[Paper Review] A Note on Fine-Tuning in Mirage Mediation

Oleg Lebedev, Hans Peter Nilles+1 more|ArXiv.org|Nov 29, 2005

Radio Wave Propagation Studies22 citations

TL;DR

This paper investigates fine-tuning in the mirage mediation supersymmetry breaking scenario, showing that reduced gluino masses due to the $ M_3 < M_2 $ hierarchy at the GUT scale lead to significantly lower fine-tuning compared to other mediation mechanisms. Despite this advantage, simple realizations face constraints from tachyonic boundary conditions and the Higgs mass bound, limiting viable low-fine-tuning regions.

ABSTRACT

Recent progress in string theory moduli stabilization has motivated a mixed modulus-anomaly mediated supersymmetry breaking scenario, also dubbed `mirage mediation'. This scenario has a number of phenomenologically attractive features, in particular with respect to the cosmological gravitino/moduli problem. In this note, we investigate the issues of fine-tuning associated with obtaining the correct electroweak symmetry breaking scale in the mirage mediation scenario. We find that, due to lighter gluinos, the fine-tuning is smaller than that in other mediation mechanisms.

Motivation & Objective

• To assess the degree of fine-tuning required to achieve correct electroweak symmetry breaking in the mirage mediation scenario.
• To examine whether the phenomenologically attractive features of mirage mediation—such as resolving the gravitino/moduli problem—also alleviate the MSSM's little hierarchy problem.
• To identify parameter regions where fine-tuning is minimized while satisfying constraints from the Higgs mass bound and absence of tachyons.
• To explore whether model-dependent choices of effective modular weights can resolve tensions between low fine-tuning and physical consistency.

Proposed method

• Analyzes the renormalization group evolution of soft masses from the GUT scale to the electroweak scale using the mirage mediation framework.
• Applies the one-loop effective potential method to compute the Z-boson mass and its sensitivity to input parameters.
• Uses the key relation $ rac{1}{2}m_Z^2 = -\mu^2 + \frac{m_{H_d}^2 - m_{H_u}^2 \tan^2\beta}{\tan^2\beta - 1} $ to determine electroweak symmetry breaking conditions.
• Evaluates fine-tuning via the sensitivity $ \Delta \sim \partial \ln m_Z^2 / \partial \ln \text{input parameters} $, particularly $ \alpha $ and $ m_{3/2} $.
• Applies constraints from the LEP Higgs mass bound ($ m_{\text{Higgs}} \gtrsim 114\,\text{GeV} $) and the absence of tachyonic squarks at the GUT scale.
• Uses numerical analysis to map fine-tuning $ \Delta $ as a function of $ \alpha $ and $ m_{3/2} $, identifying regions of low tuning.

Experimental results

Research questions

• RQ1 To what extent does mirage mediation reduce the fine-tuning required for electroweak symmetry breaking compared to anomaly or gravity mediation?
• RQ2 Why does the region of low fine-tuning in mirage mediation often lead to tachyonic boundary conditions at the GUT scale?
• RQ3 How do the Higgs mass bound and chargino mass constraints limit the viable parameter space in mirage mediation?
• RQ4 Can the suppression of the gluino mass in mirage mediation ($ M_3 < M_2 $) be systematically exploited to reduce fine-tuning?
• RQ5 Is it possible to achieve low fine-tuning without tachyonic states by adjusting effective modular weights in a more general mirage mediation model?

Key findings

• The mirage mediation scenario reduces fine-tuning due to the $ M_3 < M_2 $ hierarchy at the GUT scale, which suppresses the gaugino contribution to the Z-boson mass.
• Fine-tuning decreases sharply around $ \alpha \approx 2 $, where the gaugino contribution to $ m_Z^2 $ vanishes due to cancellation in $ \delta m_Z^2 \sim 5.5 M_s^2 (\alpha - 1.1)(\alpha - 2.1) $.
• Despite this, regions with $ \Delta < 100-1000 $ are excluded by the LEP Higgs mass bound and the presence of tachyons in the soft masses at the GUT scale.
• The gravitino mass $ m_{3/2} $ sets the scale of soft masses, and fine-tuning increases rapidly with $ m_{3/2} $, especially in the gravity-dominated regime ($ \alpha \to \infty $).
• The model-independent prediction $ M_2 > M_3 $ at the GUT scale ensures a reduced sensitivity of $ m_Z $ to soft parameters, supporting lower fine-tuning.
• While simple mirage mediation does not fully solve the fine-tuning problem, more general models with tuned effective modular weights may achieve both low fine-tuning and consistency with physical constraints.