Naturalness of asymptotically safe Higgs

Preprint number: CP3-Origins-2017-1 DNRF90
Authors: Giulio Maria Pelaggi (Dipartimento di Fisica dell’università di Pisa and INFN), Francesco Sannino (CP3-Origins & DIAS), Alessandro Strumia (CERN, Theory Division, Geneva, Switzerland), and Elena Vigiani (Dipartimento di Fisica dell’università di Pisa)
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We introduce a model that contains a Higgs-like scalar $H$,
charged under a gauge group and with Yukawa and quartic interactions that enter a perturbative asymptotically safe regime at energies above the renormalization invariant scale $Lambda$. The models serves as concrete basis to establish the quantum corrections to the Higgs mass in these theories. We show that the latter does not receive quantum correction of order $Lambda$ along the RG flow connecting the infrared Gaussian fixed point and the interacting ultraviolet one. We further argue on the generality of the result. Although we do not have a firm answer to whether the Standard Model hypercharge coupling growth towards a Landau pole around $Lambda sim 10^{40}GeV$ can be tamed by asymptotic safety our concrete and calculable SM-like theory shows that such a possibility is worth exploring. In fact, if successful it might also offer an explanation for the unbearable lightness of the Higgs.