$K^{\ast}(892)^0$ and $\bar{K}^{\ast}(892)^0$ production in central Pb+Pb, Si+Si, C+C and inelastic p+p collisions at 158$A$~GeV

Production of the $K^{\ast}(892)^0$ and $\bar{K}^{\ast}(892)^0$ resonances was studied via their $K^+ \pi^-$ and $K^- \pi^+$ decay modes in central Pb+Pb, Si+Si, C+C and inelastic p+p collisions at 158\agev ($\sqrt{s_{NN}}$ = 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum and rapidity distributions were measured and total yields were estimated. The yield of $K^{\ast}$ exceeds that of $\bar{K}^{\ast}$ by about a factor of two in nucleus-nucleus reactions. The total yield ratios $< K^{\ast} >/< K^+ >$ and $< \bar{K}^{\ast} >/< K^->$ are strongly suppressed in central Pb+Pb compared to p+p, C+C and Si+Si collisions in agreement with the expected attenuation of these short-lived resonance states in the hadronic phase of the expanding fireball. The UrQMD model, although incorporating such a scenario, does not provide a quantitative description of the experimental results. The statistical hadron gas model assuming the same freeze-out parameters for stable hadrons and resonances overestimates the $< K^{\ast} >/< K >$ ratios in central Pb+Pb collisions by about a factor of 2.5.