Anomalous Higgs Couplings as a Window to New Physics

The initial data on the production and decay of the Higgs boson reported significant deviations from the Standard Model (SM) expectations, prompting much speculation about its couplings to the other particles. Although the latest data has veered towards conformity with the SM, there is yet room for a sizable deviation from the SM values of the coupling of the Higgs boson with $t\bar{t}$, and to a smaller extent, of that with $W^+W^-$ and $ZZ$. Keeping the fluid nature of the data in mind, this opens up an interesting avenue to explore regarding unitarity of gauge boson scattering and the stability of the electroweak vacuum in the presence of anomalous couplings. We show that, for some typical benchmark points, unitarity in gauge boson scattering breaks down between 1 and 10 TeV. We also show that if there are no new light degrees of freedom, the Higgs quartic coupling becomes negative at around the same point, making the electroweak vacuum unstable. Thus, some new ultraviolet completing new physics is demanded at that scale to cancel both these anomalous behaviours if such deviations from the SM couplings are indeed established.