Transverse momentum dependence of the angular distribution of the Drell-Yan process

Abstract

We calculate the transverse momentum Q_{\perp} dependence of the helicity structure functions for the hadroproduction of a massive pair of leptons with pair invariant mass Q. These structure functions determine the angular distribution of the leptons in the pair rest frame. Unphysical behavior in the region Q_{\perp} --> 0 is seen in the results of calculations done at fixed-order in QCD perturbation theory. We use current conservation to demonstrate that the unphysical inverse-power and \ln(Q/Q_{\perp}) logarithmic divergences in three of the four independent helicity structure functions share the same origin as the divergent terms in fixed-order calculations of the angular-integrated cross section. We show that the resummation of these divergences to all orders in the strong coupling strength \alpha_s can be reduced to the solved problem of the resummation of the divergences in the angular-integrated cross section, resulting in well-behaved predictions in the small Q_{\perp} region. Among other results, we show the resummed part of the helicity structure functions preserves the Lam-Tung relation between the longitudinal and double spin-flip structure functions as a function of Q_{\perp} to all orders in \alpha_s.