Reduction of the $K^{*}$ meson abundance in heavy ion collisions

We study the $K^{*}$ meson reduction in heavy-ion collisions by focusing on the hadronic effects on the $K^{*}$ meson abundance. We evaluate the absorption cross sections of the $K^{*}$ and $K$ meson by light mesons in the hadronic matter, and further investigate the variation in the meson abundances for both particles during the hadronic stage of heavy-ion collisions. We show how the interplay between the interaction of the $K^{*}$ meson and kaon with light mesons in the hadronic medium determines the final yield difference of the statistical hadronization model to the experimental measurements. For the central Au+Au collision at $\sqrt{s_{NN}}=200$ GeV, we find that the $K^{*}/K$ yield ratio at chemical freeze-out decreases by $37\%$ during the expansion of the hadronic matter, resulting in the final ratio comparable to STAR measurements of 0.23 $\pm 0.05$.

Figure 1

Born diagrams for the $K^{*}$ meson absorption by $\pi ,\rho ,K$, and $K^{*}$ mesons. (a–c) $K^{*}\pi \to \rho K$. (d–f) $K^{*}\rho \to \pi K$. (g–i) $K^{*}\overline{K}\to \rho \pi$. (j–l) $K^{*}{\overline{K}}^{*}\to \pi \pi$. (m–o) $K^{*}{\overline{K}}^{*}\to \rho \rho$.

Figure 2

Born diagrams for the $K$ meson absorption by $\overline{K}$ mesons: (a, b) $K\overline{K}\to \pi \pi$ and (c–e) $K\overline{K}\to \rho \rho$.

Figure 3

Absorption cross sections for (a) the $K^{*}$ meson by $\pi ,\rho ,K$, and $K^{*}$ mesons via processes $K^{*}\pi \to \rho K,K^{*}\rho \to \pi K,K^{*}\overline{K}\to \rho \pi ,K^{*}{\overline{K}}^{*}\to \pi \pi$, and $K^{*}{\overline{K}}^{*}\to \rho \rho$, and those for (b) the $K$ meson via processes $K\overline{K}\to \pi \pi ,K\overline{K}\to \rho \rho$, and $K\pi \to K^{*}$.

Figure 4

Thermally averaged cross sections for the absorption of (a) a $K^{*}$ meson by $\pi ,\rho ,K$, and $K^{*}$ mesons via processes $K^{*}\pi \to \rho K,K^{*}\rho \to \pi K,K^{*}\overline{K}\to \rho \pi ,K^{*}{\overline{K}}^{*}\to \pi \pi$, and $K^{*}{\overline{K}}^{*}\to \rho \rho$, and those for (b) a $K$ meson via processes $K\overline{K}\to \pi \pi ,K\overline{K}\to \rho \rho$, and $K\pi \to K^{*}$. Thermally averaged cross sections for their inverse processes (c) $\rho K\to K^{*}\pi ,\pi K\to K^{*}\rho ,\rho \pi \to K^{*}\overline{K},\pi \pi \to K^{*}{\overline{K}}^{*}$, and $\rho \rho \to K^{*}{\overline{K}}^{*}$ for a $K^{*}$ meson and (d) $\pi \pi \to K\overline{K}$ and $\rho \rho \to K\overline{K}$ for a $K$ meson.

Figure 5

Time evolution of the $K^{*}$ meson and kaon abundances during the hadronic stage in central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The ratio of the $K^{*}$ meson abundance to the sum of the $K^{*}$ meson and kaon abundances is shown in the inset.

Figure 6

A comparison between the $K^{*}$ meson and kaon abundances due to all hadronic interactions shown in Figs. 1 and 2 and those from the thermal model prediction at each time and temperature.

Figure 7

(a) Variations of ${\gamma }_K,{\gamma }_{K^{*}}$, and $\gamma ={\gamma }_K+{\gamma }_{K^{*}}$ in time during the hadronic stage. (b) A comparison of the abundance ratio variation $N_{K^{*}}/(N_K+N_{K^{*}})$ obtained numerically from Eq. (16) for RHIC and $R(\tau =\infty )={\gamma }_K/\gamma$ from Eq. (24) evaluated at each time and temperature. We show in the inset how $\gamma (\tau -{\tau }_h)$ changes in time.

Figure 8

Variations of ${\gamma }_K/\gamma$ and $N_{K^{*}}/(N_K+N_{K^{*}})$ from Eq. (16) in temperature during the hadronic stage. We show measurements of the abundance ratio between $K^{*}$ mesons and kaons, $N_{K^{*}}/(N_K+N_{K^{*}})0.23\pm 0.05$ at RHIC [13] and $0.19\pm 0.05$ at LHC [23].