity for a new theoretical paradigm. This review synthesizes recent advances in hadronic spectroscopy, arguing that the unquenched picture, which incorporates coupled-channel effects such as hadronic loops, is essential for a unified description of these new states and associated anomalies. We demonstrate how unquenched effects provide compelling solutions to long-standing puzzles in charmonium decays (e.g., the "$ρπ$ puzzle" and anomalous dipion transitions), predict and explain the existence of exotic charged states like $Z_c(3900)$ and $Z_b(10610)$ via mechanisms such as Initial Single Pion Emission, and offer a framework for understanding interactions between charmonia and with nucleons. Furthermore, we emphasize the universality of unquenched effects, extending their application to bottomonium and light-flavor sectors. With improving precision, we advocate systematic development of unquenched hadronic spectroscopy.

Figures (132)

• Figure 1: A paradigm shift from the quenched to the unquenched picture.
• Figure 2: Comparison of the dipion invariant-mass distribution between the experimental measurement CLEO:2005zky and the result from the QCD multipole expansion Kuang:1989ub. The $2S$–$1D$ mixing angle is taken as $\theta_{2S-1D} = -10^\circ$, and several representative values of $|c_1|$ and $|c_2|$ suggested in Ref. Kuang:1989ub are illustrated.
• Figure 3: Quark-level short-distance contribution for the $J/\psi\to VP$ decay. Here, (a) and (b) represent the single-OZI-suppressed (SOZI) and double-OZI-suppressed (DOZI) processes for the decays of $J/\psi \to VP$, respectively. Figure adapted from Ref. Liu:2006dq.
• Figure 4: Quark-level (left) and hadron level (right) long-distance contribution for the $J/\psi\to VP$ decay. The left figure adapted from Ref. Liu:2006dq.
• Figure 5: Feynman diagrams for $J/\psi\to \rho^0\pi^0$ via $D^{(*)}$-meson loops. Diagrams (a)--(f) involve neutral charmed mesons; charged-meson loops follow by replacement $D^{(*)0} \to D^{(*)\pm}$. Adapted from Ref. Liu:2006dq.