  We present a novel method for studying the shape of the Z boson transverse
momentum distribution, Q_T, at hadron colliders in ppbar/pp -> Z/gamma* ->
l^+l^-. The Q_T is decomposed into two orthogonal components; one transverse
and the other parallel to the di-lepton thrust axis. We show that the
transverse component is almost insensitive to the momentum resolution of the
individual leptons and is thus more precisely determined on an event-by-event
basis than the Q_T. Furthermore, we demonstrate that a measurement of the
distribution of this transverse component is substantially less sensitive to
the dominant experimental systematics (resolution unfolding and Q_T dependence
of event selection efficiencies) reported in previous measurements of the Q_T
distribution.
