[Paper Review] Low-scale SUSY breaking by modular fields and Higgs mass bounds

S. Mukhopadhyay, Biswarup Mukhopadhyaya+1 more|arXiv (Cornell University)|Mar 18, 2011

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes a low-scale supersymmetry (SUSY) breaking mechanism mediated by modular fields in extra compact spacelike dimensions, where the vacuum expectation values (vev) of these fields set a cut-off scale near 10 TeV. This framework enables both tree-level and loop-level contributions to the lightest neutral Higgs mass from hard and soft SUSY-breaking terms, leading to a significant upward revision of the Higgs mass bound—up to 380 GeV for a 1 TeV cut-off, and 150–170 GeV for a 10 TeV cut-off—thus relaxing the tension with LEP limits.

ABSTRACT

We consider a scenario where supersymmetry (SUSY) is broken at a relatively low scale by modular fields of extra compact spacelike dimensions. The effect of both soft and hard SUSY breaking terms on the mass of the lightest neutral Higgs boson are investigated. An important conclusion is that the lightest neutral Higgs can be considerably more massive than what is expected in the MSSM, if the overseeing theory breaks SUSY at a scale not too far above a TeV. An explicit model that implements this has been shown for illustration.

Motivation & Objective

• To address the naturalness problem in the MSSM by proposing a low-scale SUSY breaking mechanism that avoids the hierarchy problem associated with high-scale breaking.
• To resolve the tension between the LEP Higgs mass limit (below 140 GeV) and the MSSM prediction, which typically caps the lightest Higgs at ~130 GeV.
• To explore how hard SUSY-breaking terms and higher-dimensional operators suppressed by a scale near 10 TeV can enhance the Higgs mass beyond MSSM expectations.
• To demonstrate a concrete realization of this mechanism in a string-inspired higher-dimensional supergravity model with modular fields.

Proposed method

• The model employs modular fields arising from compactified extra spacelike dimensions, whose scalar components develop vacuum expectation values (vev) that set the effective cut-off scale for higher-dimensional operators.
• Soft SUSY-breaking terms are generated via higher-dimensional operators suppressed by the vev of the modular field ⟨T⟩, which acts as a dynamical cut-off scale.
• Hard SUSY-breaking terms are retained in the Lagrangian and contribute to the Higgs mass at both tree level and loop level, with their effects enhanced due to the low cut-off scale.
• The scalar potential is explicitly constructed to include both F-term vev (FT) and modular field vev (⟨T⟩), both in the few TeV range, ensuring TeV-scale soft masses.
• Radiative corrections to the Higgs mass are computed using a cut-off scale of approximately 10 TeV, leading to significant loop contributions.
• Numerical estimates are performed across the phenomenologically allowed MSSM parameter space to assess the Higgs mass enhancement.

Experimental results

Research questions

• RQ1 Can a low-scale SUSY breaking mechanism mediated by modular fields in extra dimensions lead to a substantial upward shift in the lightest neutral Higgs mass beyond the standard MSSM prediction?
• RQ2 How do hard SUSY-breaking terms contribute to the Higgs mass at tree level and through loop corrections in a theory with a cut-off scale near 10 TeV?
• RQ3 What is the quantitative impact of a modular field vev at ~10 TeV on the Higgs mass bound, particularly in comparison to the MSSM limit?
• RQ4 Can this framework reconcile the non-observation of the Higgs boson below 130 GeV at LEP with potential SUSY signals (e.g., missing energy) observed at the LHC?
• RQ5 How does the interplay between soft and hard SUSY-breaking terms in a low-cut-off effective theory affect the Higgs mass spectrum?

Key findings

• For a cut-off scale of approximately 1 TeV, the corrected upper bound on the lightest neutral Higgs mass can reach up to about 380 GeV, significantly exceeding the standard MSSM limit.
• For a more modest cut-off scale of 10 TeV, the Higgs mass can still be enhanced to 150–170 GeV, offering a viable resolution to the LEP-Higgs tension.
• The tree-level contribution from hard SUSY-breaking terms plays a crucial role in shifting the Higgs mass upward, especially when the cut-off scale is low.
• Loop corrections to the Higgs mass are enhanced due to the suppression scale being around 10 TeV, leading to a substantial radiative correction.
• The model provides a viable mechanism to explain the non-observation of the Higgs boson below 130 GeV at LEP, even if SUSY signals such as missing transverse momentum appear at the LHC.
• The scenario distinguishes itself from other MSSM extensions (e.g., U(1) gauge extensions or singlet models) by predicting higher Higgs mass eigenvalues due to the combined effect of hard terms and low cut-off scale.