Investigating perturbative unitarity in the presence of anomalous couplings

Abstract

We perform a model independent analysis of the helicity amplitudes at high energy for all the $2\ensuremath{\rightarrow}2$ scattering processes involving gauge and Higgs bosons in the presence of anomalous $WWV$, $WWVV$, $VVH$, $VVHH$ ($V\ensuremath{\equiv}Z$, $\ensuremath{\gamma}$ and ${W}^{\ifmmode\pm\else\textpm\fi{}}$), $HHHH$ and $HHH$ interactions. We obtain the perturbative unitarity constraints on anomalous couplings by demanding the vanishing of terms proportional to ${s}^{2}$ and ${s}^{3/2}$ in the helicity amplitudes. Using these constraints, we also compute the upper bound on all the anomalous couplings from terms linear in $s$. Further, assuming all anomalous couplings to have arisen only from dimension six operators, we show that the perturbative unitarity violation can be evaded up to $\ensuremath{\sim}9\text{ }\text{ }\mathrm{TeV}$ corresponding to the best fit values of ${f}_{WW}/{\mathrm{\ensuremath{\Lambda}}}^{2}$ and ${f}_{BB}/{\mathrm{\ensuremath{\Lambda}}}^{2}$ from the combined analysis of Tevatron and LHC data.