J/Psi Production from Electromagnetic Fragmentation in Z decay

The rate for $ Z^{0}\to J/ \psi + \ell^{+}\ell^{-} $ is suprisingly large with about one event for every million $Z^{0}$ decays. The reason for this is that there is a fragmentation contribution that is not suppressed by a factor of $M^{2}_{\psi}/M^{2}_{Z}$. In the fragmentation limit $ M_{Z}\to\infty$ with $E_{\psi}/M_{Z}$ fixed, the differential decay rate for $ Z^{0}\to J/ \psi + \ell^{+}\ell^{-} $ factors into electromagnetic decay rates and universal fragmentation functions. The fragmentation functions for lepton fragmentation and photon fragmentation into $J/\psi$ are calculated to lowest order in $\alpha$. The fragmentation approximation to the rate is shown to match the full calculation for $E_{\psi}$ greater than about $3 M_{\psi}$.