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Effective field theory analysis of Higgs naturalness

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Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale M∼O(10)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≥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 Λ

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