  The next to leading order (NLO) quarkonium-hadron cross section is calculated
in perturbative QCD. The corresponding leading order (LO) result was performed
by Peskin more than 20 years ago using the operator product expansion (OPE). In
this work, the calculation is performed using the Bethe-Salpeter amplitude and
the factorization formula. The soft divergence appearing in the intermediate
stages of the calculations are shown to vanish after adding all possible
crossed terms, while the collinear divergences are eliminated by mass
factorization. Applying the result to the Upsilon system, one finds that there
are large higher order correction near the threshold. The relevance of the
present result to the charmonium case is also discussed.
