# Setting limits on Effective Field Theories: the case of Dark Matter

## TL;DR

This paper examines the limitations of using Effective Field Theories for Dark Matter searches at the LHC, proposing a validated method to set more accurate limits considering the EFT validity range.

## Contribution

It introduces a modified likelihood approach to properly set limits on EFT parameters, accounting for the theory's cutoff, and demonstrates its application to CMS mono-jet data.

## Key findings

- Standard EFT limits can be invalid due to energy surpassing the cutoff.
- The proposed method provides more reliable constraints on Dark Matter EFT models.
- Applicability extends to other EFTs in Electroweak and Higgs sectors.

## Abstract

The usage of Effective Field Theories (EFT) for LHC new physics searches is receiving increasing attention. It is thus important to clarify all the aspects related with the applicability of the EFT formalism in the LHC environment, where the large available energy can produce reactions that overcome the maximal range of validity, i.e. the cutoff, of the theory. We show that this does forbid to set rigorous limits on the EFT parameter space through a modified version of the ordinary binned likelihood hypothesis test, which we design and validate. Our limit-setting strategy can be carried on in its full-fledged form by the LHC experimental collaborations, or performed externally to the collaborations, through the Simplified Likelihood approach, by relying on certain approximations. We apply it to the recent CMS mono-jet analysis and derive limits on a Dark Matter (DM) EFT model. DM is selected as a case study because the limited reach on the DM production EFT Wilson coefficient and the structure of the theory suggests that the cutoff might be dangerously low, well within the LHC reach. However our strategy can also be applied to EFT's parametrising the indirect effects of heavy new physics in the Electroweak and Higgs sectors.