[Paper Review] Charmonium at BES and CLEO-c

T. Barnes|ArXiv.org|Jun 29, 2004

Quantum Chromodynamics and Particle Interactions8 references5 citations

TL;DR

This paper presents a nonrelativistic potential model for charmonium spectroscopy at BES and CLEO-c, using a Coulomb-plus-linear potential with spin-dependent terms to predict electromagnetic decays and strong decay branching fractions. It identifies key tests for S-D mixing and decay amplitudes in states like ψ(3770), ψ(4040), and ψ(4415), particularly emphasizing D*D* decay amplitudes and their sensitivity to theoretical models.

ABSTRACT

This paper gives a short summary of some of the aspects of charmonium which can be addressed at BES and CLEO-c and other $e^+e^-$ facilities. These topics include the spectroscopy of charmonium states, radiative transitions, $e^+e^-$ widths, two-photon widths, hadron loop effects and open-flavor strong decays.

Motivation & Objective

• To explore charmonium spectroscopy and decay properties at e+e− colliders like BES and CLEO-c, particularly for states above 3.73 GeV.
• To test the validity of nonrelativistic potential models with spin-dependent interactions against experimental data on electromagnetic and strong decays.
• To investigate the role of hadron loop effects and open-flavor strong decays in explaining anomalous branching fractions, such as the dominance of D*D* over DD in ψ(4040).
• To evaluate the potential of high-mass charmonium states like ψ(4415) as sources of exotic DsJ states such as D*sJ(2317) and Ds1(2460).
• To provide a framework for testing theoretical models of strong decays using precise measurements of branching fractions and decay amplitudes.

Proposed method

• A zeroth-order Hamiltonian is constructed with a Coulomb-like potential, linear confining term, and a Gaussian-smeared spin-spin hyperfine interaction to describe c¯c bound states.
• The Schrödinger equation is solved numerically using this Hamiltonian to generate zeroth-order wavefunctions for charmonium states below 4.2 GeV.
• Spin-dependent corrections are applied via the one-gluon-exchange Breit-Fermi Hamiltonian, including spin-orbit and tensor terms, with a Thomas precession term from a scalar confining interaction.
• Electromagnetic transitions (E1, M1, two-photon, e+e−) are calculated using the resulting wavefunctions to predict branching fractions.
• Strong decays into open-charm final states (DD, DD*, D*D*) are modeled using the 3P0 decay model, with amplitude ratios derived from angular momentum coupling.
• The model is fitted to 11 well-established charmonium states, yielding parameters: αs = 0.5461, b = 0.1425 GeV², mc = 1.4794 GeV, σ = 1.0946 GeV, with a 13.6 MeV rms error.

Experimental results

Research questions

• RQ1 How well does a nonrelativistic potential model with spin-dependent interactions describe the spectroscopy and electromagnetic decays of charmonium states above 3.73 GeV?
• RQ2 What do the branching fractions of ψ(4040) into DD, DD*, and D*D* reveal about the validity of the 3P0 decay model and the role of hadron loop effects?
• RQ3 Can the D*D* decay amplitudes in ψ(4040) and ψ(4159) be used to test predictions of the 3P0 model, particularly the ratio of 5P1 to 1P1 amplitudes?
• RQ4 To what extent can ψ(4415) serve as a source of D*sJ(2317) and Ds1(2460) resonances via S-wave decays to D*sD*sJ(2317) and DsDs1(2460)?
• RQ5 How do the predicted decay amplitudes for D*D* final states—particularly the dominance of 5F1 and the 1P1/5P1 ratio—differ between the ψ(4159) and ψ(4040) states?

Key findings

• The potential model with parameters αs = 0.5461, b = 0.1425 GeV², mc = 1.4794 GeV, and σ = 1.0946 GeV reproduces the masses of 11 known charmonium states with a 13.6 MeV rms error.
• The model successfully predicts both mean level positions and splittings within 1S, 1P, and 2S multiplets, indicating that the interquark potential and spin-dependent forces are well described by the model.
• The 3P0 decay model predicts a strong suppression of the DD* decay mode in ψ(4040), consistent with experimental data showing DD* branching fractions much smaller than D*D*.
• For ψ(4159), the model predicts that D*D* is the dominant decay mode, with a 1P1/5P1 amplitude ratio of -√5, and a dominant 5F1 amplitude in the D*D* final state.
• The ψ(4415) state is predicted to have a significant branching fraction to D*sD*sJ(2317) and DsDs1(2460), making it a promising source for studying these newly observed narrow DsJ states.
• The model predicts that the D*D* decay amplitude in ψ(4415) is dominated by the 5F1 partial wave, with a 1P1 amplitude larger than 5P1 by a factor of √5, providing a distinctive signature for testing the model.