Phenomenology of Mixed Modulus-Anomaly Mediation in Fluxed String Compactifications and Brane Models

TL;DR

This work addresses how soft SUSY-breaking terms arise in string/brane scenarios where light moduli are stabilized by nonperturbative dynamics and lifted by sequestered uplifting, and what this implies for low-energy sparticle spectra. It develops a mixed modulus-anomaly mediation framework, parameterized by $\alpha = m_{3/2}/[M_0\ln(M_{Pl}/m_{3/2})]$, and derives the corresponding soft terms at $M_{GUT}$, then analyzes RG evolution to $M_{SUSY}$ to map phenomenology across $\alpha$ values. The key contributions include explicit expressions for $M_a$, $A_{ijk}$, and $m_i^2$, the interpretation of a mirage messenger scale $\Lambda_{mirage} \sim (m_{3/2}/M_{Pl})^{\alpha/2} M_{GUT}$, and a detailed exploration of collider-scale patterns for $\alpha \approx 1$ and $\alpha \approx 2$, including EW breaking and LSP composition. This framework links concrete string-inspired stabilization and uplifting to testable TeV-scale spectra, offering guidance for collider searches and dark matter scenarios compatible with mixed mediation.

Abstract

In some string compactifications, for instance the recently proposed KKLT set-up, light moduli are stabilized by nonperturbative effects at supersymmetric AdS vacuum which is lifted to a dS vacuum by supersymmetry breaking uplifting potential. In such models, soft supersymmetry breaking terms are determined by a specific mixed modulus-anomaly mediation in which the two mediations typically give comparable contributions to soft parameters. Similar pattern of soft terms can arise also in brane models to stabilize the radion by nonperturbative effects. We examine some phenomenological consequences of this mixed modulus-anomaly mediation, including the pattern of low energy sparticle spectrum and the possibility of electroweak symmetry breaking. It is noted that adding the anomaly-mediated contributions at $M_{GUT}$ amounts to replacing the messenger scale of the modulus mediation by a mirage messenger scale $(m_{3/2}/M_{Pl})^{α/2}M_{GUT}$ where $α=m_{3/2}/[M_0\ln(M_{Pl}/m_{3/2})]$ for $M_0$ denoting the modulus-mediated contribution to the gaugino mass at $M_{GUT}$. The minimal KKLT set-up predicts $α=1$. As a consequence, for $α={\cal O}(1)$, the model can lead to a highly distinctive pattern of sparticle masses at TeV scale, particularly when $α= 2$.

Figures (4)

• Figure 1: Sparticle mass spectrum (relative ratios) at $M_{SUSY}=1$ TeV for the entire range of the anomaly to modulus ratio $\alpha=m_{3/2}/[M_0\ln(M_{Pl}/m_{3/2})]$. Here $M_0=F^T/(T+T^*)$ and $m_{3/2} =F^C/C_0$. The shaded region indicates the range $2/3\leq \alpha\leq 2$ and the short-dashed curves denote the 3rd generation squarks/sleptons. Note that the sign convention of the gaugino masses (and $A_{ijk}$) for $0\leq \tan(\alpha/4)\leq \pi/2$ is different from the convention for $\pi/2\leq \tan(\alpha/4)\leq \pi$.
• Figure 2: Sparticle mass spectrum at $M_{SUSY}=1$ TeV for $0\leq \alpha\leq 3$. The shaded regions correspond to the moduli Kähler and superpotential (2.3) and the uplifting potential (2.13) with $n_P=-1, 0, 1$ ($\alpha=2/3, 1, 2$), taking into account $10\%$ uncertainty. Again the short-dashed curves denote the 3rd generation sfermions.
• Figure 3: The behavior of the Higgsino mass parameter $\mu$. The shaded region is same as in Fig.2. The dashed (thin--solid) curve corresponds to $M_Z=0.3 M_0$ ($M_0/M_Z\rightarrow \infty$).
• Figure 4: A model for unified soft parameters at $M_{SUSY}$ for $\alpha=2$. We choose $n_{q,u,d,l,e}=1/2$ and $n_{H_1, H_2}=1$ to obtain $a_{ijk}=c_i+c_j+c_k=1$. A little hierarchy between the Higgs boson masses and the sparticle masses for $\alpha=2$ is protected at 1-loop level. Note that the results on $\mu/M_0$ and $B/M_0$ at $\alpha\approx 2$ have an uncertainty of ${\cal O}(10^{-1})$ due to the threshold corrections of ${\cal O}(M_0^2/8\pi^2)$ to the Higgs mass-squares at $M_{GUT}$.