Restoring good high energy behaviour in Higgs production via W fusion at the LHC

Abstract.

The W-fusion scattering process $W^+W^-\!\rightarrow ZZ$ for off-shell W bosons is studied, focusing on the issue of its high-energy behaviour which is known to be anomalous. It is shown that the unitarity violating terms can be isolated and extracted in a well-defined and efficient way using the pinch- technique. This restores the good high energy behaviour of the cross section and, in particular, makes possible the identification of the Higgs resonance in the invariant mass distribution $m_{ZZ}$ of the Z pair. The discarded terms, which are proportional to the off-shellness of the W bosons, cancel against similar terms originating from the remaining diagrams for the full physical process $f_1 f_2\rightarrow \overline{f'}_1 \overline{f'}_2 Z Z$. This cancellation ensures the gauge invariance of our result, which therefore constitutes a meaningful separation between signal andbackground when they both contribute coherently. Equipped with this result, we are able to define a resonant approximation for the process $p p \rightarrow Z Z +\mbox{2 jets} + X ,$ which circumvents the problem of good high energy behaviour without having to resort to the lengthy calculation of the complete set of diagrams. In this approximation only the W- and Z-fusion signal graphs are included, i.e. the ones which contain the Higgs resonance. We have verified that the approximate resonant cross section describes very well the full result not only close to the resonance but also beyond it.