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Gravitational wave spectrum from first-order QCD phase transitions based on a parity doublet model

Bikai Gao, Jingdong Shao, Hong Mao

Abstract

We investigate the gravitational wave spectrum from first-order QCD phase transitions using the parity doublet model at finite baryon chemical potential. The model incorporates the chiral invariant mass $m_0$, representing the portion of nucleon mass that persists even when chiral symmetry is restored. Within the model, we identify two first-order phase transition regions: the nuclear liquid--gas transition and the chiral phase transition. By solving the bounce equation and computing the Euclidean action $S_3/T$, we obtain the gravitational wave spectra from both transitions. The liquid--gas transition yields $α\sim \mathcal{O}(1)$ and $β/H \sim \mathcal{O}(10)$--$\mathcal{O}(100)$ near the endpoint of the first-order line, producing signals with peak frequencies from the millihertz to the nanohertz band that can fit the existing data. In contrast, the chiral transition produces signals suppressed by approximately five orders of magnitude, well below the sensitivity of all current and planned detectors. These results connect the chiral invariant mass to the gravitational wave spectrum, offering a novel probe of the origin of nucleon mass through gravitational wave astronomy.

Gravitational wave spectrum from first-order QCD phase transitions based on a parity doublet model

Abstract

We investigate the gravitational wave spectrum from first-order QCD phase transitions using the parity doublet model at finite baryon chemical potential. The model incorporates the chiral invariant mass , representing the portion of nucleon mass that persists even when chiral symmetry is restored. Within the model, we identify two first-order phase transition regions: the nuclear liquid--gas transition and the chiral phase transition. By solving the bounce equation and computing the Euclidean action , we obtain the gravitational wave spectra from both transitions. The liquid--gas transition yields and -- near the endpoint of the first-order line, producing signals with peak frequencies from the millihertz to the nanohertz band that can fit the existing data. In contrast, the chiral transition produces signals suppressed by approximately five orders of magnitude, well below the sensitivity of all current and planned detectors. These results connect the chiral invariant mass to the gravitational wave spectrum, offering a novel probe of the origin of nucleon mass through gravitational wave astronomy.

Paper Structure

This paper contains 5 sections, 31 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Parity doublet model
  3. HOMOGENEOUS THERMAL NUCLEATION
  4. GW spectra from first-order phase transition
  5. Summary and Discussion

Figures (5)

  • Figure 1: Expectation value of the $\sigma$ mean field as a function of baryon chemical potential for $T = 0$ and $20$ MeV.
  • Figure 2: Low-temperature phase diagram from the parity doublet model. The upper panel shows the region near the liquid-gas phase transition, while the lower panel presents the region near the chiral phase transition.
  • Figure 3: Bounce solution $\sigma(r)$ as a function of radial distance for several values of baryon chemical potential $\mu_B$ at various temperatures. The upper panels correspond to the region near the liquid--gas transition, while the lower panels correspond to the region near the chiral transition.
  • Figure 4: $S_3/T$ as a function of temperature $T$ for several values of $\mu_B$ in the vicinity of the liquid–gas phase transition (upper panel) and the chiral phase transition (lower panel).
  • Figure 5: GW spectra with different chemical potential from the liquid-gas transition ( Solid curves) and the chiral transition (dashed curves).