Heterotic String Theory Suggests a QCD Axion Near 0.5 neV

TL;DR

This paper demonstrates that heterotic string theory predicts a lower bound on the QCD axion mass around 0.5 neV, with implications for future detection experiments and cosmological models.

Contribution

It provides explicit calculations of the QCD axion mass in heterotic compactifications and establishes a narrow mass window relevant for experiments.

Findings

QCD axion mass is bounded from below by ~0.5 neV in heterotic models.

Most compactifications yield axion masses in the range 0.5 to 0.8 neV.

Heavy axions decay before big bang nucleosynthesis and support leptogenesis.

Abstract

We show that in heterotic string theory -- and dual corners of the landscape including Type I string theory -- the QCD axion mass is bounded from below by $m_a \gtrsim 0.5$ neV, a direct consequence of the model-independent axion whose decay constant is fixed by the grand unified theory (GUT) gauge coupling. We explicitly compute the mass of the QCD axion in an ensemble of heterotic compactifications on Calabi-Yau hypersurfaces of toric varieties sampled from the Kreuzer-Skarke (KS) ensemble, as well as on complete intersection Calabi-Yau manifolds. We then perform an extensive search over the K\"ahler moduli space of KS compactifications with up to $11$ axions -- the maximum we identify as consistent with unification in our sample. We establish that for all but a handful of manifolds the QCD axion mass is precisely the model-independent value, lying in $[0.5, 0.8]$ neV, depending on the GUT gauge coupling. This window should be a high-priority target for future lumped-element detectors such as DMRadio-GUT. We show that the heavy axion population in our heterotic ensemble generically decays before big bang nucleosynthesis and can naturally accommodate leptogenesis, unlike in Type IIB axiverse constructions.