Colloquium: Hadron Production in Open-charm Meson Pair at $e^+e^-$ Collider

The standard model of particle physics is a well-established theoretical framework, yet several unresolved issues remain that warrant further experimental and theoretical exploration. In the realm of quark physics, these include understanding the nature of quark confinement and elucidating the mechanism linking quarks and gluons to strongly interacting particles within the standard model theory, which may offer insights into the underlying physics mechanisms. These inquiries can be addressed through the study of hadrons produced at $e^+e^-$ collisions and decaying to open-charm meson pairs utilizing the capabilities of {\it BABAR}, Belle, BESIII, and CLEO-c experiments, which have yielded valuable insights into non-standard hadrons over recent decades. This Colloquium examines the contributions of $e^+e^-$ colliders from {\it BABAR}, Belle, BESIII, and CLEO-c experiments to such studies in the past two decades and discusses future prospects for $e^+e^-$ collider experiments.

💡 Research Summary

This colloquium reviews two decades of experimental work on hadron production in electron‑positron annihilation, focusing on final states that contain open‑charm meson pairs. The authors discuss results from the BABAR, Belle, BESIII, and CLEO‑c experiments, and they outline the theoretical tools needed to interpret the wealth of data, especially in the context of the so‑called X Y Z states—exotic hadrons that contain hidden charm.

The paper begins with a historical overview, reminding the reader that the discovery of the J/ψ in 1974 confirmed the existence of the charm quark and opened the field of charmonium spectroscopy. While the conventional charmonium spectrum is well described by non‑relativistic potential models, many newly observed states (the X, Y, and Z particles) do not fit into this picture. In particular, the vector Y states (J^PC = 1^−−) are produced directly in e⁺e⁻ annihilation and have been seen both in hidden‑charm decay modes (e.g., J/ψ π⁺π⁻) and in open‑charm channels (e.g., D * \bar D *). The authors stress that, above the open‑charm threshold (~3.9 GeV), the OZI‑allowed decays into pairs of charmed mesons dominate the total widths of these resonances, making the study of e⁺e⁻ → open‑charm processes essential for unraveling their internal structure.

The experimental apparatus section provides concise but detailed descriptions of the four major facilities. BABAR (SLAC) operated at the Υ(4S) with a peak luminosity of 3 × 10³³ cm⁻² s⁻¹ and pioneered the use of initial‑state‑radiation (ISR) to scan a broad energy range. Its detector combined a silicon vertex tracker, a drift chamber, a CsI(Tl) electromagnetic calorimeter, and muon identification via resistive‑plate chambers. Belle (KEKB) achieved a ten‑times higher luminosity (10³⁴ cm⁻² s⁻¹) with a similar detector layout, and its successor Belle II (superKEKB) now provides even larger data samples. BESIII (BEPCII) is a symmetric collider covering √s = 2.0–4.6 GeV with excellent energy resolution, allowing precise measurements of cross‑sections for processes such as e⁺e⁻ → π⁺π⁻ J/ψ and e⁺e⁻ → D * \bar D *. CLEO‑c, operating at the ψ(3770) resonance, contributed high‑precision measurements of D‑pair production near threshold.

The authors then summarize the key experimental findings. In the open‑charm sector, cross‑section measurements of e⁺e⁻ → D⁰\bar D⁰, D⁺D⁻ reveal a rapid rise at the ψ(3770) and subsequent structures associated with ψ(4040), ψ(4160), and ψ(4415). ISR studies have uncovered that the Y(4260) signal actually consists of two nearby resonances, Y(4220) and Y(4320), a conclusion supported by BESIII’s high‑statistics energy scan. Production of D * \bar D and D * \bar D * final states shows pronounced peaks at 4.04 GeV, 4.22 GeV, and 4.42 GeV, which align with the masses of several Y states. Three‑body processes such as e⁺e⁻ → π⁺ D⁰ * D⁻ and e⁺e⁻ → π⁺π⁻ D⁺D⁻ provide additional evidence for intermediate Z_c(3900)‑like structures, indicating that the Y resonances may couple strongly to both hidden‑ and open‑charm channels.

In the charm‑strange sector, BESIII has measured e⁺e⁻ → D_s⁺D_s⁻, D_s⁺D_s *⁻, and e⁺e⁻ → D_s⁺D_{s0}(2317)⁻, revealing new thresholds and possible resonant enhancements around 4.6 GeV, which could be related to the Y(4660). These measurements are crucial for testing models that predict the existence of exotic configurations involving strange quarks, such as tetraquarks with the composition c s \bar c \bar s.

The theoretical discussion emphasizes that a simple Breit‑Wigner description is insufficient for overlapping resonances and for states close to thresholds. The authors advocate the use of coupled‑channel potential models, originally developed by Eichten and collaborators, which respect unitarity and analyticity. Such models can simultaneously describe the energy‑dependent R‑ratio (σ_hadrons/σ_μμ) and the observed line shapes of the Y states, including the interference patterns between neighboring resonances. They also explain why OZI‑allowed decays dominate above 3.9 GeV: the creation of an additional light quark‑antiquark pair allows the c \bar c system to reorganize into two open‑charm mesons (e.g., D * \bar D *), a process naturally accommodated in coupled‑channel frameworks.

Looking forward, the paper outlines the prospects offered by next‑generation e⁺e⁻ facilities. SuperKEKB/Belle II will accumulate an integrated luminosity of 50 ab⁻¹, enabling unprecedented precision in ISR studies and direct scans of the Y region. BESIII’s ongoing data‑taking and planned detector upgrades will improve the resolution of charm‑strange thresholds. Proposed high‑luminosity circular colliders such as FCC‑ee or CEPC could reach luminosities of 10³⁶ cm⁻² s⁻¹, allowing detailed amplitude analyses of multi‑body final states, precise determination of resonance parameters, and the disentanglement of possible mixing between conventional charmonium, tetraquark, molecular, and hybrid components. The authors suggest that combined analyses of hidden‑charm and open‑charm channels, together with sophisticated coupled‑channel fits, will finally resolve the “Y‑problem” – the puzzling pattern of vector states observed in e⁺e⁻ annihilation.

In conclusion, the colloquium argues that open‑charm meson‑pair production is a powerful probe of the internal dynamics of high‑mass charmonium‑like states. The synergy between high‑statistics experimental data from BABAR, Belle, BESIII, and CLEO‑c, and advanced coupled‑channel theoretical tools, is essential for advancing our understanding of non‑perturbative QCD and the spectrum of exotic hadrons. Future e⁺e⁻ colliders promise to deliver the decisive measurements needed to map out the full landscape of X Y Z states and to clarify the role of multiquark configurations in the strong interaction.