Exact SMEFT formulation and expansion to $\mathcal{O}(v^4/\Lambda^4)$

TL;DR

This paper presents an exact formulation of the SMEFT up to dimension-eight, compares it with truncated expansions, and analyzes the impact of higher-order terms and input-parameter scheme dependence.

Contribution

It introduces an exact SMEFT solution using geometric formulation and compares it to approximate expansions up to order v^4/Λ^4, including scheme dependence analysis.

Findings

Exact SMEFT solutions up to dimension-eight are obtained.

Truncated expansions can significantly differ from the exact solution.

Input-parameter scheme dependence increases at higher orders.

Abstract

The Standard Model Effective Field Theory (SMEFT) theoretical framework is increasingly used to interpret particle physics measurements and constrain physics beyond the Standard Model. We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to mass-dimension eight. Using this construction, we compare the exact solution to the expansion at ${\mathcal{O}}(v^2/\Lambda^2)$, partial ${\mathcal{O}}(v^4/\Lambda^4)$ using a subset of terms with dimension-6 operators, and full ${\mathcal{O}}(v^4/\Lambda^4)$, where $v$ is the vacuum expectation value and $\Lambda$ is the scale of new physics. This comparison is performed for general values of the coefficients, and for the specific model of a heavy U(1) gauge field kinetically mixed with the Standard Model. We additionally determine the input-parameter scheme dependence at all orders in $v/\Lambda$, and show that this dependence increases at higher orders in $v/\Lambda$.