Next-to-leading order calculation of the color-octet S-3(1) gluon fragmentation function for heavy quarkonium

The short-distance coefficients for the color-octet S-3(1) term in the frag mentation function for a gluon to split into heavy quarkonium states is cal culated to order alpha(s)(2). The gauge-invariant definition of the fragmen tation function by Collins and Soper is employed. Ultraviolet divergences a re removed using the MS renormalization procedure. The longitudinal term in the fragmentation function agrees with a previous calculation by Beneke an d Rothstein. The next-to-leading order correction to the transverse term di sagrees with a previous calculation, (C) 2000 Elsevier Science B,V. All rig hts reserved.