Elusive vector glueball

While theorists expect that the glueballs exist as the flavorless hadrons made of gluons alone, the predicted masses vary from lattice QCD [1] to phenomenological models such as the bag-type model [2] and a naive constituent model [3]. Experiment provided a few candidates for the ground-state glueball of J = 0 in the past, but no consensus has been reached. The glueball O of 1−− is made of three gluons in the constituent picture so that its mass is expected to be roughly 50% higher than the lowest glueball mass. The recent lattice QCD calculation [1] predicts the mass of O at 3850± 50± 190 MeV in the quenched approximation. It is amusing that this value happens to be very close to the ψ′ mass (3686 MeV). In contrast to the masses, very little is known even theoretically about the widths since they are determined by how the glueballs couple to light quarks. A few puzzles exist in the hadronic ψ′ decay. One is the so-called ρπ puzzle, i.e., the severe suppression of ψ′ → ρπ [4]. If both J/ψ and ψ′ decay into hadrons through the perturbative ggg from the S1 states of cc, we expect that their hadronic decays should be very similar to each other. Contrary to this expectation, the branching fractions are very different not only for ρπ but also for many other exclusive hadron channels [5]. Since B(J/ψ → ρπ)/B(J/ψ → ωπ) is close to B(J/ψ → ggg → hadrons)/B(J/ψ → γ∗ → hadrons) [6], the decay J/ψ → ρπ is just as strong as the naive expectation. The experimental fact that B(ψ′ → ωπ)/B(J/ψ → ωπ) ≈ B(ψ′ → `+`−)/B(J/ψ → `+`−) assures us that there is nothing anomalous about the 1−0− modes in the one-photon annihilation. There appears to be no perturbative 1−0− suppression that was once suggested as a resolution to the ρπ puzzle [7]. Therefore the source of the ρπ puzzle is in some property of ψ′. The other puzzle is an apparent excess of ψ′ → hadrons relative to J/ψ→ hadrons [8,9]. To establish it quantitatively, we need more an accurate determination of the cascade decay branchings of ψ′. The current data hint that there exists some unknown decay mechanism for ψ′ → hadrons other than the standard perturbative three-gluon decay. It is the ψ′-O mixing that may resolve both puzzles by one shot [8]. In view of the precision charm experiment proposed at CESR and at Beijing, we pursue here the O-ψ′ mixing as quantitatively as possible. Assuming that the excess ψ′ → hadrons really exists and that it is caused by the O-ψ′ mixing, we estimate the resonant O production cross sections. We find that the O resonance peak will be detected in e+e− annihilation only if the decay width is very narrow (ΓO < a few MeV). If the width is wider, we shall be able to find only indirect evidences for O through the ψ′ decay. In a dedicated charmonium experiment, experimentalists should first confirm the excess in ψ′ → hadrons by determining more accurately the ψ′ → J/ψ cascade decay branchings, and then examine individual exclusive hadron channels of even G-parity such as ωπ, π+π−, and ρη.