[Paper Review] Moduli stabilization and the pattern of soft SUSY breaking terms

Kiwoon Choi|ArXiv.org|Nov 14, 2005

Logic, programming, and type systems8 citations

TL;DR

This paper investigates how moduli stabilization in string compactifications affects the pattern of soft supersymmetry-breaking terms in 4D effective supergravity, showing that perturbative Kähler corrections lead to moduli-mediated dominance, while non-perturbative superpotential effects induce a mixed moduli-anomaly mediation scenario. The key result is a hierarchical mirage messenger scale that leads to qualitatively distinct superparticle spectra, differing from mSUGRA, gauge, or pure anomaly mediation.

ABSTRACT

In string compactification preserving N=1 SUSY, moduli fields are plausible candidates for the messenger of SUSY breaking at low energy scales. In a scenario that moduli-mediated SUSY breaking is significant, the pattern of soft SUSY breaking terms depends crucially on how the light moduli with mass m \lesssim O(8π^2 m_{3/2}) are stabilized. We discuss the correspondence between the pattern of soft terms and the stabilization mechanism of light moduli within the framework of 4D effective supergravity which is generalized to include a SUSY-breaking uplifting potential which might be necessary to get the phenomenologically viable de-Sitter (or Minkowski) vacuum. In some special case, light moduli can be stabilized by controllably small perturbative corrections to the Kähler potential, yielding the soft terms dominated by the moduli-mediated contribution. In more generic situation, light moduli are stabilized by non-perturbative effects encoded in the superpotential and a quite different pattern of soft terms emerges: the anomaly-mediated soft terms become comparable to the moduli-mediated ones. Such mixed moduli-anomaly mediated soft terms lead to low energy superparticle masses qualitatively different from those of other mediation models such as mSUGRA scenario, gauge-mediation, and anomaly-mediation.

Motivation & Objective

• To understand how the stabilization mechanism of light moduli fields affects the pattern of soft supersymmetry-breaking terms in 4D effective supergravity.
• To identify conditions under which moduli-mediated or anomaly-mediated contributions dominate the soft terms in string compactifications.
• To explore how uplifting potentials, as in the KKLT construction, affect moduli stabilization and soft term generation in phenomenologically viable de-Sitter or Minkowski vacua.
• To determine whether flavor and CP violations can be naturally avoided in models with light moduli and mixed mediation.
• To establish a correspondence between the ratio of anomaly to moduli mediation and the resulting low-energy superparticle mass spectrum.

Proposed method

• Formulates a 4D effective supergravity framework generalized to include a SUSY-breaking uplifting potential, necessary for de-Sitter or Minkowski vacuum solutions.
• Analyzes moduli stabilization via perturbative corrections to the Kähler potential, which can stabilize light moduli with $ m_T \lesssim 8\pi^2 m_{3/2} $, leading to dominant moduli-mediated soft terms.
• Considers non-perturbative superpotential effects (e.g., gaugino condensation) for stabilizing light moduli, resulting in comparable contributions from moduli and anomaly mediation.
• Derives the soft terms using the supergravity Lagrangian with auxiliary components $ F^i $, computing $ m_{\text{soft}} $, $ A $-terms, and gaugino masses via renormalization group evolution.
• Introduces a mirage messenger scale $ M_{\text{mirage}} = (m_{3/2}/M_{\text{Pl}})^{\alpha/2} M_{\text{GUT}} $, which describes the effective scale of mixed mediation and cancels mass splittings from RG running.
• Uses running anomalous dimensions $ \gamma_I(\mu) $, gauge couplings $ g_a(\mu) $, and hypercharges $ Y_I $ to compute the full running of soft masses from $ M_{\text{GUT}} $ down to the TeV scale.

Experimental results

Research questions

• RQ1 How does the stabilization of light moduli via perturbative Kähler corrections affect the hierarchy and structure of soft SUSY-breaking terms?
• RQ2 What is the resulting pattern of soft terms when light moduli are stabilized by non-perturbative superpotential effects, such as gaugino condensation?
• RQ3 How does the ratio of anomaly-mediated to moduli-mediated contributions determine the low-energy superparticle mass spectrum?
• RQ4 Can the resulting soft terms preserve flavor and CP symmetries in the presence of light moduli and mixed mediation?
• RQ5 What is the physical significance of the mirage messenger scale in relating mixed moduli-anomaly mediation to pure moduli mediation?

Key findings

• When light moduli are stabilized by perturbative corrections to the Kähler potential, the soft terms are dominated by moduli mediation, with negligible anomaly-mediated contributions.
• In generic cases stabilized by non-perturbative superpotentials, the anomaly-mediated and moduli-mediated contributions to soft terms become comparable, leading to a mixed mediation scenario.
• The mixed moduli-anomaly mediation scenario can be described by an effective mirage messenger scale $ M_{\text{mirage}} = (m_{3/2}/M_{\text{Pl}})^{\alpha/2} M_{\text{GUT}} $, where $ \alpha $ controls the relative strength of the two contributions.
• For $ \alpha = 2 $, the mirage scale leads to nearly degenerate gaugino and sfermion masses at the TeV scale, canceling mass splittings from RG evolution.
• The resulting superparticle mass spectrum is qualitatively different from those in mSUGRA, gauge mediation, or pure anomaly mediation, especially in the 3rd generation squark and slepton masses.
• Flavor and CP violations are naturally avoided if matter fields have universal modular weights and the relative CP phases between $ F^i $ and $ F^C $ are removable via axion redefinition.