Gaugino and Scalar Masses in the Landscape

TL;DR

The paper proves that in IIB string landscapes with moduli stabilised nonperturbatively, gaugino masses are generically suppressed relative to the gravitino mass by a factor of order $1/\ln(m_{3/2})$, a result extending KKLT to multi-moduli and large-volume scenarios. It provides an explicit large-volume calculation for a two-moduli Calabi–Yau, showing $|M_b| \approx m_{3/2}$ and $|M_s| \approx \frac{m_{3/2}}{\ln(m_{3/2})}$, along with a boosted small modulus mass $m_{\tau_s} \gtrsim 2\ln(m_{3/2})\,m_{3/2}$. The work also shows that soft scalar masses in LVS are generically not suppressed and are approximately universal, with fractional non-universalities $\epsilon_i \sim \frac{1}{\ln(m_{3/2})^2} \sim 10^{-3}$, suggesting flavour-universal gravity mediation with a mixed anomaly contribution for gauginos. Overall, the results indicate phenomenologically appealing scenarios with an intermediate string scale and natural flavour universality, while cautioning that not all Kähler moduli can be stabilised nonperturbatively in realistic setups.

Abstract

In this letter we demonstrate the genericity of suppressed gaugino masses M_a \sim m_{3/2}/ln(M_P/m_{3/2}) in the IIB string landscape, by showing that this relation holds for D7-brane gauginos whenever the associated modulus is stabilised by nonperturbative effects. Although m_{3/2} and M_a take many different values across the landscape, the above small mass hierarchy is maintained. We show that it is valid for models with an arbitrary number of moduli and applies to both the KKLT and exponentially large volume approaches to Kahler moduli stabilisation. In the latter case we explicitly calculate gaugino and moduli masses for compactifications on the two-modulus Calabi-Yau P^4_[1,1,1,6,9]. In the large-volume scenario we also show that soft scalar masses are approximately universal with m_i^2 \sim m_{3/2}^2 (1 + ε_i), with the non-universality parametrised by ε_i \sim 1/ln (M_P/m_{3/2})^2 \sim 1/1000. We briefly discuss possible phenomenological implications of our results.