Ultralight axion in supersymmetry and strings and cosmology at small scales

Dynamical mechanisms to generate an ultralight axion of mass $\sim {10}^{-21}–{10}^{-22}\mathrm{eV}$ in supergravity and strings are discussed. An ultralight particle of this mass provides a candidate for dark matter that may play a role for cosmology at scales of 10 kpc or less. An effective operator approach for the axion mass provides a general framework for models of ultralight axions, and in one case recovers the scale ${10}^{-21}–{10}^{-22}\mathrm{eV}$ as the electroweak scale times the square of the hierarchy with an $O(1)$ Wilson coefficient. We discuss several classes of models realizing this framework where an ultralight axion of the necessary size can be generated. In one class of supersymmetric models an ultralight axion is generated by instanton-like effects. In the second class higher-dimensional operators involving couplings of Higgs, standard model singlets, and axion fields naturally lead to an ultralight axion. Further, for the class of models considered the hierarchy between the ultralight scale and the weak scale is maintained. We also discuss the generation of an ultralight scale within string-based models. In the single-modulus Kachru-Kallosh-Linde-Trivedi moduli stabilization scheme an ultralight axion would require an ultralow weak scale. However, within the large volume scenario, the desired hierarchy between the axion scale and the weak scale is achieved. A general analysis of couplings of Higgs fields to instantons within the string framework is discussed and it is shown that the condition necessary for achieving such couplings is the existence of vector-like zero modes of the instanton. Some of the phenomenological aspects of these models are also discussed.

Figure 1

Axion relic abundance and mass as a function of axion decay constant $F$ and Wilson coefficient $A$. The dashed contours denote the axion relic abundance and are labeled by ${\log }_{10}({\mathrm{\Omega }}_{ax}{h}^2)$; the $-1$ contour is the observed relic abundance. The blue, orange, and green bands are mass regions ${10}^{-23}\mathrm{eV}\le m_a\le {10}^{-22}\mathrm{eV}$, ${10}^{-22}\mathrm{eV}\le m_a\le {10}^{-21}\mathrm{eV}$, and ${10}^{-21}\mathrm{eV}\le m_a\le {10}^{-20}\mathrm{eV}$, respectively, so that the $m_a={10}^{-22}\mathrm{eV}$ line is the boundary between the blue and orange bands. Left: The $n=3$ case, which accommodates the relic abundance and mass by using the electroweak hierarchy. Right: The $n=0$ case, which accommodates these solely with instanton suppression.