  To offer a possible resolution to the apparent discrepancy between the
experimental and the theoretical values of the $W + 1$ jet to $W + 0$ jets
ratio reported by the \D0 group, we examine the effects of the multiple soft
gluon radiation on the $W$ boson production at the Tevatron. Based on the
calculation of the $W$ boson transverse momentum ($Q_T$) distribution in the
Collins-Soper-Sterman resummation formalism, we conclude that the effect of the
soft gluon radiation is important in the region of $Q_T < 50$ GeV, and it can
be better tested by a more inclusive observable $R_{CSS}(Q_T^{\min})\equiv
\frac{\sigma(Q_T>Q_T^{\min})}{\sigma _{Total}}$.
