# Which EFT

## TL;DR

This paper classifies effective field theory deformations of the Standard Model based on the analyticity of the Higgs sector, revealing deep physical distinctions and implications for Higgs interactions and new physics scales.

## Contribution

It introduces a novel classification of EFTs into analytic and non-analytic types based on the Higgs Lagrangian's properties, providing new physical insights and implications for Higgs phenomenology.

## Key findings

- Analytic EFTs allow for O(1) deviations in Higgs cubic coupling within current experimental bounds.
- Non-analytic EFTs lead to strong coupling at O(4πv), independent of the cubic coupling size.
- The classification clarifies the connection between UV properties and IR phenomenology of the Higgs sector.

## Abstract

We classify effective field theory (EFT) deformations of the Standard Model (SM) according to the analyticity property of the Lagrangian as a function of the Higgs doublet H. Our distinction in analytic and non-analytic corresponds to the more familiar one between linearly and non-linearly realized electroweak symmetry, but offers deeper physical insight. From the UV perspective, non-analyticity occurs when the new states acquire mass from electroweak symmetry breaking, and thus cannot be decoupled to arbitrarily high scales. This is reflected in the IR by the anomalous growth of the interaction strength for processes involving many Higgs bosons and longitudinally polarized massive vectors, with a breakdown of the EFT description below a scale $O(4 \pi v)$. Conversely, analyticity occurs when new physics can be pushed parametrically above the electroweak scale. We illustrate the physical distinction between these two EFT families by discussing Higgs boson self-interactions. In the analytic case, at the price of some unnaturalness in the Higgs potential, there exists space for $O(1)$ deviations of the cubic coupling, compatible with single Higgs and electroweak precision measurements, and with new particles out of the direct LHC reach. Larger deviations are possible, but subject to less robust assumptions about higher-dimensional operators in the Higgs potential. On the other hand, when the cubic coupling is produced by a non-analytic deformation of the SM, we show by an explicit calculation that the theory reaches strong coupling at $O(4 \pi v)$, quite independently of the magnitude of the cubic enhancement.