Approximating multileg processes: Higgs production via W-fusion

Abstract

Meaningful approximations for multileg processes at tree level are constructed which circumvent the problems of unitarity violation and gauge invariance. In this article we study the LHC: pp → ZZ + 2 jets + X and the Linear Collider: e+e− → ZZνeν̄e processes both of which contain the W-fusion scattering process for off-shell Ws. Using the pinch technique the signal and background, which contribute coherently, are separated in a well defined and gauge invariant way thus defining a resonant approximation which behaves well at high energies. The speed of the numerical calculation is greatly reduced compared to the lengthy calculation of the complete set of diagrams while at the same time the approximations describe very well the full result not only close to the resonance but also beyond it, as shown in various differential distributions of the cross section. The problem of regulating the resonant Higgs diagram is treated both with the naïve approach of adding a constant width to the Higgs propagator and with the minimal field theoretic approach of dressing both the Higgs propagator and the ZZH vertex with their one loop imaginary parts, both fermionic and bosonic, as calculated by the pinch technique. No significant numerical differences were observed between the two approaches in this particular example.