Summation of large corrections to short-distance hadronic cross sections

The large soft gluon corrections to short-distance hadronic cross sections are summed to all orders in perturbation theory. The arguments apply to any cross section whose Born contribution is initiated by quarks, including Drell-Yan and heavy vector boson cross sections. The exponentiation of leading and non-leading ln(n) terms in moments of these cross sections is verified. In particular, the ln³(n) terms computed by van Neervan at two loops are rederived on the basis of one-loop calculations.