Toward the Effective Light and Heavy QCD Axion Scenarios

TL;DR

This paper addresses how the QCD axion mass and decay constant parameters map onto viable light and heavy axion scenarios within an axiverse containing multiple ALPs. It adopts a two-axion toy model with definitions $\zeta=m_{A}/m_{a,0}$ and $\eta=f_{A}/f_a$, analyzes the temperature-dependent level-crossing through $\Delta m$, $\Delta m_\times$, and $T_\times$, and generalizes to $N$ ALPs to derive hierarchical bounds. The key finding is that axion mass ratios exhibit similar behavior in both scenarios, while decay-constant ratios are opposite: $0<\zeta\lesssim\tfrac{1}{2}$ with $0<\eta\ll 1$ for the light case and $0<\zeta\lesssim\tfrac{1}{2}$ with $\eta\gg 1$ for the heavy case, with $\langle\Delta m_\times\rangle$ largely independent of $\zeta$. These results are extended to multi-axion configurations, yielding hierarchical constraints $\zeta_i\lesssim(\tfrac{1}{2})^{N-i+1}$ and corresponding $\eta_i$ regimes, providing quantitative guidance for maximal mixing and axion cosmology in string-inspired models.

Abstract

In this work, we investigate the effective parameter space associated with the axion mass and the axion decay constant in both the light and heavy QCD axion scenarios. We initiate our discussion by considering the simplest case of two axions, quantitatively analyzing the parameter space in these two distinct scenarios. We find that the axion mass ratios exhibit a high degree of similarity in these two situations. In contrast, the ratios of axion decay constants display a complete opposition. Furthermore, we generalize our conclusions to encompass the case of multiple axions.

Figures (6)

• Figure 1: Left panel: The distribution of the delta mass eigenvalue $\Delta m$ with different values of the parameter $\zeta$. Here we set $\eta=0.3$. The red, blue, and purple solid lines represent $\zeta=0.1$, 0.01, and 0.001, respectively. Right panel: The distribution of the delta mass eigenvalue $\Delta m$ with different values of the parameter $\eta$. Here we set $\zeta=0.01$. The red, blue, and purple solid lines represent $\eta=0.5$, 0.3, and 0.08, respectively. In these panels, we set $f_a=10^{12}\,{\rm GeV}$.
• Figure 2: Left panel: The delta mass eigenvalue at level crossing $\Delta m_\times$ as a function of the parameter $\zeta$. Here we set $\eta=0.3$. Right panel: The delta mass eigenvalue at level crossing $\Delta m_\times$ as a function of the parameter $\eta$. Here we set $\zeta=0.01$.
• Figure 3: Left panel: The distribution of the delta mass eigenvalue at level crossing $\log_{10}(\Delta m_\times)$ in the $\{\zeta, \eta\}$ parameter plane. Right panel: The distribution of the normalized delta mass eigenvalue at level crossing $\log_{10}(\langle\Delta m_\times\rangle)$ in the $\{\zeta, \eta\}$ parameter plane. Notice that in these panels $\zeta\neq 1$ and $\eta\neq 1$.
• Figure 4: Same as the right panel of figure \ref{['fig_deltam']} but for larger values of the parameter $\zeta$. Left panel: We have $\Delta m|_{T\to 0}=\Delta m|_{T\to +\infty}$ with $\zeta=0.5$. Right panel: We have $\Delta m|_{T\to 0}<\Delta m|_{T\to +\infty}$ with $\zeta=0.75$. The red, blue, and purple solid lines represent $\eta=0.5$, 0.3, and 0.08, respectively.
• Figure 5: Same as figure \ref{['fig_deltam']} but for the heavy QCD axion scenario. Left panel: The distribution of the delta mass eigenvalue $\Delta m$ with different values of the parameter $\zeta$. Here we set $\eta=5$. The red, blue, and purple solid lines represent $\zeta=0.1$, 0.01, and 0.001, respectively. Right panel: The distribution of the delta mass eigenvalue $\Delta m$ with different values of the parameter $\eta$. Here we set $\zeta=0.01$. The red, blue, and purple solid lines represent $\eta=2$, 5, and 12.5, respectively. We set $f_a=10^{12}\,{\rm GeV}$.