[Paper Review] The manifestly gauge-invariant spectrum of the Minimal Supersymmetric Standard Model

Axel Maas, Philipp Schreiner|arXiv (Cornell University)|Jul 18, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy3 citations

TL;DR

This paper presents a manifestly gauge-invariant analysis of the Minimal Supersymmetric Standard Model (MSSM) using augmented perturbation theory (APT), which ensures non-perturbative gauge invariance by incorporating the Brout-Englert-Higgs effect through the Fröhlich-Morchio-Strocchi mechanism. The key result is that the MSSM spectrum remains dominated by its 2-Higgs doublet model (2HDM)-like subsector, with corrections to standard perturbation theory being sub-leading, implying that phenomenological predictions in the MSSM remain robust under non-perturbative gauge invariance constraints.

ABSTRACT

Formal field theory requires, even in the presence of a Brout-Englert-Higgs effect, to maintain manifest non-perturbative gauge invariance. The Fröhlich-Morchio-Strocchi mechanism allows nonetheless an augmented perturbative treatment. We perform such an augmented tree-level analysis for the minimal supersymmetric standard model. We find that, as for the standard model, corrections to standard perturbation theory are only sub-leading.

Motivation & Objective

• To investigate whether manifest gauge invariance, enforced via the Fröhlich-Morchio-Strocchi mechanism, alters the physical spectrum of the Minimal Supersymmetric Standard Model (MSSM).
• To determine whether the superpartner sector significantly affects the gauge-invariant spectrum or if the MSSM behaves like a 2Higgs doublet model (2HDM) in this context.
• To assess the validity of standard perturbative predictions in the MSSM under non-perturbative gauge invariance constraints, particularly for the lightest supersymmetric particle (LSP).
• To explore the implications of manifest gauge invariance for supersymmetry-breaking scenarios and the potential absence of physical superpartners in certain SUSY realizations.

Proposed method

• The study employs augmented perturbation theory (APT), an extension of standard perturbation theory that ensures manifest non-perturbative gauge invariance by constructing composite, gauge-invariant operators from fields.
• The Higgs field is decomposed into vacuum expectation value (vev) and fluctuation components: $\phi = v n + \eta$, where $v$ is the vev, $n$ is a unit vector fixed by gauge choice, and $\eta$ is the fluctuation field.
• The Fröhlich-Morchio-Strocchi mechanism is applied to rewrite matrix elements of gauge-invariant composite operators, such as $\phi^\dagger\phi$, into a sum of terms including $v^2 \langle (n^\dagger \eta)(n^\dagger \eta) \rangle$, $v \langle (n^\dagger \eta)(\eta^\dagger \eta) \rangle$, and $\langle (\eta^\dagger \eta)(\eta^\dagger \eta) \rangle$, ensuring gauge invariance to all orders.
• The analysis is performed at tree level, starting from the supersymmetric electroweak sector, then extending to leptons and the full MSSM, with special attention to the LSP.
• The method avoids perturbative BRST, which breaks down due to the Gribov-Singer ambiguity, and instead uses non-perturbative gauge-invariant formulations.
• The approach is tested for consistency with known results in the Standard Model and 2HDM, and extended to the MSSM by analyzing whether superpartners alter the dominant 2HDM-like behavior.

Experimental results

Research questions

• RQ1 Does the manifestly gauge-invariant formulation via APT lead to qualitative changes in the MSSM spectrum compared to standard perturbation theory?
• RQ2 Is the MSSM spectrum dominated by its 2HDM-like subsector, such that corrections from the superpartner sector are sub-leading?
• RQ3 Can the lightest supersymmetric particle (LSP) be consistently described within the APT framework without violating gauge invariance?
• RQ4 How does the presence of supersymmetry affect the Fröhlich-Morchio-Strocchi mechanism, especially when SUSY is explicitly broken as in the MSSM?
• RQ5 Under what conditions might manifest gauge invariance lead to qualitative differences in the MSSM spectrum, particularly in gauge- or gravity-mediated SUSY-breaking scenarios?

Key findings

• The MSSM spectrum is found to be dominated by its 2-Higgs doublet model (2HDM)-like subsector, with corrections to standard perturbation theory being sub-leading, indicating that the SM-like behavior persists under non-perturbative gauge invariance.
• The superpartner sector does not actively affect the Fröhlich-Morchio-Strocchi mechanism, meaning that the gauge-invariant spectrum is primarily determined by the Higgs sector's structure.
• The lightest supersymmetric particle (LSP) remains a stable, gauge-invariant state under APT, consistent with its role in dark matter phenomenology.
• Manifestly gauge-invariant operators in the MSSM, such as $\phi^\dagger\phi$, decompose into terms that preserve gauge invariance to all orders, with the dominant contribution matching standard perturbation theory.
• The study suggests that in the MSSM, the global symmetry carried by the Higgs is at least as large as the gauge group, which explains why no qualitative changes in the spectrum arise from manifest gauge invariance.
• In scenarios with explicit SUSY breaking, such as the MSSM, the APT framework simplifies, as the full supermultiplet structure is not required to be manifest, allowing standard APT techniques to apply directly.