Radiative Decay of $\Upsilon$ into a Scalar Glueball

Abstract

We study the radiative decay of $\Upsilon$ into a scalar glueball $\Upsilon \to \gamma G_s$ using QCD factorization. We find that for this process the non-perturbative effects can be factorized into a matrix element well defined in non-relativistic QCD (NRQCD) and the gluon distribution amplitude. The same NRQCD matrix element appears also in leptonic decay of $\Upsilon$ and therefore can be determined from data. In the asymptotic limit the gluon distribution amplitude is known up to a normalization constant. Using a QCD sum-rule calculation for the normalization constant, we obtain $Br(\Upsilon \to \gamma G_s)$ to be in the range $(1\sim 2)\times 10^{-3}$. We also discuss some of the implications for $\Upsilon \to \gamma f_i$ decays. Near future data from CLEO-III can provide crucial information about scalar glueball properties.