Soft SUSY Breaking Terms for Chiral Matter in IIB String Compactifications

TL;DR

The paper computes soft SUSY-breaking terms for chiral D7 matter in IIB Calabi–Yau flux compactifications with full moduli stabilization, focusing on KKLT and Large Volume scenarios. Using the chiral bifundamental matter metrics from CCQPaper, it demonstrates a simple, flavor-universal soft-term structure in the large-volume regime, with gaugino masses $M_i = F^s/(2\tau_s)$ and scalar masses tied to a universal factor $m_{\alpha}^2 \sim M_i^2/3$ for the minimal model ($\lambda=1/3$), while anomaly-mediated contributions are subdominant due to no-scale cancellations. The analysis shows soft terms are suppressed relative to the gravitino mass by $\log(M_P/m_{3/2})$, and includes a phenomenological RG running study that yields regions with neutralino LSP compatible with current constraints, illustrating viable low-energy spectra. It also contrasts the large-volume results with the one-modulus KKLT case, where different modular weights (notably $n_{\lambda}=2/3$) can alter the soft-term pattern and confronts potential cosmological and model-building challenges. Overall, the work provides a concrete, flavour-universal soft-term framework for chiral D7 matter in IIB flux models, with clear phenomenological implications and avenues for refinement beyond the dilute-flux approximation.

Abstract

This paper develops the computation of soft supersymmetry breaking terms for chiral D7 matter fields in IIB Calabi-Yau flux compactifications with stabilised moduli. We determine explicit expressions for soft terms for the single-modulus KKLT scenario and the multiple-moduli large volume scenario. In particular we use the chiral matter metrics for Calabi-Yau backgrounds recently computed in hep-th/0609180. These differ from the better understood metrics for non-chiral matter and therefore give a different structure of soft terms. The soft terms take a simple form depending explicitly on the modular weights of the corresponding matter fields. For the large-volume case we find that in the simplest D7 brane configuration, scalar masses, gaugino masses and A-terms are very similar to the dilaton-dominated scenario. Although all soft masses are suppressed by ln(M_P/m_{3/2}) compared to the gravitino mass, the anomaly-mediated contributions do not compete, being doubly suppressed and thus subdominant to the gravity-mediated tree-level terms. Soft terms are flavour-universal to leading order in an expansion in inverse Kahler moduli. They also do not introduce extra CP violating phases to the effective action. We argue that soft term flavour universality should be a property of the large-volume compactifications, and more generally IIB flux models, in which flavour is determined by the complex structure moduli while supersymmetry is broken by the Kahler moduli. For the simplest large-volume case we run the soft terms to low energies and present some sample spectra and a basic phenomenological analysis.

Figures (7)

• Figure 1: Contour plots of (a) $BR(b\to s\gamma)$ (b) $\delta a_{\mu}$ and (c) $\Omega h^2$ on $\tan\beta$ and $M$, for $\mu>0$ and $m_s\sim 10^{11}$ GeV. $2\sigma$ bounds are used. The blue region in (d) denotes that the LSP is stau, the white that it is neutralino.
• Figure 2: Contour plots of (a) $BR(b\to s\gamma)$ (b) $\delta a_{\mu}$ and (c) $\Omega h^2$ on $\tan\beta$ and $M$ for $\mu<0$ and $m_s\sim 10^{11}$ GeV. Note that $3\sigma$ bounds are used. The blue region in (d) denotes that the LSP is stau, the white that it is neutralino.
• Figure 3: Experimental constraints on the parameter space: If a neutralino LSP is to account for the CDM part of the Universe, then the allowed regions $0.085 < \Omega_{\tilde{\chi}_1^0}h^2 < 0.125$ for (left) $\mu>0$ and $0.075 < \Omega_{\tilde{\chi}_1^0}h^2 < 0.135$ for (right) $\mu<0$ are bounded by the red contours. The bounds are at $2\sigma$ and $3\sigma$ respectively. The white region represents non neutralino (stau) LSP points. The blue and pink curves respectively are the $\delta a_\mu$ and $BR(b\to s\gamma)$ bounds. The cyan curve is the 111 GeV bound on the Higgs mass.
• Figure 4: Contour plots of $\delta a_{\mu}$, $BR(b\to s\gamma)$ and $\Omega h^2$ on $\tan\beta$ and $M$ for (a) $\mu>0$ and (b) $\mu<0$ and $m_s\sim 10^{11}$ GeV. $2\sigma$ bounds are used for $\mu>0$ while $3\sigma$ ones are used for $\mu<0.$
• Figure 5: The ratio $B/(-4M/3)$ over a range of values of $\tan\beta$ for (a) $\mu>0$ and (b) $\mu<0$ and $m_s\sim 10^{11}$ GeV.