Kaons ($K^\pm$) in hot and dense QCD

Abstract

We present a systematic QCD sum-rule analysis of the in-medium properties of the charged kaon doublet $K^{\pm}$ over the full $(T,ρ)$ plane relevant to current and forthcoming heavy-ion experiments. Working within the QCD sum-rule framework and incorporating temperature-and density-dependent quark, gluon, and mixed condensates, we derive Borel-transformed sum rules for the effective masses $m_{K^{\pm}}$, the pseudoscalar decay constants $f_{K^{\pm}}$, and the vector self-energy $Σ_{v}$ of both charged states simultaneously. Our vacuum results, $m_{K^{-}} = 494.6^{+4.9}_{-6.9}$~MeV and $f_{K^{-}} = 157.3^{+4.1}_{-2.9}$~MeV (with near-degenerate $K^{+}$ values), are in excellent agreement with Particle Data Group values at the sub-percent level. In the medium, $m_{K^{\pm}}$ decreases monotonically with increasing baryon density and temperature, signalling progressive partial restoration of chiral symmetry. A pronounced mass splitting $Δm = m_{K^{-}} - m_{K^{+}}$ develops in baryonic matter, driven by the opposite sign of the Weinberg--Tomozawa vector interaction for the two charge states; it reaches $|Δm| \sim 0.35$~GeV near $ρ\simeq 3.2\,ρ_{\rm sat}$ at $T = 0$ and is partially quenched by thermal fluctuations. A central outcome of this study is the extraction of the critical onset density $ρ_c$, defined as the threshold beyond which the in-medium modifications of $K^{-}$ properties signal the onset of the transition toward the chirally restored phase. We stress that $ρ_c(T)$ should not be interpreted as a precise determination of the QCD critical point-a task beyond the reach of any current effective framework-but rather as an indicator ....

Figures (9)

• Figure 1: Dependence of the vacuum masses of $K^{-}$ (left) and $K^{+}$ (right) on the Borel mass parameter $M^2$ for various values of the continuum threshold $s_0$.
• Figure 2: Density dependence of the modified masses of $K^{-}$ (left panel) and $K^{+}$ (right panel) normalized to the nuclear saturation density ($0\leqslant\rho/\rho_{\text{sat}}\leqslant 5$), at several fixed temperatures ($T=0, 0.050, 0.100, 0.155$ GeV).
• Figure 3: The modified masses of $K^{-}$ (left panel) and $K^{+}$ (right panel) as a function of temperature for fixed baryon densities ($\rho/\rho_{\text{sat}}=0.0, 0.5, 1.0, 1.5, 2.0., 2.5$) over the range ($0\leqslant T\leqslant 0.20$ GeV).
• Figure 4: Density and temperature dependence of the in-medium masses of the $K^{-}$ (left panel) and $K^{+}$ (right panel) mesons shown as three-dimensional surfaces. The horizontal axes represent the baryon density normalized to the nuclear saturation density, $\rho/\rho_{\rm sat}$, and the temperature $T$ (in GeV), while the vertical axis gives the meson mass (in GeV). The progressive suppression of both masses with increasing density and temperature reflects the partial restoration of chiral symmetry in the hot and dense nuclear medium.
• Figure 5: Density dependence of the in-medium decay constants of $K^{-}$ (left panel) and $K^{+}$ (right panel) normalized to the nuclear saturation density ($\rho_{\text{sat}}$), at several fixed temperatures ($T=0, 0.050, 0.100, 0.155$ GeV).