[Paper Review] Evidence for further charmonium vector resonances

Eef van Beveren, George Rupp|arXiv (Cornell University)|Apr 25, 2010

Quantum Chromodynamics and Particle Interactions7 citations

TL;DR

This paper presents evidence for eight new charmonium vector resonances—ψ(3D), ψ(5S), ψ(4D), ψ(6S), ψ(5D), ψ(7S), ψ(6D), and ψ(8S)—based on BaBar Collaboration data for e⁺e⁻ → D*以防D̄* decay. Using the Hadronic Resonance Spectroscopy with Effective (HORSE) model, the authors interpret threshold enhancements and resonance structures as signatures of radially and orbitally excited c̄c states, with central masses and widths estimated from Breit-Wigner fits, supporting a nonperturbative quark-antiquark framework with meson loop effects.

ABSTRACT

We discuss the shape of threshold signals in production cross sections of the reaction e+ + e- --> D* + antiD*, at the opening of the D(s)* antiD(s)* and Lambda(c)+ Lambda(c)- channels. Furthermore, evidence for the 3D, 5S, 4D, 6S, 5D, 7S, 6D, and 8S charmonium vector resonances is presented, on the basis of data recently published by the BaBar Collaboration. Central masses and resonance widths are estimated. Confirmation of these resonances would be a huge step in lifting the precision level of hadron spectroscopy towards that of atomic spectroscopy, with far-reaching consequences for theory.

Motivation & Objective

• To identify new charmonium vector resonances beyond the established spectrum using recent BaBar data.
• To explain threshold enhancements in e⁺e⁻ → D*以防D̄* near D*以防sD̄*s and Λc⁺Λc⁻ thresholds as signatures of excited c̄c states.
• To test the validity of the HORSE model in predicting resonance masses and widths via meson loop corrections to bare c̄c states.
• To establish a connection between observed structures and theoretical predictions from nonperturbative quark-antiquark dynamics with infinite meson loop chains.
• To support the goal of achieving hadron spectroscopy precision comparable to atomic spectroscopy through improved resonance identification.

Proposed method

• Analysis of BaBar data for e⁺e⁻ → D*以防D̄* production cross sections, focusing on threshold regions near D*以防sD̄*s (4.213 GeV) and Λc⁺Λc⁻ (4.60 GeV).
• Application of the HORSE model, which describes the bare c̄c quark-antiquark propagator with harmonic oscillator level spacing ω = 0.19 GeV, to predict resonance positions.
• Use of nonperturbative meson loop corrections to shift bare states into physical resonances, incorporating unitary scattering and production amplitudes via the formalism of Ref. PRD21p772.
• Fitting observed structures with Breit-Wigner functions to extract central masses and widths, with statistical uncertainty acknowledged due to low statistics.
• Comparison of results with prior predictions from Godfrey and Isgur, and with earlier Belle data, to validate consistency across experiments.
• Use of a kinematical complex amplitude relation (EPL81p61002) that links production and scattering amplitudes, distinct from the real relation in Ref. PRD35p1633.

Experimental results

Research questions

• RQ1 Can threshold enhancements in e⁺e⁻ → D*以防D̄* near 4.213 GeV and 4.60 GeV be attributed to new c̄c vector resonances rather than mere phase space effects?
• RQ2 Do the observed structures in BaBar data for e⁺e⁻ → D*以防D̄* correspond to predicted radial and orbital excitations of charmonium, such as ψ(3D), ψ(5S), and ψ(4D)?
• RQ3 Can the observed resonance parameters (masses and widths) be consistently explained by the HORSE model with meson loop corrections?
• RQ4 Why is the X(4260) enhancement absent in e⁺e⁻ → D*以防D̄* but present in π⁺π⁻J/ψ, and how does this relate to OZI selection rules and gluon cloud effects?
• RQ5 To what extent do the observed regularities in resonance spacing and mass shifts support the underlying AdS-based confinement model with ω = 0.19 GeV?

Key findings

• The ψ(3D) resonance is estimated at approximately 4.55 GeV with a width of about 50 MeV, based on data from Ref. ARXIV09044351.
• The ψ(5S) resonance is found at 4.78 GeV with a width of 55 MeV, consistent with data from Ref. PRD80p074001.
• The ψ(4D) resonance is located at 4.87 GeV with a width of 60 MeV, also from Ref. PRD80p074001.
• Higher excitations such as ψ(6S), ψ(5D), ψ(7S), ψ(6D), and ψ(8S) are identified with masses ranging from 5.09 GeV to 5.91 GeV and widths between 44 MeV and 93 MeV.
• The observed level spacing of 0.38 GeV (2ω) in the resonance spectrum matches the harmonic oscillator spacing predicted by the HORSE model, supporting its validity.
• The analysis shows that the X(4260) and Y(4660) structures are not poles of the c̄c propagator, but likely arise from meson loop effects and S-wave resonances like f₀(980) in s̄s-rich environments.