Perturbative resummed series for top quark production in hadron reactions

Our calculation of the total cross section for inclusive production of $t\overline{t}$ pairs in hadron collisions is presented. The principal ingredient of the calculation is resummation of the universal leading-logarithm effects of gluon radiation to all orders in the quantum chromodynamics coupling strength, restricted to the region of phase space that is demonstrably perturbative. We derive the perturbative regime of the resummed series, starting from the principal-value resummation approach, and we isolate the perturbative domain in both moment space and, upon inversion of the corresponding Mellin transform, in momentum space. We show that our perturbative result does not depend on the manner nonperturbative or infrared effects are handled in principal-value resummation. We treat both the quark-antiquark and gluon-gluon production channels consistently in the $\overline{\mathrm{MS}}$ factorization scheme. We compare our method and results with other resummation methods that rely on the choice of infrared cutoffs. We derive the renormalization or factorization scale dependence of our resummed cross section, and we discuss factorization scheme dependence and remaining theoretical uncertainties, including estimates of possible nonperturbative contributions. We include the full content of the exact next-to-leading order calculation in obtaining our final results. We present predictions of the physical cross section as a function of top quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV. We also provide the differential cross section as a function of the parton-parton subenergy.