Double transverse spin asymmetries in vector boson production

We investigate a helicity non-flip double transverse spin asymmetry in vector boson production in hadron-hadron scattering, which was first considered by Ralston and Soper at the tree level. It does not involve transversity functions and in principle also arises in W-boson production for which we present the expressions. The asymmetry requires observing the transverse momentum of the vector boson, but it is not suppressed by explicit inverse powers of a large energy scale. However, as we will show, inclusion of Sudakov factors causes suppression of the asymmetry, which increases with energy. Moreover, the asymmetry is shown to be approximately proportional to $x_1{g}_1{(x}_1\left)x_2{g}_1{(x}_2\right),$ which gives rise to additional suppression at small values of the light cone momentum fractions. This implies that it is negligible for Z or W production and is mainly of interest for ${\gamma }^{*}$ at low energies. We also compare the asymmetry with other types of double transverse spin asymmetries and discuss how to disentangle them.