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Impact of chirality imbalance and nonlocal interactions on the QCD biased axionic domainwall interpretation of NANOGrav 15 year data

Ruotong Zhao, Zhao Zhang

Abstract

We investigate the influence of the chirality imbalance with local CP-breaking in hot QCD on the generation of a stochastic gravitational wave background (SGWB) sourced by the axion-like particle (ALP) domain-wall annihilation, induced by the QCD bias. Such a bias is quantified by the QCD topological susceptibility $χ_t$, and its dependence on the $θ$ angle and the chiral chemical potential $μ_5$ is investigated at temperatures near the QCD scale within a nonlocal Nambu-Jona-Lasinio (NJL) model. We find that, besides the small-$θ$ range, the axionic domain-wall interpretation of NANOGrav 15-year data on the nHz gravitational waves is still possible for a certain large-$θ$ range if $μ_5$ is large enough. We confirm that the peak of $|χ_t|$ at the critical temperature $T_c$ for the CP restoration at $θ=π$ exhibits a pronounced width compared to the local NJL result. Thus, for $θ$ at and around $π$, the QCD bias near $T_c$ can also produce a GW signal strength compatible with the NANOGrav 15-year data.

Impact of chirality imbalance and nonlocal interactions on the QCD biased axionic domainwall interpretation of NANOGrav 15 year data

Abstract

We investigate the influence of the chirality imbalance with local CP-breaking in hot QCD on the generation of a stochastic gravitational wave background (SGWB) sourced by the axion-like particle (ALP) domain-wall annihilation, induced by the QCD bias. Such a bias is quantified by the QCD topological susceptibility , and its dependence on the angle and the chiral chemical potential is investigated at temperatures near the QCD scale within a nonlocal Nambu-Jona-Lasinio (NJL) model. We find that, besides the small- range, the axionic domain-wall interpretation of NANOGrav 15-year data on the nHz gravitational waves is still possible for a certain large- range if is large enough. We confirm that the peak of at the critical temperature for the CP restoration at exhibits a pronounced width compared to the local NJL result. Thus, for at and around , the QCD bias near can also produce a GW signal strength compatible with the NANOGrav 15-year data.
Paper Structure (10 sections, 44 equations, 14 figures, 1 table)

This paper contains 10 sections, 44 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Axionic domain walls with QCD bias
  3. Axionic domain walls and QCD-bias potential
  4. GWs from DW network collapse
  5. NNJL model analysis of $\chi_{\text{t}}$ and axionic DW energy density at nonzero $\theta$ and $\mu_5$
  6. The formalism
  7. The model parameters
  8. Evaluation of topological susceptibility in NNJL
  9. Numerical results and discussion
  10. Conclusions

Figures (14)

  • Figure 1: Normalized scalar and pseudoscalar condensates versus temperature for different $\mu_5$ and $\theta$. The data are obtained using NNJL I.
  • Figure 2: Absolute value of topological susceptibility $\chi_{\text{t}}$ versus temperature under the same conditions as that in Fig. \ref{['fg:condensates1']}.
  • Figure 3: The signal strength $\alpha_*(T_*,\theta,\mu_5)$ versus the axionic DM annihilation temperature $T_*$ for different $\theta$ at $\mu_5 = 0~\text{MeV}$, calculated within NNJL I. The lines for $0\leq\theta<0.5\pi$ ($0.5\pi<\theta\leq\pi$) are shown in the left (right) panel. The two purple lines correspond to the 2$\sigma$ contour from Ref.NANOGrav:2023hvm, with the region inside denoting the allowed parameter space for the nHz GWs. Left panel: $0\leq\theta\leq 0.34\pi$; right panel: $0.98\pi\leq\theta\leq \pi$ can access the two-line regime.
  • Figure 4: Same as in Fig. \ref{['fg:signal1_0']}, but for $\mu_5 = 300~\text{MeV}$. Left panel: $0\leq\theta\leq 0.39\pi$; right panel: $0.68\pi\leq\theta\leq 0.81\pi$ and $0.98\pi\leq\theta\leq \pi$ can access the two-line regime.
  • Figure 5: Same as in Fig. \ref{['fg:signal1_0']}, but for $\mu_5 = 400~\text{MeV}$. Left panel: $0\leq\theta\leq 0.4\pi$; right panel: $0.63\pi\leq\theta\leq 0.86\pi$ and $0.98\pi\leq\theta\leq \pi$ can access the two-line regime.
  • ...and 9 more figures