SUSY meets SMEFT: Complete one-loop matching of the general MSSM

TL;DR

This work delivers the first complete one-loop matching of the general, $R$-parity conserving MSSM onto the SMEFT (dimension-six) using the Matchete package, keeping a non-degenerate heavy spectrum and full flavor structure. The authors perform a fully automated procedure, rotate to the appropriate mass bases, apply gauge-threshold and evanescent-operator treatments, and map the results onto the Warsaw basis, while also providing an MSSM-to-2HDM-EFT alternative. They validate the results against existing analytic expressions, derive complete tree- and one-loop Wilson coefficients, and illustrate the framework with a stop–bino benchmark showing typically small SMEFT effects within current experimental sensitivities. The work enables systematic, global EFT analyses of MSSM parameter space and supplies extensive auxiliary material and code to facilitate future studies, including multi-scale matching directions. Overall, this advances the practical use of EFT tools to connect rich SUSY UV theories to low-energy observables and collider phenomenology.

Abstract

We present the complete one-loop matching of the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model Effective Field Theory (SMEFT), considering the most general case for the MSSM with conserved $R$-parity, which has 124 free parameters. The matching is performed with the Matchete package, which integrates out all superpartners at once with non-degenerate masses, while also retaining the most general flavor structure. Our results include all correlations among the different SMEFT Wilson coefficients that are governed by supersymmetry and thus provide a basis for future systematic and global studies of the MSSM parameter space employing EFT methods. A detailed discussion is provided on the treatment of the Higgs sector and electroweak symmetry breaking, along with the reduction of redundant operators in the EFT Lagrangian to the Warsaw basis. Furthermore, we validate against existing results in the literature and present a minimal phenomenological example. As an alternative low-energy scenario, we also provide the complete one-loop matching of the MSSM onto the two-Higgs-doublet-model EFT, where the second Higgs doublet is retained in the infrared spectrum. Extensive auxiliary material, including the code utilized for the matching, is available on GitHub.

Figures (3)

• Figure 1: Bar-plot highlighting the order of magnitudes for the various Wilson coefficients relevant for top-pair production at the LHC in the stop-bino model. Considered are three sets of ($m_{\tilde{t}_R}$, $m_1$) values: (1.6, 0.5), (1.6, 1.5) and (2.0, 1.5) TeV. The relevant gauge couplings are taken at 1 TeV, $g_1 \sim 0.37$, $g_3 \sim 1.1$.
• Figure 2: Two-dimensional plots highlighting the patterns of variation of the Wilson coefficients $C_G$, $C_{uG}^{33}$, $C_{qu}^{(1)1133}$, and $C_{uu}^{3333}$ in the ($m_{\tilde{t}_R}$, $m_1$) plane. The shaded regions correspond to $m_1 > m_{\tilde{t}_R}$.
• Figure 3: Bar-plot highlighting the order of magnitudes for the Wilson coefficients relevant for Higgs physics in the stop-bino model, for the same sets of ($m_{\tilde{t}_R}$, $m_1$) as in Fig. \ref{['fig:bar-plot']}. The relevant gauge couplings are again taken at 1 TeV, roughly $g_1 = 0.37$, $g_3 = 1.1$.