Natural Higgs Mass from Power-Law Running

Abstract

The renormalized scalar mass squared is a function of the energy scale and power-runs as its square. Well above the electroweak scale, its dimensionless couplings evolve only slowly, so the Standard Model is approximately scale invariant, and an order-one boundary value supplied at the unification scale is mapped exponentially down to the electroweak scale, much as the QCD scale arises from a dimensionless coupling alone. The 28 orders of magnitude separating the two then measure the smallness of an anomalous dimension, dominated by the top-quark Yukawa coupling, rather than a tuning. Naturalness is thereby recast as the value of an order-one ratio, with no protective symmetry required.