Couplings between QCD axion and photon from string compactification

TL;DR

This paper explores the coupling between QCD axions and photons derived from string theory compactifications, highlighting bounds, model dependencies, and a method to compute the coupling at high energy scales.

Contribution

It provides a detailed analysis of axion-photon couplings from string compactifications, including bounds and a new method for high-scale coupling calculation.

Findings

Derived a lower bound on the axion-photon coupling from string theory.

Identified conditions under which the bound does not apply in approximate models.

Presented a simple method to compute the high-scale axion-photon coupling.

Abstract

The QCD axion couplings of various invisible axion models are presented. In particular, the exact global symmetry U(1)$_{\rm PQ}$ in the superpotential is possible for the anomalous U(1) from string compactification, broken only by the gauge anomalies at one loop level, and is shown to have the resultant invisible axion coupling to photon, $c_{a\gamma\gamma}\ge \frac83-c_{a\gamma\gamma}^{\rm ch\,br}$ where $c_{a\gamma\gamma}^{\rm ch\,br}\simeq 2$. However, this bound is not applicable in approximate U(1)$_{\rm PQ}$ models with sufficiently suppressed U(1)$_{\rm PQ}$-breaking superpotential terms. We also present a simple method to obtain $c_{a\gamma\gamma}^0$ which is the value obtained above the electroweak scale.