Comparison of exact and effective-gauge-boson calculations for gauge-boson fusion processes

The exact perturbative calculations for the gauge-boson fusion processes $W^{+}$ $W^{\mathrm{-}}$→$W^{+}$ $W^{\mathrm{-}}$, $W^{+}$ $W^{\mathrm{-}}$→$Z^0$ $Z^0$, and $W^{+}$ $W^{\mathrm{-}}$→$H^0$ $H^0$ are compared with the corresponding effective-gauge-boson calculations. These comparisons enable us to study the several forms of the gauge-boson distribution functions and draw some conclusions about their nonleading terms. In addition, it is possible to study the effects of various rapidity cuts on the exact and approximate calculations. For rapidity cuts ${\eta }_C$ satisfying 1.0≤${\eta }_C$≤2.0, the agreement is excellent. Larger rapidity cuts reveal disagreements of a factor of 2–3 when the invariant mass of the final state is large compared to the Higgs-boson mass. In all cases, the agreement near the Higgs-boson peak is good. The discrepancies are discussed in terms of the extra diagrams which occur in the exact calculation and the t-channel singularities which are present in the effective-gauge-boson calculation.