Static correlation lengths in QCD at high temperatures and finite densities

TL;DR

This work develops and tests a dimensional-reduction framework that maps hot QCD to a 3d SU(3)+adjoint Higgs theory to study static screening lengths in the deconfined plasma. By combining perturbative matching with high-precision 3d lattice simulations, it refines the Debye screening length at $\mu=0$ and characterizes the full spectrum of static masses across $N_f$ and $N_c$, then extends the method to finite density using a controlled reweighting approach that is validated against imaginary chemical potential. The results show Debye screening is dominated by nonperturbative dynamics, reveal clear $N_f$- and $N_c$-dependent shifts in the spectrum, and demonstrate that finite density shortens certain screening lengths while some gluonic channels remain comparatively insensitive. The approach enables quantitative access to finite-density static observables in a regime previously inaccessible to full 4d simulations, with implications for understanding the quark–gluon plasma in heavy-ion collisions.

Abstract

We use a perturbatively derived effective field theory and three-dimensional lattice simulations to determine the longest static correlation lengths in the deconfined QCD plasma phase at high temperatures (T\gsim 2 Tc) and finite densities (μ\lsim 4 T). For vanishing chemical potential, we refine a previous determination of the Debye screening length, and determine the dependence of different correlation lengths on the number of massless flavours as well as on the number of colours. For non-vanishing but small chemical potential, the existence of Debye screening allows us to carry out simulations corresponding to the full QCD with two (or three) massless dynamical flavours, in spite of a complex action. We investigate how the correlation lengths in the different quantum number channels change as the chemical potential is switched on.

Figures (6)

• Figure 1: The spectrum of screening masses in various quantum number channels at $N_f=0, T=2T_c$ (left), $N_f=0, T\sim 10^{11} T_c$ (right). Filled symbols denote 3d glueball states, which have become the lightest excitations at $T\sim 10^{11} T_c$. The states $1_+$ are much heavier than $1_-$ at high temperatures, and thus not visible on the right.
• Figure 2: The scaling with $N_c$ of some of the low lying $0_+^{++}$ (left) and $0_-^{-+}, 2_+^{++}$ (right) states. Filled symbols denote glueballs, and the lines are to guide the eye only.
• Figure 3: The $N_f$ dependence of the $J=0$ spectrum at $T = 2T_c$ (to be more precise, for $N_f>0$$T_c$ means really $\Lambda_{\overline{\rm MS}}$, see Sec. \ref{['contform']}). Filled symbols denote glueball states. We should stress that only the part $M \mathop{\hbox{$<$$\sim$}} 2 \pi T$ of the spectrum can be expected to directly represent the lowest states in 4d finite temperature QCD.
• Figure 4: The function ${\cal D}(\omega)$ from Eq. (\ref{['Dx']}), compared with the small-$\omega$ limit.
• Figure 5: Distribution of $zS_z[A_0]$ for the reweighting procedure (Eq. (\ref{['meas']})).