Quarkonium momentum distributions in photoproduction andBdecay

According to our present understanding many $J/\psi$ production processes proceed through a colored $c\overline{c}$ state followed by the emission of soft particles in the quarkonium rest frame. The kinematic effect of soft particle emission is usually a higher-order effect in the non-relativistic expansion, but becomes important near the kinematic end point of quarkonium energy (momentum) distributions. In an intermediate region a systematic resummation of the non-relativistic expansion leads to the introduction of so-called “shape functions.” In this paper we provide an implementation of the kinematic effect of soft gluon emission which is consistent with the non-relativistic shape function formalism in the region where it is applicable and which models the extreme end point region. We then apply the model to photoproduction of $J/\psi$ and $J/\psi$ production in B meson decay. A satisfactory description of B decay data is obtained. For inelastic charmonium photoproduction we conclude that a sensible comparison of theory with data requires a transverse momentum cut larger than the currently used 1 GeV.