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

Abstract

We calculate the transverse momentum ${Q}_{\ensuremath{\perp}}$ 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 ${Q}_{\ensuremath{\perp}}\ensuremath{\rightarrow}0$ 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 $\mathrm{ln}(Q/{Q}_{\ensuremath{\perp}})$ 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 ${\ensuremath{\alpha}}_{s}$ 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 ${Q}_{\ensuremath{\perp}}$ 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 ${Q}_{\ensuremath{\perp}}$ to all orders in ${\ensuremath{\alpha}}_{s}$.