NLO corrections to c- and b- quark fragmentation into j/ψ and γ

We present the next-to-leading-order (NLO) corrections to the fragmentation process of a heavy quark to a S-3(1) wave heavy quarkonium. The virtual and real corrections are calculated by using the dimensional regularization method. The divergences due to virtual NLO corrections are analytically extracted then we explain how the poles from phase-space integrals and from loop integrals are canceled by renormalization. We use the eikonal scheme to evaluate the soft real corrections in 4 - 2 epsilon dimensions. Our numerical calculations show the fragmentation function (FF) at NLO is dependent on both the mu scale and the initial quark energy. These corrections have a significant effect on the shape and probability of the FF.