[Paper Review] QCD-Collapsed Domain Walls: QCD Phase Transition and Gravitational Wave Spectroscopy

Y. Bai, Ting-Kuo Chen+1 more|arXiv (Cornell University)|Jun 29, 2023

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper proposes that QCD-anomalous discrete symmetries lead to domain walls that collapse via QCD instanton effects near the QCD phase transition, generating gravitational waves (GWs) detectable by pulsar timing arrays. It shows that first-order QCD phase transitions in domains with large effective θ angles can produce additional high-frequency GWs, resulting in a multi-band GW spectroscopy spanning from nanohertz to 100 Hz, offering a testable signature for new physics beyond the Standard Model.

ABSTRACT

For a discrete symmetry that is anomalous under QCD, the domain walls produced in the early universe from its spontaneous breaking can naturally annihilate due to QCD instanton effects. The gravitational waves generated from wall annihilation have their amplitude and frequency determined by both the discrete symmetry breaking scale and the QCD scale. The evidence of stochastic gravitational waves at nanohertz observed by pulsar timing array experiments suggests that the discrete-symmetry-breaking scale is around 100 TeV, assuming the domain-wall explanation. The annihilation temperature is about 100 MeV, which could naturally be below the QCD phase transition temperature. We point out that the QCD phase transition within some domains with an effective large QCD $θ$ angle could be a first-order one. To derive the phase diagram in $θ$ and temperature, we adopt a phenomenological linear sigma model with three quark flavors. The domain-wall explanation for the NANOGrav, EPTA, PPTA and CPTA results hints at a first-order QCD phase transition, which predicts additional gravitational waves at higher frequencies. If the initial formation of domain walls is also a first-order process, this class of domain-wall models predicts an interesting gravitational wave spectroscopy with frequencies spanning more than ten orders of magnitude, from nanohertz to 100 Hz.

Motivation & Objective

• To explore the gravitational wave (GW) signatures from domain walls that collapse due to QCD instanton effects in the early universe.
• To investigate whether the QCD phase transition can be first-order in domains with large effective θ angles, particularly near θ = π.
• To derive a multi-frequency GW spectrum from both domain wall annihilation and first-order QCD phase transitions, enabling a comprehensive GW spectroscopy.
• To connect the observed nanohertz stochastic gravitational wave background from pulsar timing arrays to a first-order QCD phase transition via domain wall dynamics.
• To constrain the discrete symmetry breaking scale f ≈ 100 TeV and the QCD phase transition temperature T_QCD ≈ 100 MeV using GW phenomenology.

Proposed method

• Adopt a phenomenological three-flavor linear sigma model (LSM q) to study the finite-temperature phase diagram in θ and T, extending previous two-flavor studies.
• Use CosmoTransitions to compute the thermal evolution of condensates (σ, π) and identify phase transition types (crossover vs. first-order) across θ values.
• Model the domain wall evolution under two scenarios: radiation-dominated (T_dom < T_ann) and domain-wall-dominated (T_dom > T_ann) eras.
• Compute gravitational wave spectra from three sources: bubble collisions (Ω_col), sound waves (Ω_sw), and turbulence (Ω_turb), using standard GW emission formulas.
• Integrate the GW spectra from domain wall collapse and QCD phase transitions, accounting for redshift and frequency evolution to the present day.
• Use the ζ factor to denote the fraction of the universe undergoing first-order phase transitions, and include wall velocity v_w and energy conversion fractions (κ_col, κ_sw, κ_turb).

Experimental results

Research questions

• RQ1 Can QCD-anomalous discrete symmetries lead to domain walls that collapse naturally via QCD instanton effects, and what are the resulting GW signatures?
• RQ2 Does the QCD phase transition become first-order in domains with large effective θ angles, particularly near θ = π, and what is the phase diagram in θ–T space?
• RQ3 Can the observed nanohertz stochastic gravitational wave background from pulsar timing arrays be explained by domain wall annihilation, and what does this imply for the discrete symmetry breaking scale?
• RQ4 What is the frequency distribution of gravitational waves from both domain wall collapse and QCD phase transitions, and can this lead to a multi-band GW spectroscopy?
• RQ5 How do the group theory properties of the discrete symmetry (e.g., Z_N with N > 2) affect the timing and spectral features of GW emission?

Key findings

• The QCD phase transition is first-order in a region centered at θ = π, with a critical θ_c ≈ 0.3π, as confirmed by the three-flavor linear sigma model and CosmoTransitions simulations.
• For θ = 0, the phase transition is a crossover at T ≈ 146 MeV; for θ = π, it is a first-order transition at T ≈ 129 MeV, indicating a significant shift in phase structure.
• The domain wall annihilation generates a stochastic GW background peaking in the nanohertz band, consistent with pulsar timing array observations (NANOGrav, EPTA, PPTA, CPTA).
• Assuming the domain wall explanation, the discrete symmetry breaking scale is constrained to f ≈ 100 TeV, and the annihilation temperature is T_ann ≈ 100 MeV.
• The model predicts a multi-band GW spectroscopy spanning over ten orders of magnitude in frequency—from nanohertz (from wall collapse) to ~100 Hz (from QCD phase transition), due to multiple first-order transitions.
• The GW spectrum from the QCD phase transition includes contributions from bubble collisions, sound waves, and turbulence, with peak frequencies f_col ≈ 1.6×10⁻⁶ Hz, f_sw ≈ 1.8×10⁻⁴ Hz, and f_turb ≈ 2×10⁻⁴ Hz, redshifted to today.