Axionlike particle-assisted supercooling chiral phase transition in QCD: Identifying Coleman-Weinberg type-chiral phase transition in QCD-like scenarios

TL;DR

The paper investigates how Coleman–Weinberg type chiral phase transitions can occur in QCD-like theories by separating scale violations into a soft-scale breaking term $m_0^2 M^2$ and a CW-type scale anomaly $M^4 \ln M$, then uses a two-flavor NJL model with $\mu_B$, $\mu_5$, and $\theta$ to map the transition structure onto the thermodynamic potential $\Omega$. It finds that ordinary QCD at $\mu_B=0$ yields a chiral crossover, while finite $\mu_B$ can reintroduce CW-type supercooling and first-order behavior under suitable conditions; the authors then propose an ALP-assisted mechanism in which a portal scalar $\Phi$ cancels the soft-scale breaking near $T_c$, enabling CW-type dynamics and rich cosmology including mini-inflation, preheating, gravitational waves, and primordial black holes. A key prediction is a heavy axion-like particle with mass $m_a \sim 4$–$8$ MeV and a small diphoton coupling $g_{a\gamma\gamma}$, consistent with current constraints, with indirect tests via GW/PBH signatures from the CW transition. The work thereby links ALP phenomenology to the QCD phase transition epoch, offering a novel pathway to probe new physics through cosmology and subtle laboratory bounds, and it suggests that the CW-type scale anomaly remains robust across regularization schemes in QCD-like frameworks.

Abstract

We propose a new scenario to realize the Coleman-Weinberg (CW) type chiral phase transition in the QCD thermal history. This scenario predicts a heavy axionlike particle (ALP) with mass $\sim$ 5 MeV, consistently with the current experimental and cosmological bounds. The chiral phase transition is evaluated by monitoring ordinary QCD setup in a view of a two-flavor Nambu-Jona-Lasinio model including a simplified meson fluctuation contribution. The present work thus can open a new window to search for the ALP associated with the QCD phase transition epoch of the thermal history. The new QCD cosmological scenario potentially predicts rich epochs around the QCD scale: a mini-inflation; a nonperturbative preheating and/or reheating, which can provide characteristic gravitational wave and primordial black hole productions. This proposal is based on a generic classification of the order of the chiral phase transition at the level of the mean field approximation in view of the scale violation classes: the soft-scale breaking term and the CW-type scale anomaly term, in or off the medium with or without chemical potentials. On this theoretical ground, we also revisit existing scenarios which undergo the supercooling chiral phase transition, such as nearly scale-invariant QCD and QCD with a large baryon chemical potential.

Figures (4)

• Figure 1: The variation of the thermodynamic potential with respect to $\mu_B$ at low $T$ ($T=20$ MeV), as a function of $S = \frac{M - m}{2(g_s + g_d)}$ at $\theta=0$, in the NJL-MF description monitoring two-flavor QCD at physical point (for details, see the text).
• Figure 2: The thermal chiral phase transition of the CW type including a soft-scale breaking mass term induced from the Debye mass at $\mu_B=1100$ MeV and dynamical chiral symmetry breaking. The model parameters have been setup at physical point as in Fig. \ref{['fig:2']}.
• Figure 3: The plot of the thermal evolution of the effective potential $V_{\rm eff}$ in Eq.(\ref{['Veff-sigma']}) with $M^2(\sigma)=0$ plus the Debye mass term correction in Eq.(\ref{['T2-term']}), normalized by the vacuum energy $V_0 = |V_{\rm eff}(\langle \sigma_0\rangle )|$ measured at the true vacuum $\langle \sigma_0 \rangle_{\rm true} \simeq 461$ MeV. The critical temperature of the first order phase transition is observed as $T_c \simeq 628$ MeV (corresponding to the moment denoted by red curve) The false vacuum is set away from the origin because of the $\mu_5$-induced tadpole term, which is at $\langle \sigma_0 \rangle_{\rm false} \simeq 7.9$ MeV when $T=T_c$, as depicted in the zoomed-in figure on the bottom-left interior panel.
• Figure 4: The predicted curve of $g_{a\gamma\gamma}$ as a function of $m_a$ with the soft-scale breaking-cancellation condition in Eq.(\ref{['y-lambda']}) taken into account. The plot range ensures the perturbatively small enough quark loop correction to the ALP sector (i.e., $y^4 \ll \lambda$, or equivalently $m_a \ll 169$ MeV). All the domains plotted not overlapping with the constraint regimes survive over the current experimental constraint summarized in the website https://cajohare.github.io/AxionLimits or https://cajohare.github.io/AxionLimits/docs/ap.html. The case with $m_a< 1$ MeV has also been ruled out by the bound from the "Cosmic Background".