# Scheming in the SMEFT... and a reparameterization invariance!

## TL;DR

The paper investigates a reparameterization invariance in the Standard Model Effective Field Theory that causes certain Wilson coefficient combinations to remain unconstrained in specific scattering measurements, impacting global data analysis.

## Contribution

It introduces a new input parameter scheme and demonstrates the invariance's implications for data analysis and parameter degeneracies in SMEFT.

## Key findings

- Reparameterization invariance leads to unconstrained Wilson coefficient combinations.
- Input parameter choice does not affect these unconstrained combinations.
- Conceptual issues related to degeneracies are relevant for LHC data analysis.

## Abstract

We explain a reparameterization invariance in the Standard Model Effective Field Theory present when considering $\bar{\psi} \psi \rightarrow \bar{\psi} \psi$ scatterings (with $\psi$ a fermion) and how this leads to unconstrained combinations of Wilson coefficients in global data analyses restricted to these measurements. We develop a $\{\hat{m}_W, \hat{m}_Z,\hat{G}_F\}$ input parameter scheme and compare results to the case when an input parameter set $\{\hat{\alpha}, \hat{m}_Z,\hat{G}_F\}$ is used to constrain this effective theory from the global data set, confirming the input parameter independence of the unconstrained combinations of Wilson coefficients, and supporting the reparameterization invariance explanation. We discuss some conceptual issues related to these degeneracies that are relevant for LHC data reporting and analysis.