Effective field theory analysis of Higgs naturalness

Abstract

Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale $M\ensuremath{\sim}\mathcal{O}(10)\text{ }\text{ }\mathrm{TeV}$, we investigate the naturalness of the Higgs sector at scales below $M$ using an effective field theory (EFT) approach. We obtain the complete set of higher-dimensional effective operators (at any dimension $n\ensuremath{\ge}5$) that give the leading one-loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff and discuss the (fine-) tuning between these terms and the SM one-loop contribution, which is required in order to alleviate the little hierarchy problem. We then show that this tuning can be translated into a condition for naturalness in the underlying new physics, a condition we denote by ``EFT naturalness'' and which we express as constraints on the corresponding higher-dimensional operator coefficients up to the scale of the effective action $\mathrm{\ensuremath{\Lambda}}lM$. We also determine the types of physics that can lead to EFT naturalness and discuss the current experimental constraints on the relevant operator coefficients. We show that these types of new physics are best probed in vector-boson and multiple-Higgs production.