Using of collisions collected by the D0 detector at the Fermilab Tevatron, we measure the distribution of the variable , which probes the same physical effects as the boson transverse momentum, but is less susceptible to the effects of experimental resolution and efficiency. A QCD prediction is found to describe the general features of the distribution, but is unable to describe its detailed shape or dependence on boson rapidity. A prediction that includes a broadening of transverse momentum for small values of the parton momentum fraction is strongly disfavored.