Comment on the $W+1$ jet to $W+0$ jets ratio

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 $R_{CSS}(Q_T^{\min})\equiv \frac{\sigma(Q_T>Q_T^{\min})}{\sigma _{Total}}$.