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 W and Z 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 less than or similar to 19 TeV. We show that the level of fine-tuning required is O(0.1% - 1%) 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 similar to 19 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.