  Study of the polarized heavy quarkonium production in recently proposed QCD
factorization formalism requires knowledge of a large number of input
fragmentation functions (FFs) from a single parton or a heavy quark-antiquark
pair to a polarized heavy quarkonium. In this paper, we calculate these FFs at
the input scale in terms of nonrelativistic QCD (NRQCD) factorization. We
derive all relevant polarized NRQCD long-distance matrix elements based
symmetries and propose a self-consistent scheme to define them in arbitrary $d$
dimensions. We then calculate polarized input FFs contributed from all $S$-wave
and $P$-wave NRQCD intermediate states. With our calculation of the polarized
input FFs, and the partonic hard part available in literatures, the QCD
factorization formalism is ready to be applied to polarized heavy quarkonium
production.
