Identification ofWbosons inp¯pcollisions: A detailed study

We study the decay-lepton distribution of $W$ bosons produced in high-energy $\overline{p}p$ collisions $\overline{p}p\to W^{\pm }X\to l^{\pm }X$. The accuracy that one can reach in calculating the shape of the lepton momentum distribution determines, along with the statistics of the experimental data, the accuracy of measuring $M_W$. Our study shows that in the experimentally relevant region, where the lepton's transverse momentum $p_T\simeq \frac{M_W}{2}$, the calculation is dominated by the behavior of the cross section for producing the $W$ at small transverse momentum $Q_T$, e.g., $Q_T\simeq 5$ GeV for $\sqrt{s}=540\mathrm{}$ GeV. As $Q_T\ll M_W$, $O\left({\alpha }_s\right)$ calculations are unreliable, in fact irrelevant. We calculate the $Q_T$ distribution of the $W$ to all orders in ${\alpha }_s$ using an impact-parameter formalism to sum the leading double logarithms. We present the lepton transverse-momentum distribution for $\overline{p}p$ collider energies of $\sqrt{s}=540\mathrm{}$ GeV, and 2 TeV. Further attention is devoted to the dependence of the signal on the center-of-mass angle $\theta$, to the calculation of the prompt-lepton background, and to the relevance of identifying the missing energy associated with the neutrino from $W\to l\nu$.