[Paper Review] Anomaly Mediated Supersymmetry Breaking, D-terms and R-symmetry

D.R.T. Jones|ArXiv.org|Jan 15, 2001

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes two RG-invariant extensions of Anomaly Mediated Supersymmetry Breaking (AMSB) in the MSSM by introducing an anomaly-free U(1) or R-symmetry, enabling stable, tachyon-free slepton masses via Fayet-Iliopoulos D-terms. The key result is a distinctive sparticle spectrum with sum rules linking masses, preserving near-degenerate winos while allowing large third-generation splittings and a tau sneutrino LSP in some cases.

ABSTRACT

We explore two distinct resolutions to the tachyonic slepton puzzle in the Anomaly Mediated Supersymmetry Breaking scenario. Both are based on extending the MSSM by an anomaly free U(1) symmetry, and in both cases exact RG invariance is preserved.

Motivation & Objective

• To resolve the tachyonic slepton problem in the standard Anomaly Mediated Supersymmetry Breaking (AMSB) scenario, where scalar masses become negative.
• To preserve exact renormalization group (RG) invariance in extended AMSB models, ensuring low-energy predictions are insensitive to high-scale physics.
• To construct viable supersymmetry-breaking scenarios using Fayet-Iliopoulos D-terms from an extended U(1) or R-symmetry, avoiding tachyonic states.
• To derive and analyze sum rules for sparticle masses that emerge from the RG-invariant structure of the extended models.
• To explore phenomenological viability, including the possibility of a tau sneutrino as the lightest supersymmetric particle (LSP).

Proposed method

• Introduce an anomaly-free U(1) or R-symmetry to the MSSM, extending the gauge sector with new U(1) charges and singlet fields to cancel anomalies.
• Modify the scalar mass matrix via a RG-invariant shift: (m²)^i_j → (m²)^i_j + m₀² Σₐ kₐ(Yₐ)^i_j, where Yₐ are U(1) charges of chiral multiplets.
• Implement Fayet-Iliopoulos (FI) D-terms as the physical origin of the mass shift, ensuring gauge invariance and RG invariance under the extended symmetry.
• Enforce vanishing mixed anomalies between the new U(1) and MSSM gauge groups to preserve RG invariance and anomaly cancellation.
• Derive sum rules for sparticle masses by exploiting the structure of the RG-invariant mass corrections, independent of FI parameter values.
• Perform numerical scans over parameters (e.g., ζ₁, ζ₂, tanβ, m₀) to identify viable spectra with positive scalar masses and acceptable LSPs.

Experimental results

Research questions

• RQ1 Can the tachyonic slepton problem in AMSB be resolved while preserving RG invariance?
• RQ2 How can Fayet-Iliopoulos D-terms be consistently incorporated into an RG-invariant extension of AMSB?
• RQ3 What are the phenomenological consequences of introducing an R-symmetry or U(1) extension on the sparticle mass spectrum?
• RQ4 Do the extended models lead to sum rules for sparticle masses, and are these sum rules independent of FI parameters?
• RQ5 Can the tau sneutrino become the lightest supersymmetric particle (LSP) in such models, and under what parameter conditions?

Key findings

• The model successfully resolves the tachyonic slepton problem by introducing a U(1) or R-symmetry extension, ensuring all scalar masses are positive in a substantial region of parameter space.
• For m₀ = 40 TeV, the heaviest sparticle masses scale as M_SUSY ≈ m₀/40, yielding gluino masses near 1 TeV.
• The spectrum features near-degenerate wino and neutralino masses, preserving a key prediction of AMSB, while the third-generation sfermions exhibit large splittings due to generation-dependent R-charges.
• In specific parameter regions (e.g., tanβ = 2, e = -1/9, m̄₀² = -0.1 TeV²), the τ sneutrino is the lightest supersymmetric particle (LSP), with mass ~83 GeV.
• Sum rules for sparticle masses are derived, such as m̃t₁² + m̃t₂² + m̃b₁² + m̃b₂² - 2(mₜ² + m_b²) - 2.75m̃g² = 0.92 m̄₀² TeV² for tanβ = 5 and m₀ = 40 TeV, independent of FI parameters.
• The model remains compatible with braneworld scenarios, as shown in prior work, and the R-symmetry extension opens avenues for further exploration in such frameworks.