  We present a measurement of the $W$ boson production charge asymmetry in
$p\bar{p}\rightarrow W+X \rightarrow e\nu +X$ events at a center of mass energy
of 1.96 TeV, using 9.7 fb$^{-1}$ of integrated luminosity collected with the D0
detector at the Fermilab Tevatron Collider. The neutrino longitudinal momentum
is determined using a neutrino weighting method, and the asymmetry is measured
as a function of the $W$ boson rapidity. The measurement extends over wider
electron pseudorapidity region than previous results, and is the most precise
to date, allowing for precise determination of proton parton distribution
functions in global fits.
