  LHCb provides unique opportunities to study $W$ and $Z$ boson production at
forward rapidities at the LHC. It has recently been suggested that a
measurement of the $W$ boson mass by LHCb would complement measurements by
ATLAS and CMS. All measurements of the $W$ mass at hadron colliders are subject
to PDF uncertainties, but there would be a partial cancellation of the overall
PDF uncertainty when the LHCb result is included in an average with
measurements by ATLAS and CMS. Here we review measurements of $W$ and $Z$ boson
production by LHCb, and report on a new study of the PDF uncertainty on the
LHCb measurement of the $W$ mass. The latter study includes the proposal of a
new approach that should reduce the PDF uncertainty by roughly a factor of two
with LHCb Run 2 data.
