We analyse inclusive photoproduction of polarized ^3P_1 quarkonium in the framework of QCD. To separate nonperturbative and perturbative parts in the density matrix of the produced quarkonium we use a method , which is equivalent to the diagramatic expansion widely used in analysing deeply inelastic scatterings. A systematic expansion in a small velocity v, with which a heavy quark moves inside the quarkonium in its rest frame, is performed for the nonperturbative parts, and they are expressed

more »

... s matrix elements in nonrelativistic QCD. At the leading order of v there are four matrix elements representing nonperturbative physics. The perturbative parts are calculated at the leading order of coupling constants. Some numerical results, especially, numerical results for HERA are given.