Radiative Decay of Υ into a

We study the radiative decay of Υ into a scalar glueball Υ → γGs using QCD factorization. We find that for this process the non-perturbative effects can be factorized into a matrix element defined in non-relativistic QCD which can be determined from leptonic decay of Υ, and into the gluon parton distribution amplitude, whose asymptotic form is known up to a normalization constant. Normalizing this constant to a QCD sum-rule calculation, we obtain Br(Υ → γGs) to be in the range (1 ∼ 2)×10−3. Combining with data this result rules out the possibility that the candidate scalar glueball f0(1500) or f0(1710) to be a pure glueball. Using existing data on mixing, we predict the branching ratios for several radiative decays, such as Υ → γf0(1370, 1500, 1710) → γKK̄(ππ). The mixing pattern suggested in the literature is also shown to be in conflict with data. Near future data from CLEO-III can provide crucial information about scalar glueball properties. PACS numbers: 13.25.Gv, 12.39.Mk, 12.38.Bx, 12.38.-t Typeset using REVTEX 1 The existence of glueballs are natural predictions of QCD. Some of the low lying states are 0, 0, 1 and 2 with the lowest mass eigenstate to be 0 in the range of 1.5 ∼ 1.7 GeV from theoretical calculations [1]. There are indications that f0(1370), f0(1500) and f0(1710) contain substantial scalar glueball content. For the search of glueballs, decays of quarkonia are well suited processes because the decays are mediated by gluons. Among these decays, two-body radiative decays are ideal places to study this subject, because there is no complication of interactions between light hadrons. Radiative decays of Υ have been studied before, in particularly by CLEO [2,3] recently. With the current data sample, there are already several observations of radiative decay of Υ into mesons. Among them only a few with good precisions, such as the decay Υ → γf2(1270), Υ → γf0(1710) → γKK̄), while the others have large errors [3]. About 4 fb bb̄ resonance data are planned to be taken at CLEO-III in the year prior to conversion to low energy operation (CLEO-C) [4]. This will produce the largest data sample of Υ in the world. More radiative decay modes of Υ will be observed. Combining experimental data in the near future and theoretical results glueball properties can be studied in details. In this paper we carry out a theoretical study of the radiative decay of Υ into a scalar glueball using QCD factorization. We find that the unknown non-perturbative effects can be factorized into a matrix element defined in non-relativistic QCD (NRQCD), and the gluon parton distribution amplitude. The unknown NRQCD matrix element can be determined from leptonic Υ decays. The asymptotic form of the gluon parton distribution amplitude is known in QCD upto a normalization constant. Using a QCD sum rule calculation for this constant, the branching ratio Br(Υ → γGs) is predicted to be in the range of (1 ∼ 2)×10−3. Combining this result with experimental data, we find that none of the candidate scalar glueballs f0(1500) and f0(1710) can be a pure glueball. Existing information on glueball mixing allow us to predict the branching ratios for several radiative decays, such as Υ → γf0(1370, 1500, 1710) → γKK̄(ππ). A mixing pattern suggested in the literature is shown to be in conflict with data. Near future experimental data from CLEO-III will provide crucial information about scalar glueball properties.