  We present a measurement of the distribution of the variable $\phi^*_\eta$
for muon pairs with masses between 30 and 500 GeV, using the complete Run II
data set collected by the D0 detector at the Fermilab Tevatron
proton-antiproton collider. This corresponds to an integrated luminosity of
10.4 fb$^{-1}$ at $\sqrt{s}$ = 1.96 TeV. The data are corrected for detector
effects and presented in bins of dimuon rapidity and mass. The variable
$\phi^*_\eta$ probes the same physical effects as the $Z/\gamma^*$ boson
transverse momentum, but is less susceptible to the effects of experimental
resolution and efficiency. These are the first measurements at any collider of
the $\phi^*_\eta$ distributions for dilepton masses away from the $Z\rightarrow
\ell^+\ell^-$ boson mass peak. The data are compared to QCD predictions based
on the resummation of multiple soft gluons.
