Inhomogeneous instabilities in high-density QCD

TL;DR

Understanding the QCD phase structure at high density, including the moat regime and potential inhomogeneous phases near the chiral crossover, is addressed with a self-consistent functional renormalisation group analysis. The approach resolves full momentum-dependent pion and sigma propagators, includes dynamical hadronisation for emergent composites, and treats the glue sector with a flowing mass gap and Polyakov loop effects, yielding a quantitative phase diagram. The study finds a moat regime for $\mu_B/T \gtrsim 4$, with instabilities at intermediate momentum scales emerging around $\mu_B/T \gtrsim 5.5$ and onset scales $k_{on}$ around $100$ MeV with modulated momentum $p_M \sim 200$ MeV, suggesting inhomogeneous or quasi-long-range order and implications for the CEP and ONP. These results provide a first-principles, quantitative description of dense QCD dynamics and establish a foundation for identifying experimental signatures of the moat and related instabilities.

Abstract

QCD at large densities exhibits a moat regime in the scalar-pseudoscalar sector. The resolution of its dynamics is pivotal for the access to the onset of new phases including the potential critical endpoint of QCD. In this work we present the first selfconsistent analysis of this regime with the functional renormalisation group approach to QCD. We map out the moat regime, including a first analysis of potential inhomogeneous instabilities at baryon chemical potential $μ_B\gtrsim 600$ MeV on the chiral crossover line.

Figures (7)

• Figure 1: QCD Phase structure of 2+1 flavour QCD: Our results for the chiral crossover is depicted by the red straight line. We also display the moat regimes of the pions (hatched grey) and the sigma mode (hatched red). The region with signatures of inhomogeneous condensation is shown with a heatmap whose colour indicate value of $k_\textrm{on}$ which is the lowest value of the RG-scale that can be reached before the instability terminates the flow. These instabilities emerge at intermediate length scales. Whether or not this persists up to macroscopic scales, implying inhomogeneous (quasi-) long-range order, requires further studies. The current computation pushes the quantitative reliability bound of functional QCD to $\mu_B/T\approx 4.5$ (dashed black line) with 10% accuracy. We also show the previous bound $\mu_B/T\approx 4$ (dotted black line). For comparison we also show a compilation of state-of-the-art functional and lattice QCD results: Black dashed line Fu:2019hdw (fRG, fQCD), Gao:2020fbl (DSE, fQCD), dashed green line Gunkel:2021oya (DSE). Violet area Bellwied:2015rza (lattice, WB), brown area Bazavov:2018mes (lattice, HotQCD).
• Figure 2: The reduced light condensate $\Delta_{l,R}$\ref{['eq:Delta']}, light quark mass $m_l$ and Polyakov loop expectation value $L(A_0)$ along the temperature axis. The pseudo-critical temperature $T_{pc}$ is indicated together with its error band. We compare this to lattice data from the Wuppertal-Budapest collaboration Borsanyi:2010bp.
• Figure 3: Static pion and sigma two-point functions at different cutoff scales. The upper row shows the instability in the vicinity of the chiral crossover line. The lower row is at higher temperatures deep in the chirally restored phase.
• Figure 4: The pion propagator $G_{\pi\pi}(\boldsymbol{p})$ along the crossover line and inside the instability region. The values of $T$ associated with the respective $\mu_B$ are shown in the inlay plot. Note that the onset of the instability leads to a divergence in $G_{\pi\pi}(|\boldsymbol{p}|\approx 200\,\textrm{MeV})$, which at this point is no longer the propagator as found in the ground state of the theory. The shown propagator is normalised to 1 at $|\boldsymbol{p}| = 5\,\textrm{GeV}$.
• Figure 5: Heatmap of the ratio $\Gamma_{\sigma\sigma}(\boldsymbol{p}_{M_\sigma})/\Gamma_{\pi\pi}(\boldsymbol{p}_{M_\pi})$, evaluated at their respective minima $\boldsymbol{p}_{M_\sigma},\,\boldsymbol{p}_{M_\pi}$, see \ref{['eq:motedef']}. This ratio is a rough estimate for that of the correlation lengths $\xi_\sigma/\xi_\pi$. The dotted line indicates where the ratio becomes 1.