Radiative Decays of Charmonium into Light Mesons

Abstract

We apply perturbative QCD to the radiative decays of charmonia J/ψ and χcJ into light mesons. We perform a complete numerical calculation for the quark-gluon loop diagrams involved in these processes. The calculated J/ψ decay branching ratios into P-wave mesons f2(1270) and f1(1285) fit the data well, while that of f0(980) (if treated as an ss meson) is predicted to be 1.6 × 10 −4 , which implies that f0(1710) can not be the ss or (uū + dd)/ √ 2 meson. Decays of P-wave charmonia χcJ → ρ(ω, φ)γ (J=0,1,2) are also studied, and the branching ratio of χc1 → ργ is predicted to be 1.4 × 10 −5 , which may be tested by CLEO-c and BESIII with future experiments.Decays of heavy quarkonium into light hadrons are forbidden processes by the OZI rules. The radiative decays of J/ψ into light hadrons such as J/ψ → γf 2 (1270) are expected to proceed via two virtual gluons that subsequently convert to light mesons, with the photon emitted by the charm quarks (see Fig.1 for the three Feynman diagrams). These processes are interesting since they can provide useful information for understanding the fundamental theory of strong interactions, namely, quantum chromodynamics (QCD).In this letter, we will report calculations for radiative decays of charmonia J/ψ and χ cJ into various light mesons based on nonrelativistic quantum chromodynamics. Hopefully, the J/ψ mass is large enough for using perturbative QCD to calculate these processes.Differing from previous works (see, e.g.,[1, 2]), we will perform a complete numerical calculation for the quark-gluon loop diagrams involved in these processes.Here, it is emphasized that in our approach the description of J/ψ as a nonrelativistic cc bound state is a good approximation; while treating the light mesons such as f 2 (1270) as nonrelativistic qq bound states (q = u, d, s) with constituent quark masses m u = m d ≈ 350 M eV, m s ≈ 500 M eV is only an approximation for describing the nonperturbative dynamics that has been used in the nonrelativistic constituent quark models rather successfully, and was also used in previous studies for these radiative decay processes [1,2]. In fact, if the current quark masses for the light quarks, which will vanish in the chiral limit, were used in the quark-gluon loop diagram, we would encounter difficulties with soft and collinear divergences.In the following, we will first focus on the radiative decays of J/ψ to P-wave light mesons such as f 2 (1270), f 1 (1285), and f 0 (980). We adopt the descriptions of nonrelativistic bound states, i.e., both J/ψ and light mesons are described by the color-singlet non-relativistic wave functions. As widely accepted assignments we assume that f 2 (1270) and f 1 (1285) are mainly composed of (uū + dd)/ √ 2 (neglecting the mixing with ss for simplicity). But for f 0 (980), there are many possible assignments such as the tetraquark state, the KK molecule, and the P-wave ss dominated state (for related discussions on f 0 (980) and other scalar mesons, see, e.g., the topical review-note on scalar mesons in [3] and [4]). Si...