A phenomenological approach to direct ${\mathrm{K}}^{\ast }$ production and hadronic medium effects in nucleus-nucleus collisions at high baryon density

Abstract

Short-lived hadron resonances serve as sensitive probes of the late-stage hadronic medium in heavy-ion collisions. Using the AMPT-HC model, we study ${\mathrm{K}}^{\ast }(892)$ production and its hadronic medium effects in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=3$ GeV, a region of high baryon density. We introduce a phenomenological direct-production mechanism for ${\mathrm{K}}^{\ast }$ by replacing a fraction of the final-state kaons produced in the $\mathrm{NN}\to \mathrm{NYK}$ and $\mathrm{MN}\to \mathrm{YK}$ channels with ${\mathrm{K}}^{\ast }$ resonances, with the substitution fraction controlled by a parameter $\alpha$ while conserving four-momentum. The direct ${\mathrm{K}}^{\ast }$ is produced early, at about 6 fm/$c$, with little centrality dependence, whereas resonance fusion via $\mathrm{K}+\pi \to {\mathrm{K}}^{\ast }$ occurs later, with the mean production time increasing from about 8 to 10 fm/$c$ toward central collisions. Consequently, direct ${\mathrm{K}}^{\ast }$ mesons suffer stronger daughter rescattering, leading to a pronounced decrease in reconstruction efficiency toward central collisions, while the ${\mathrm{K}}^{\ast }$ survival rate remains close to unity. Elastic scattering of the daughters also shifts the invariant mass away from the resonance peak, contributing to the background-like component. The ${\mathrm{K}}^{\ast }/\mathrm{K}$ centrality dependence reflects the competition between direct production and resonance fusion and is sensitive to $\alpha$. At 3 GeV, a moderate direct-production contribution may result in an increasing ${\mathrm{K}}^{\ast }/\mathrm{K}$ ratio toward central collisions, providing a testable prediction for future measurements.