Naturalness of Asymptotically Safe Higgs

We extend the list of theories featuring a rigorous interacting ultraviolet fixed point by constructing the first theory featuring a Higgs-like scalar with gauge, Yukawa and quartic interactions. We show that the theory enters a perturbative asymptotically safe regime at energies above a physical scale 3. We determine the salient properties of the theory and use it as a concrete example to test whether scalars masses unavoidably receive quantum correction of order 3. Having at our dispose a calculable model allowing us to precisely relate the IR and UV of the theory we demonstrate that the scalars can be lighter than 3. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around 3 ∼ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful, it might also offer an explanation for the unbearable lightness of the Higgs.