We calculate factorized cross sections for lepton pair production mediated by a virtual photon in hadron-hadron collisions using the jet calculus scheme, in which a kinematical constraint due to parton radiation is taken into account. This method guarantees a proper phase space boundary for subtraction terms. Some properties of the calculated cross sections are examined. We also discuss matching between the hard scattering cross sections and parton showers at the next-to-leading logarithmic (NLL) order of quantum chromodynamics (QCD). In the evaluation of hadron-hadron scattering cross sections, logarithmic contributions due to collinear parton production are subtracted from the hard scattering cross section, and they are absorbed into the parton distributions of hadrons. However, the leading-logarithmic (LL) order of quantum chromodynamics (QCD
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