Model-independent Veltman condition,naturalness and the little hierarchy problem

We adopt a bottom-up Effective Field Theory (EFT) approach to derive a model-independent Veltman condition to cancel out the quadratic divergences in the Higgs mass. We show using the equivalence theorem that all the deviations in the Higgs couplings to the \begin{document}$ W $\end{document} and \begin{document}$ Z $\end{document} from the SM predictions should vanish. We argue based on tree-level unitarity that any new physics that naturally cancels out the quadratic divergences should be \begin{document}$ \lesssim 19 $\end{document} TeV. We show that the level of fine-tuning required is \begin{document}$ O(0.1\%-1\%) $\end{document} unless the UV sector has a symmetry that forces the satisfaction of the model-independent Veltman condition, in which case all fine-tuning is eliminated. We also conjecture that, if no new physics that couples to the Higgs is observed up to \begin{document}$ \sim 19 $\end{document} TeV, or if the Higgs couplings to the SM particles conform to the SM predictions, then the Higgs either does not couple to any UV sector or is fine-tuned.