Study of $e^+ e^- \to π^+ π^- J/ψ$ and Observation of a Charged Charmonium-like State at Belle

Abstract: The cross section for $e^+ e^- \to \pi^+ \pi^- J/\psi$ between 3.8 GeV and 5.5 GeV is measured with a 967 fb$^{-1}$ data sample collected by the Belle detector at or near the $\Upsilon(nS)$ ($n = 1,\ 2,\ ...,\ 5$) resonances. The Y(4260) state is observed, and its resonance parameters are determined. In addition, an excess of $\pi^+ \pi^- J/\psi$ production around 4 GeV is observed. This feature can be described by a Breit-Wigner parameterization with properties that are consistent with the Y(4008) state that was previously reported by Belle. In a study of $Y(4260) \to \pi^+ \pi^- J/\psi$ decays, a structure is observed in the $M(\pi^\pm\jpsi)$ mass spectrum with $5.2\sigma$ significance, with mass $M=(3894.5\pm 6.6\pm 4.5) {\rm MeV}/c^2$ and width $\Gamma=(63\pm 24\pm 26)$ MeV/$c^{2}$, where the errors are statistical and systematic, respectively. This structure can be interpreted as a new charged charmonium-like state.

• The paper presents a precise measurement of e⁺e⁻→π⁺π⁻J/ψ cross sections using 967 fb⁻¹ of Belle data, revealing detailed resonance structures.
• It confirms the presence of Y(4260) and Y(4008) states by refining their resonance parameters through rigorous data analysis.
• The discovery of a charged charmonium-like state with a mass of ~3894.5 MeV/c² and a width of 63 MeV significantly expands the exotic hadron spectrum.

Study of $e^+ e^- \to \pi^+ \pi^- J/\psi$ and Observation of a Charged Charmonium-like State at Belle

The academic paper under review provides a comprehensive analysis of the process $e^+ e^- \to \pi^+ \pi^- J/\psi$ in the energy range 3.8 GeV to 5.5 GeV, utilizing data from the Belle detector. The study further investigates possible intermediate structures, particularly examining the $Y(4260)$ and $Y(4008)$ states and reporting on the observation of a new charged charmonium-like state.

Key Findings

1. Measurement of Cross Sections:
   • The paper presents a precise measurement of cross sections for the reaction $e^+ e^- \to \pi^+ \pi^- J/\psi$, carried out using data from the Belle experiment. The dataset amounted to 967 fb$^{-1}$ of integrated luminosity collected at or near the $\Upsilon(nS)$ resonances.
2. Observation of Resonant States:
   • The $Y(4260)$ state was clearly observed. The resonance parameters were precisely measured, contributing to a detailed understanding of the state’s properties.
   • Additionally, an excess in $\pi^+ \pi^- J/\psi$ production was detected around 4 GeV. This feature was consistent with the $Y(4008)$ state reported previously by the Belle collaboration, modeled using a Breit-Wigner parameterization.
3. Discovery of a Charged Charmonium-like State:
   • A significant breakthrough from the study is the discovery of a charged charmonium-like state in the $M(\pi^\pm J/\psi)$ mass spectrum with a mass of approximately 3894.5 MeV/$c^2$ and a width of 63 MeV/$c^2$. The statistical significance of this state exceeds $5.2\sigma$, suggesting a robust identification, and it presents an intriguing addition to the landscape of exotic states.

Implications and Theoretical Considerations

The detection of the $Z(3900)^\pm$ state adds to the growing list of exotic hadrons that defy the traditional quark model, implying an exotic configuration such as a tetraquark or molecular state. This understanding challenges current theoretical frameworks and stimulates further theoretical and experimental advances in hadron physics.

The precise measurements of the $Y(4260)$ and its decay products facilitate further exploration into the nature of such states that appear prominently in $e^+e^-$ collision interfaces. If confirmed in other experiments, these findings could significantly advance theoretical models related to quark confinement and hadron spectroscopy.

Future Directions

The results from this collaborative international effort lay a solid foundation for further investigations into the charged charmonium-like states and other potential exotic configurations. Future experimental endeavors could focus on:

• Independent verifications by other experiments like BESIII and potential observations in new data from upgraded facilities.
• Extended studies including different decay channels to accumulate more statistics and enrich the analysis of interference effects.
• Complementary analysis using partial wave decomposition to gain further insights into the dynamics of identified resonant states.

In conclusion, this paper furnishes critical insights into the processes surrounding $e^+ e^-$ annihilation, resonant state formation, and exotic hadron spectroscopy. It advances the narrative within high energy physics concerning the structure and dynamics of exotic states, providing a pivotal reference for future theoretical and experimental endeavors.