Moduli stabilization and the pattern of soft SUSY breaking terms

TL;DR

This work investigates how moduli stabilization in string-derived $N=1$ SUGRA controls the pattern of soft SUSY-breaking terms, focusing on light moduli with $m_T \lesssim 8\pi^2 m_{3/2}$. It introduces a 4D effective SUGRA framework with an uplifting sector to realize viable vacua and analyzes two stabilization routes: perturbative Kähler corrections and KKLT-type non-perturbative superpotential, showing that the relative strength of modulus- and anomaly-mediated contributions yields qualitatively different low-energy spectra. In KKLT-like setups, anomaly mediation can be comparable to modulus mediation, producing a mixed pattern termed mirage mediation, characterized by a mirage scale $M_{\rm mirage}$ where RG effects cancel; perturbative Kähler stabilization tends to favor modulus mediation with suppressed anomaly contributions. The resulting TeV-scale spectra are distinct from mSUGRA, gauge mediation, and pure anomaly mediation and can naturally suppress flavor and CP violations if modular weights are universal, providing a concrete link between high-scale stabilization mechanisms and observable collider phenomenology.

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.

Figures (2)

• Figure 1: The pattern of superparticle masses at $M_{SUSY}=1$ TeV for the entire range of the anomaly to moduli mediation ratio $\alpha$. Note that the sign convention of the gaugino masses for $0\leq \tan(\alpha/4)\leq \pi/2$ is different from the convention for $\pi/2\leq \tan(\alpha/4)\leq \pi$. Here we choose $a_{IJK}=3$ and $n_I\equiv 1-c_I=0$. The shaded region indicates the range $2/3\leq \alpha\leq 2$ and the short-dashed curves denote the 3rd generation squarks/sleptons.
• Figure 2: Superparticle masses at $M_{SUSY}=1$ TeV for $0\leq \alpha\leq 3$. The shaded regions correspond to $\alpha=2/3, 1, 2$, taking into account $10\%$ uncertainty. Again the short-dashed curves denote the 3rd generation squarks/sleptons.