Contribution of a kaon component in the viscosity and conductivity of a hadronic medium

With the help of effective Lagrangian densities of strange hadrons, we calculated the kaon relaxation time from several loop and scattering diagrams at tree level, which basically represent contributions from $1\leftrightarrow 2$ and $2\leftrightarrow 2$ types of collisions. Using the total relaxation time of a kaon, the shear viscosity and electrical conductivity of this kaon component have been estimated. The high temperature, close to transition temperature, where the kaon relaxation time is lower than the lifetime of Relativistic Heavy Ion Collider or Large Hadron Collider matter may be the only relevant domain for this component to contribute in hadronic dissipation. Our results suggest that the kaon can play an important role in the enhancement of shear viscosity and electrical conductivity of hadronic matter near the transition temperature.

Figure 1

(a) Schematic one-loop representation of viscous-stress tensor for the medium with constituents of $K$ mesons. The double dashed lines for the $K$-meson propagators indicate that they have some finite thermal width. (b) Kaon self-energy for $\pi K^{*}$ and $K\varphi$ loops.

Figure 2

Tree-level Feynman diagrams of $Kx\to Kx$ scattering, where $x=K,\overline{K},\pi$.

Figure 3

The thermal width of kaon self-energy from (a) $K^{*}\varphi$ and (b) $K\varphi$ loops as a function of invariant mass $M=\sqrt{k_0^2-|{\mathbf{k}|}^2}$ at fixed temperature $T=0.150$ GeV for two different momenta $\mathbf{k}=0.300$ GeV (solid line) and $0.500\mathrm{GeV}$ (dashed line). The vertical dotted red line represents the on-shell value $M=m_K$.

Figure 4

Temperature dependence of (a) thermal width and (b) the mean free path of the kaon for two different momenta $\mathbf{k}=0.100$ GeV (solid line) and $\mathbf{k}=0.300$ GeV (dashed line). The horizontal dashed red line represents an approximate dimension of the fireball.

Figure 5

$T$ dependence of (a) average thermal widths and (b) relaxation times for $KK$ (dashed line), $K\pi$ (dash-double-dotted line), and $K\overline{K}$ (dash-dotted line) scatterings and their total (solid line) and Landau damping part (dotted line).

Figure 6

Temperature dependence of average (a) thermal widths and (b) relaxation times of pions (dotted lines) and kaons (solid lines). The horizontal dashed line represents the approximate lifetime of the fireball.

Figure 7

Temperature dependence of shear viscosity for kaons (solid line) and pions (dotted line) by using (a) $\tau =1$ fm and (b) $\tau =\tau \left(T\right)$.

Figure 8

Same as Fig. 7 for electrical conductivity.