Investigating Unitarity in Presence of Anomalous Couplings

We perform a model independent analysis of the helicity amplitudes at high energy for all the $2\to 2$ scattering processes involving gauge and Higgs bosons in the presence of anomalous $WWV$, $WWVV$, $VVH$, $VVHH$ ($V\equiv Z,\gamma$and$W^\pm$),$HHHH$and$HHH$ interactions. We obtain the perturbative unitarity constraints on anomalous couplings by demanding the vanishing of terms proportional to $s^2$ and $s^{3\mathrm{/}2}$ 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 $\sim$ 9 TeV corresponding to the best fit values of $f_{WW}\mathrm{/}{\mathrm{\Lambda }}^2$ and $f_{BB}\mathrm{/}{\mathrm{\Lambda }}^2$ from the combined analysis of Tevatron and LHC data.