13 pages, 10 figuresThe process ppbar -> photon + jet + X is studied using 1.0 fb^-1 of data collected by the D0 detector at the Fermilab Tevatron ppbar collider at a center-of-mass energy sqrt(s)=1.96 TeV. Photons are reconstructed in the central rapidity region |y_gamma|<1.0 with transverse momenta in the range 3015 GeV. The differential cross section d^3sigma/dPt_gamma dy_gamma dy_jet is measured as a function of Pt_gamma in four regions, differing by the relative orientations of the photon and the jet in rapidity. Ratios between the differential cross sections in each region are also presented. Next-to-leading order QCD predictions using different parameterizations of parton distribution functions and theoretical scale choices are compared to the data. The predictions do not simultaneously describe the measured normalization and Pt_gamma dependence of the cross section in any of the four measured regions
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