Weak-boson production at Fermilab Tevatron energies

Weak bosons are produced in hadron collisions by quarks and antiquarks with average fractional momenta $x=\frac{M_{W,Z}}{\sqrt{s}}$. When $\sqrt{s}$ is increased by a factor of 3, the average value of $x$ shifts from about 0.15 at CERN $p\overline{p}$ collider energies to 0.05 at the Fermilab Tevatron, i.e., from a regime where valence quarks dominate to a regime where sea quarks dominate the production features of weak bosons. We investigate systematically the problem of calculating $W$ and $Z$ cross sections in this new regime, paying special attention to the ratio $\frac{\sigma \mathrm{}\left(W\right)\mathrm{}}{\sigma \mathrm{}\left(Z\right)\mathrm{}}$ which is necessary for determining the ratio of totals widths $\frac{\Gamma \mathrm{}\left(W\right)\mathrm{}}{\Gamma \mathrm{}\left(Z\right)\mathrm{}}$ from hadron-collider data. We emphasize that with the increased statistics in $p\overline{p}$ experiments, the parton fluxes responsible for the production of weak bosons can be controlled internally by a study of the asymmetry of the rapidity distribution of the $W$ boson. We derive a relation between the asymmetry in $W^{\pm }$ rapidity distributions and the ratio $\frac{F_2^n}{F_2^p}$ of deep-inelastic lepton-hadron scattering structure functions. The production rates of weak bosons also become sensitive to production via the charm quark. This calculation raises some interesting theoretical issues. We discuss both problems in detail. We also study the implications of our results for the determination of the number of light neutrinos and the mass of the top quark via a measurement of the $W$-to-$Z$ event ratio.