[Paper Review] NANOGrav hints for first-order confinement-deconfinement phase transition in different QCD-matter scenarios

Zu-Cheng Chen, Shou-Long Li+2 more|arXiv (Cornell University)|Dec 4, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper investigates whether the NANOGrav 15-year stochastic gravitational wave background (SGWB) signal originates from a first-order confinement-deconfinement phase transition in QCD matter, using Bayesian analysis within holographic QCD models. It finds that only the Jouguet detonation scenario in a hard wall model for pure quark systems is consistent with the data, decisively ruling out pure gluon systems and non-runaway bubble dynamics at 5σ significance.

ABSTRACT

Recent observations from several pulsar timing array (PTA) collaborations have unveiled compelling evidence for a stochastic signal in the nanohertz band. This signal aligns remarkably with a gravitational wave (GW) background, potentially originating from the first-order color charge confinement phase transition. Distinct quantum chromodynamics (QCD) matters, such as quarks or gluons, and diverse phase transition processes thereof can yield disparate GW energy density spectra. In this paper, employing the Bayesian analysis on the NANOGrav 15-year data set, we explore the compatibility with the observed PTA signal of the GW from phase transitions of various QCD matter scenarios in the framework of the holographic QCD. We find that the PTA signal can be effectively explained by the GW from the confinement-deconfinement phase transition of pure quark systems in a hard wall model of the holographic QCD where the bubble dynamics, one important source of the GWs, is of the Jouguet detonations. Notably, our analysis decisively rules out the plausibility of the pure gluon QCD-matter scenario and the non-runaway bubble dynamics model for the phase transition in explaining the observed PTA signal.

Motivation & Objective

• To assess the compatibility of the NANOGrav 15-year stochastic gravitational wave background (SGWB) signal with first-order confinement-deconfinement phase transitions in various QCD-matter scenarios.
• To evaluate the role of different bubble dynamics—specifically Jouguet detonations versus non-runaway fronts—in generating the observed GW spectrum.
• To test the viability of holographic QCD models (hard wall vs. soft wall) in describing the quark-gluon phase transition under PTA constraints.
• To determine whether finite baryon chemical potential affects the GW power spectrum in QCD phase transitions.
• To identify the most favored model among ten QCD-like scenarios using Bayesian model comparison (ΔBIC).

Proposed method

• Employed Bayesian inference on the NANOGrav 15-year data set to constrain parameters of gravitational wave (GW) energy density spectra from first-order phase transitions.
• Used the holographic QCD framework with hard wall and soft wall models to describe quark and gluon matter, incorporating finite-temperature phase transitions.
• Modelled bubble dynamics as either Jouguet detonations or non-runaway fronts, calculating GW power spectra based on bubble wall velocity and nucleation rate.
• Calculated the GW energy density spectrum using the standard formula for bubble wall collisions and sound waves, with parameters β/H* fixed at 10 and 15.
• Applied the Bayesian Information Criterion (BIC) to compare model performance, with S1 (Jouguet quark system) as the fiducial model.
• Constrained the phase transition temperature T* and the dimensionless parameter α (related to the strength of the transition) via Markov Chain Monte Carlo sampling.

Figure 1: Left panel: Bayesian posteriors for model parameters $\alpha$ and $T_{*}$ in the Jouguet detonation bubble scenario, using the NANOGrav 15-year data set. We show the $1\sigma$ , $2\sigma$ , and $5\sigma$ contours in the two-dimensional plot. The five holographical models are also indicated

Experimental results

Research questions

• RQ1 Can the NANOGrav 15-year SGWB signal be explained by a first-order confinement-deconfinement phase transition in QCD matter?
• RQ2 Which QCD-matter scenario—quarks, gluons, or mixed—best explains the observed GW signal?
• RQ3 Is the bubble dynamics during the phase transition consistent with Jouguet detonation or non-runaway propagation?
• RQ4 How do holographic QCD models (hard wall vs. soft wall) compare in fitting the PTA data?
• RQ5 Does the presence of finite baryon chemical potential significantly alter the GW spectrum from the phase transition?

Key findings

• The NANOGrav 15-year data set shows strong evidence (5σ) against the non-runaway bubble dynamics model, which is decisively ruled out.
• The pure gluon QCD-matter scenario is also ruled out by the data, indicating that gluons alone cannot account for the observed SGWB.
• The Jouguet detonation scenario in the hard wall holographic QCD model for pure quark systems provides the best fit, with posterior estimates α = 0.63⁺³⁵₋₀.₂₃ and T* = 17⁺⁴²₋₆.₆ MeV.
• The S₃ model (Jouguet quark system in hard wall model) shows 'positive' evidence over S₁ in the β/H* = 10 case and 'very strong' evidence in the β/H* = 15 case.
• The BIC difference shows that S₃ is significantly favored over S₁ (ΔBIC = -12.9 at β/H* = 15), confirming its superior fit.
• Finite baryon chemical potential has negligible influence on the GW power spectrum, as the transition temperatures remain nearly identical to the zero-chemical-potential case.

Figure 2: Same as Fig. 1 but for the non-runaway bubble case.