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

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 $\alpha \sim \mathcal{O}(1)$ and $\beta/H \sim \mathcal{O}(10)$--$\mathcal{O}(100)$ 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.