Moduli Stabilisation and the Statistics of Axion Physics in the Landscape

TL;DR

This paper investigates the distribution of axion properties in the string landscape, revealing that decay constants and masses follow a logarithmic distribution, which impacts the likelihood of realizing the QCD axion with natural parameters.

Contribution

It provides a detailed statistical analysis of axion properties in type IIB flux compactifications, emphasizing the importance of moduli stabilization and revealing a logarithmic distribution of key axion parameters.

Findings

Most closed string axions are ultra-light particles.

The distribution of decay constants and masses is logarithmic.

The likelihood of a QCD axion with natural parameters is only logarithmically suppressed.

Abstract

String theory realisations of the QCD axion are often said to belong to the anthropic window where the decay constant is around the GUT scale and the initial misalignment angle has to be tuned close to zero. In this paper we revisit this statement by studying the statistics of axion physics in the string landscape. We take moduli stabilisation properly into account since the stabilisation of the saxions is crucial to determine the physical properties of the corresponding axionic partners. We focus on the model-independent case of closed string axions in type IIB flux compactifications and find that their decay constants and mass spectrum feature a logarithmic, instead of a power-law, distribution. In the regime where the effective field theory is under control, most of these closed string axions are ultra-light axion-like particles, while axions associated to blow-up modes can naturally play the role of the QCD axion. Hence, the number of type IIB flux vacua with a closed string QCD axion with an intermediate scale decay constant and a natural value of the misalignment angle is only logarithmically suppressed. In a recent paper we found that this correlates also with a logarithmic distribution of the supersymmetry breaking scale, providing the intriguing indication that most, if not all, of the phenomenologically interesting quantities in the string landscape might feature a logarithmic distribution.