Graviton energy spectra arising from the KSVZ axion model

TL;DR

This work investigates ultra-high-frequency gravitational waves as a window into the ultraviolet origin of the QCD axion, focusing on the KSVZ framework with a heavy saxion and vector-like quark. By computing graviton bremsstrahlung during decays of these heavy states in the early Universe, the authors derive a stochastic GW spectrum whose peak lies around $f_{\rm peak} \sim 10^{12}$ Hz and depends on $m_s$, $m_Q$, $y_Q$, and $y_{Qq}$, with distinct signatures arising if an early matter-dominated era occurs. The spectrum includes contributions from saxion decays to VLQs and Higgses as well as VLQ decays, and shows potential for distinguishing KSVZ UV physics from other axion realizations like DFSZ. The results provide concrete targets for next-generation ultra-high-frequency GW experiments and emphasize multi-messenger synergy with direct axion searches to infer the UV origin of the axion.

Abstract

Axion, the goldstone boson arising from the spontaneous breaking of a global $U(1)$ Peccei-Quinn symmetry, provides a dynamical solution to the strong CP problem and is an excellent dark matter candidate. Various experiments are designed to search for the axion, however no confirmative signal has been observed. On the other hand, there are also hypothetical heavy particles in axion models, such as the heavy scalar $s$, which is the CP-even component of the complex scalar that carries $U(1)_{PQ}$ charge, and the vector-like heavy quark (VLQ) in the Kim-Shifman-Vainshtein-Zakharov~(KSVZ) axion model. Studying signals induced by them are helpful for axion searches. In this paper, we calculate the graviton bremsstrahlung energy spectrum arising from the decay of the heavy scalar or VLQ in the KSVZ model. The result shows that these heavy particles can emit ultrahigh-frequency gravitational waves (GWs), with the peak frequency depending on the model's parameter inputs. In addition, the graviton spectrum is distinguished from the thermal GW background at high frequencies if there is an early matter-dominated era induced by these heavy particles. Future measurements of ultrahigh-frequency GWs may provide indirect evidence for the KSVZ axion.

Figures (5)

• Figure 1: The evolution of the energy densities of the radiation (Red), $s$ (Blue) and $Q$ (Green), in the scenario where $s$ mainly decays to VLQs. We have set $m_s=f_a = 10^{12} \text{ GeV}$, $y_Q = 10^{-6}$, and $y_{Qq} = 10^{-7}$.
• Figure 2: Feynman diagrams for graviton bremsstrahlung processes in the decay of the heavy scalar.
• Figure 3: GW spectra from graviton bremsstrahlung in the $s\to Q \bar{Q} g$ decay channel. Left Panel: Dependence of the GW spectrum on $m_s$ and $y_Q$. Red and blue curves correspond to $m_s = 10^{12}$ GeV and $10^{11}$ GeV, respectively. Solid and dashed lines represent coupling strengths of $y_Q = 10^{-5}$ and $10^{-6}$, respectively. Right Panel: Comparison between the GW spectra from scalar decay (solid lines) and the thermal plasma background (dashed lines) for reheating temperatures $T_{\rm rh} = 10^{16}$ GeV and $T_{\rm rh} = 10^{13}$ GeV. In the $m_s = 10^{12}$ GeV and $y_Q = 10^{-6}$ scenario (red), an early matter-dominated phase is realized, allowing the scalar-induced GW signal to be clearly distinguished from the thermal GW background at high frequencies. Conversely, for $m_s = 10^{11}$ GeV and $y_Q = 10^{-5}$ (blue), no matter-dominated phase occurs; the high-frequency GW signal is overwhelmed by the thermal plasma contribution, leaving distinguishable spectrum in the low-frequency regime.
• Figure 4: Feynman diagrams for graviton bremsstrahlung in the decay of the vector-like quark.
• Figure 5: Gravitational wave spectra arising from graviton bremsstrahlung in VLQ decays. Black dashed line is the CGWB for reheating temperatures $T_{\rm rh} = 10^{16}$ GeV and $T_{\rm rh} = 10^{13}$ GeV. Colored dashed lines (red: $m_Q=10^7$ GeV, $y_{Qq}=10^{-6}$; blue: $m_Q=10^7$ GeV, $y_{Qq}=10^{-7}$) represent scenarios where $s$ predominantly decay into VLQs. In these cases, the small coupling $y_Q$ required to distinguish the signal from the CGWB necessitates relatively small VLQ masses, leading to a suppressed GW spectrum. Solid lines (red: $m_Q=10^{12}$ GeV, $y_{Qq}=10^{-5}$; blue: $m_Q=10^{12}$ GeV, $y_{Qq}=10^{-6}$) correspond to scenarios where $s\to Q\bar{Q}$ is forbidden, which permit larger VLQ masses. These high-frequency signals are clearly distinguishable from the CGWB, provided that the VLQs trigger an early matter-dominated era.