Gaugino and scalar masses in the landscape

In this letter we demonstrate the genericity of suppressed gaugino masses M_a ∼ m_3/2/ln (M_Planck/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 Kähler moduli stabilisation. In the latter case we explicitly calculate gaugino and moduli masses for compactifications on the two-modulus Calabi-Yau ⁴ _[1,1,1,6,9]. In the large-volume scenario we also show that soft scalar masses are approximately universal with m_i² ∼ m_3/2²(1+_i), with the non-universality parametrised by _i ∼ 1/ln (M_P/m_3/2) ² ∼ (1/1000). We briefly discuss possible phenomenological implications of our results.