  We present a study of the normalized transverse momentum distribution of $W$
bosons produced in $p \bar p$ collisions, using data corresponding to an
integrated luminosity of 4.35 fb$^{-1}$ collected with the D0 detector at the
Fermilab Tevatron collider at $\sqrt{s}=1.96$ TeV. The measurement focuses on
the transverse momentum region below 15 GeV, which is of special interest for
electroweak precision measurements; it relies on the same detector calibration
methods which were used for the precision measurement of the $W$ boson mass.
The measured distribution is compared to different QCD predictions and a
procedure is given to allow the comparison of any further theoretical models to
the D0 data.
