QCD Axion Dark Matter in String Theory: Haloscopes and Helioscopes as Probes of the Landscape

Laboratory experiments have the capacity to detect the QCD axion in the next decade, and precisely measure its mass, if it composes the majority of the dark matter. In type IIB string theory on Calabi-Yau threefolds in the geometric regime, the QCD axion mass, mₐ, is strongly correlated with the topological Hodge number h1,1. We compute mₐ in a scan of 185,965 compactifications of type IIB string theory on toric hypersurface Calabi-Yau threefolds. We compute the range of h1,1 probed by different experiments under the condition that the QCD axion can provide the observed dark matter density with minimal fine-tuning. Taking the experiments DMRadio, ADMX, MADMAX, and BREAD as indicative on different mass ranges, the h1,1 distributions peak near h1,1=24.9, \ 65.4, \ 196.8, and $310.9,$ respectively. We furthermore conclude that, without severe fine tuning, detection of the QCD axion as dark matter at any mass disfavours 80% of models with h1,1 =491, which is thought to have the most known Calabi-Yau threefolds. Measurement of the solar axion mass with IAXO is the dominant probe of all models with h1,1 250. This study demonstrates the immense importance of axion detection in experimentally constraining the string landscape.