A search for η′_c production in photon–photon fusion at LEP

Abstract

A search for the production of the η′_c meson, the first radial excitation of the ground state of charmonium η_c(2980), in the photon–photon fusion reaction at LEP has been performed using the data collected by the DELPHI detector during 1992–1996. No evidence of η′_c production is found in the mass region 3520–3800 MeV/c². An upper limit for the ratio of the two-photon widths of the η′_c and η_c is obtained.

Introduction

The properties of the charmonium states are well suited for fundamental tests of QCD dynamics 1, 2, but they have not yet been well determined. In particular, our understanding of spin-singlet states is extremely poor, being limited to the only well established singlet state in all onium spectroscopy, the η_c(${}^1\text{S}{}_0$) ground state of charmonium. The identification of the first radial excitation of the η_c was claimed by the Crystal Ball Collaboration in the inclusive photon spectrum of ψ′ decays, with a mass and width 3, 4of m_η′c=3594±5 MeV/c² and Γ(η′_c) < 8 MeV. Unfortunately, the state has not been observed in any other experiment. The search for η′_c thus poses a worthy challenge to the new ways of studying charmonium spectroscopy, namely $\text{p}\text{p}\text{̄}$ annihilation [2]and photon–photon fusion [5].

Calculations with a variety of $\text{q}\text{q}\text{̄}$ potentials [6], as well as “model independent” calculations based on measured e⁺e⁻ decay widths of J/ψ and ψ′ and the well known expression for hyperfine splitting, lead to the prediction that m_η′c=3615±10 MeV/c². Lattice gauge calculations cannot yet predict the masses of radially excited states accurately, but the first results are consistent with the above prediction [7]. To first order the two photon widths of η_c and η′_c are proportional to the squares of their respective radial wave functions at the origin [8]. A more elaborate relativistic calculation, which was able to predict Γ_γγ(η_c) successfully, predicts that Γ_γγ(η′_c)/Γ_γγ(η_c) = 0.75±0.02 [9]³.

Precision measurements of the properties of charmonium resonances have been made by Fermilab experiments E760 and E835 via their formation in $\text{p}\text{p}\text{̄}$ annihilation [2]. E760/E835 have successfully identified η_c in the reaction $\text{p}\text{p}\text{̄}\text{→η}{}_{\mathrm{c}}\text{→γγ}$ 10, 11, but have failed to find any evidence for η′_c in the two photon decay channel. E835 has established a 90% upper confidence limit [11]

$$\text{Br(p}\text{p}\text{̄}\text{→η′}{}_{\mathrm{c}}\text{)Br(η′}{}_{\mathrm{c}}\text{→γγ)}\text{Br(p}\text{p}\text{̄}\text{→η}{}_{\mathrm{c}}\text{)Br(η}{}_{\mathrm{c}}\text{→γγ)}\text{≤0.16}$$

for an η′_c anywhere in the mass region 3570 to 3670 MeV/c² with Γ(η′_c) ≥ 5 MeV. Thus the η′_c continues to be elusive.

Photon–photon fusion represents another potentially powerful technique for studying positive charge conjugation charmonium resonances R, and several attempts to study these in the reaction

$$\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{→e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{(γγ)→e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{R→e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{(}\text{hadrons}\text{)}$$

have been reported [12]. Measurements at high collider energies at LEP are especially well suited for these studies because the two photon flux increases with center-of-mass energy $\text{s}$, and the background decreases. Further, given sufficient statistics, several resonances with common decay channels can be investigated in the same invariant mass spectrum. Thus the η_c and η′_c can be searched for simultaneously.

The present search for η′_c in the DELPHI data was motivated by the experimental results mentioned above and by the potential advantages of photon–photon fusion measurements at LEP. Signals for resonance production in the invariant mass range 3520 to 3800 MeV/c² were searched for in the five decay channels in which η_c is known to have large branching ratios for producing charged particles or K⁰_s: ρ⁰ρ⁰, K⁰_sK⁺π⁻(K⁰_sK⁻π⁺), $\text{K}{}^{\mathrm{\ast 0}}\text{K}{}^{\mathrm{-}}\text{π}{}^{\mathrm{+}}$($\text{K}\text{̄}{}^{\mathrm{\ast 0}}\text{K}{}^{\mathrm{+}}\text{π}{}^{\mathrm{-}}$), K⁰_sK⁰_sπ⁺π⁻ and K⁺K⁻K⁺K⁻, with K⁰_s→π⁺π⁻ and $\text{K}{}^{\mathrm{\ast 0}}\text{→K}{}^{\mathrm{+}}\text{π}{}^{\mathrm{-}}$ [4].

The data used for the analysis were collected with the DELPHI detector at LEP in 1992–1996 with integrated luminosities of $\text{130}\text{pb}{}^{\mathrm{-1}}$ at the Z⁰ peak, $\text{6}\text{pb}{}^{\mathrm{-1}}$ at 130 and 136 GeV, and $\text{20}\text{pb}{}^{\mathrm{-1}}$ at 161 and 172 GeV.