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The nano-hertz and milli-hertz stochastic gravitational waves in the minimal clockwork axion model

Xiangwei Yin, Cheng-Wei Chiang, Bo-Qiang Lu, Tianjun Li

Abstract

The clockwork framework can realize TeV-scale $U(1)_{PQ}$ symmetry breaking while generating a large axion decay constant \(f_a\). We propose a minimal clockwork axion model with three scalar fields, in which two domain walls (DWs) have non-zero tension. The DW associated with one of the fields is formed following the Peccei-Quinn (PQ) symmetry breaking and subsequently collapses due to the potential bias induced by the QCD instanton. The nano-hertz stochastic gravitational waves (GWs) generated from this DW annihilation can be probed by Pulsar Timing Arrays experiments. In addition, the DW related to the other field is annihilated by a bias potential originating from higher-dimensional operators, producing a significant GW signal with a peak frequency around \(9.41\times10^{-5}\) Hz, which can be detected by the LISA, Taiji, and TianQin experiments. Constraints on the model from SN1987, dark matter overproduction, Big Bang Nucleosynthesis, cosmic microwave background, and primordial black holes have been considered. The relic density of QCD axion dark matter can be explained through the misalignment mechanism.

The nano-hertz and milli-hertz stochastic gravitational waves in the minimal clockwork axion model

Abstract

The clockwork framework can realize TeV-scale symmetry breaking while generating a large axion decay constant . We propose a minimal clockwork axion model with three scalar fields, in which two domain walls (DWs) have non-zero tension. The DW associated with one of the fields is formed following the Peccei-Quinn (PQ) symmetry breaking and subsequently collapses due to the potential bias induced by the QCD instanton. The nano-hertz stochastic gravitational waves (GWs) generated from this DW annihilation can be probed by Pulsar Timing Arrays experiments. In addition, the DW related to the other field is annihilated by a bias potential originating from higher-dimensional operators, producing a significant GW signal with a peak frequency around Hz, which can be detected by the LISA, Taiji, and TianQin experiments. Constraints on the model from SN1987, dark matter overproduction, Big Bang Nucleosynthesis, cosmic microwave background, and primordial black holes have been considered. The relic density of QCD axion dark matter can be explained through the misalignment mechanism.

Paper Structure

This paper contains 12 sections, 24 equations, 7 figures.

Table of Contents

  1. Introduction
  2. The minimal clockwork axion model
  3. Gravitational waves and experimental constraints
  4. GWs from DW annihilation
  5. Experimental constraints
  6. Data analysis and results
  7. Explanation of NG15 data by $A_2$-wall annihilation
  8. Consequences of $A_1$-wall
  9. conclusion
  10. An alternative scenario
  11. Explanation of NG15 data by $A_1$-wall annihilation
  12. Consequences of $A_{2}$-wall

Figures (7)

  • Figure 1: The GW signal spectrum versus frequency in the minimal clockwork axion model, originating from the $A_2$-wall annihilation. The yellow and green regions correspond to the $1 \sigma$ and $2 \sigma$ bounds derived from fitting the NG15 data, respectively. The blue violins give the posterior distributions of the free GW spectrum obtained from the NG15 data.
  • Figure 2: Constraints from NG15 NANOGrav:2023gor on the parameters of GWs generated by $A_{2}$-wall annihilation in the minimal clockwork axion model. The best-fit values are $f_{2} = 10^{2.3} \, \mathrm{TeV}$ and $\epsilon = 10^{-3}$.
  • Figure 3: Annihilation temperature $T_{\mathrm{ann}}^{\prime}$ and peak frequency $\nu_{\mathrm{peak}}$ as a function of bias potential. We use $\sigma_{w}\simeq8m_{A_1}f_1^2$, with $\epsilon=10^{-3}$, $f_1=3^{5}f_{2}$, and $f_2=10^{2.3} \text{TeV}$.
  • Figure 4: Two GW signals in the minimal clockwork axion model. The red ($\epsilon = 10^{-3}$ and $f_2 = 10^{2.3}\,\text{TeV}$) and blue ($\epsilon = 10^{-3}$, $f_1 = 3^5 f_2$, and $V_{\text{bias}}^{1/4} = 1200\,\text{GeV}$) lines represent the GW signals induced by the annihilation of the $A_2$-wall and the $A_1$-wall, respectively. In the plot, we also superimpose the sensitivity curves of SKA 5yr Janssen:2014dka, AION-km Badurina:2019hst, AEDGE AEDGE:2019nxb, AEDGE+, LISA Caprini:2019egz, LIGO O3 Shoemaker:2019bqt, Einstein telescope (ET) Maggiore:2019uih, Taiji Hu:2017mdeRuan:2018tsw, and TianQin TianQin:2015yphTianQin:2020hidLiang:2021bde experiments.
  • Figure 5: The GW signal versus frequency in the minimal clockwork model, originating from the $A_1$-wall annihilation. The yellow and green regions correspond to the $1 \sigma$ and $2 \sigma$ bounds derived from fitting the NG15 data, respectively. The blue violins represent the posterior distributions of the free GW spectrum obtained from the NG15 data.
  • ...and 2 more figures