Linear Standard Model extensions in the SMEFT at one loop and Tera-Z

TL;DR

This paper extends the mapping of linear Standard Model extensions to the SMEFT at one-loop order, providing explicit formulas and tools to assess their impact on electroweak precision measurements, especially at future Tera-Z colliders.

Contribution

It offers the first comprehensive one-loop SMEFT operator mapping for all scalar and fermion linear SM extensions, including explicit analytic expressions and computational tools.

Findings

All linear SM extensions can be probed up to ~10 TeV at Tera-Z.

Explicit one-loop matching formulas are provided for practical use.

The work enhances the sensitivity analysis of new physics in electroweak precision tests.

Abstract

Linear Standard Model (SM) extensions, defined as new particles that can couple linearly to SM fields, form a motivated and finite set of simplified models for exploring phenomenology Beyond the SM (BSM). Heavy BSM particles may be integrated out to obtain their low-energy effects in the SM Effective Field Theory (SMEFT) parametrised by the Wilson coefficients of higher-dimensional operators. We compute and map the dimension-6 SMEFT operator structure of all scalar and fermion linear SM extensions up to one-loop order, thus extending the existing tree-level dictionary of results. Explicit analytic matching expressions for the Wilson coefficients are provided as both Python and Mathematica code in a GitHub repository accessible through links embedded in our main table for each coefficient and within a Python package. We apply our map to highlight the sensitivity to heavy new physics of a $Z$-pole run at a future Tera-$Z$ factory; at one loop, with unit couplings, all linear SM extensions can be indirectly probed by electroweak precision measurements up to $\mathcal{O}(10)$ TeV.