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

Production of the $K^{*}{\left(892\right)}^0$ and ${\overline{K}}^{*}{\left(892\right)}^0$ resonances was studied via their $K^{+}{\pi }^{-}$ and $K^{-}{\pi }^{+}$ decay modes in central $\mathrm{Pb}+\mathrm{Pb}$, $\mathrm{Si}+\mathrm{Si}$, $\mathrm{C}+\mathrm{C}$, and inelastic $p+p$ collisions at 158$A$ GeV($\sqrt{s_{NN}}=17.3$ GeV) with the NA49 detector at the CERN SPS. Transverse momentum and rapidity distributions were measured and total yields were estimated. The yield of $K^{*}$ exceeds that of ${\overline{K}}^{*}$ by about a factor of two in nucleus-nucleus reactions. The total yield ratios $\langle K^{*}\rangle$$/\langle K^{+}\rangle$ and $\langle {\overline{K}}^{*}\rangle$$/\langle K^{-}\rangle$ are strongly suppressed in central $\mathrm{Pb}+\mathrm{Pb}$ compared to $p+p$, $\mathrm{C}+\mathrm{C}$, and $\mathrm{Si}+\mathrm{Si}$ 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 $\langle K^{*}\rangle$$/\langle K\rangle$ ratios in central $\mathrm{Pb}+\mathrm{Pb}$ collisions by about a factor of 2.5.

Figure 1

Specific energy loss $dE/dx$ in units of minimum ionizing particles (MIP) measured in the NA49 TPCs versus momentum $p$ for positively (a) and negatively (b) charged particles in central $\mathrm{Pb}+\mathrm{Pb}$ collisions. Curves in (a) and (b) show the acceptance limits for $K^{+}$ and ${\pi }^{-}$, respectively.

Figure 2

Invariant-mass distribution of $K^{+}{\pi }^{-}$ (a) and $K^{-}{\pi }^{+}$ (b) for $p_T<2.0$ GeV$/c$ in the rapidity region $0.6<y<0.9$ after subtraction of mixed-pair background in central $\mathrm{Pb}+\mathrm{Pb}$ collisions. The fitted polynomial background is shown by the dashed curves; the sum of fitted polynomial background and signal Breit-Wigner function is shown by the solid curves.

Figure 3

Fitted mass values $m_0$ (a),(b) and width $\Gamma$ (c),(d) of the $K^{*}{\left(892\right)}^0$ peak in the $K^{+}{\pi }^{-}$ mass distribution versus rapidity $y$ (a),(c) and transverse momentum $p_T$ (b),(d) in central $\mathrm{Pb}+\mathrm{Pb}$ collisions. Dots show the fitted values with statistical error bars, and bands indicate the systematic uncertainties. The dotted horizontal lines indicate the world average values for $m_0$ and $\Gamma$ [19]. For comparison results are shown from the STAR collaboration at RHIC [9] for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62$ GeV (triangles) and $\sqrt{s_{NN}}=200$ GeV (squares).

Figure 4

Invariant-mass spectra of simulated and embedded $K^{*}{\left(892\right)}^0$ (a) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b) calculated from reconstructed matched tracks.

Figure 5

Combined reconstruction efficiency and acceptance of $K^{*}{\left(892\right)}^0\to K^{+}{\pi }^{-}$ as a function of rapidity (transverse momentum range $0<p_T<2.0$ GeV$/c$) (a) and transverse momentum (rapidity range $0.43<y<1.78$) (b) in central $\mathrm{Pb}+\mathrm{Pb}$ collisions. Solid and open symbols show results with and without embedding into real events (see text). The decay branching ratio is not included in the plotted efficiencies.

Figure 6

Examples of invariant-mass distributions for $K^{+}{\pi }^{-}$ (a) and $K^{-}{\pi }^{+}$ (b) after subtraction of mixed-event background in inelastic $p+p$ collisions. The curves show the fits with the sum of Breit-Wigner functions to describe the signals of the $K^{*}{\left(892\right)}^0$ and $K_2^{*}{\left(1430\right)}^0$ and the contributions from their reflections (see text).

Figure 7

Invariant-mass distribution of $K^{+}{\pi }^{-}$ (a),(b) and $K^{-}{\pi }^{+}$ (c),(d) in the rapidity region $0.2<y<1.8$ and $p_T<1.5$ GeV$/c$ after subtraction of mixed-pair background. Results are plotted for $\mathrm{C}+\mathrm{C}$ collisions in (a),(c) and for $\mathrm{Si}+\mathrm{Si}$ collisions in (b),(d). The fitted residual background is shown by the dashed lines; the sum of fitted background and signal Breit-Wigner function is shown by the solid curves.

Figure 8

Rapidity distribution of $K^{*}{\left(892\right)}^0$ (a) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b) integrated over $p_T$ in central $\mathrm{Pb}+\mathrm{Pb}$ collisions. Solid symbols represent the measurements; open symbols were obtained by reflection around midrapidity. The bars show statistical errors; the bands indicate systematic errors. Solid curves show fits of Gaussian functions for estimating total yields; dashed-dotted curves depict predictions of the UrQMD model [28].

Figure 9

Differential yields in central $\mathrm{Pb}+\mathrm{Pb}$ collisions as function of transverse momentum $p_T$ (a),(c) and transverse mass $m_T$ (b),(d) for $K^{*}{\left(892\right)}^0$ (a),(b) and ${\overline{K}}^{*}{\left(892\right)}^0$ (c),(d) in the rapidity interval $0.43<y<1.78$. The bars show statistical errors; the bands indicate systematic errors. Solid curves show results of exponential fits [Eq. (3), see text]. Dotted curves result from blast-wave calculations using the parameters fitted in Ref. [29]. The dashed-dotted curves depict predictions of the UrQMD model [28].

Figure 10

Transverse momentum distribution of $K^{*}{\left(892\right)}^0$ (a) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b) for the rapidity interval $0.2<y<0.7$ in inelastic $p+p$ collisions at 158 GeV$/c$ incident momentum. Only statistical errors are shown; the overall systematic error of normalization is 9$\%$. Curves show results of fits with the exponential function Eq. (3).

Figure 11

Transverse mass distribution of $K^{*}{\left(892\right)}^0$ (a) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b) for the rapidity interval $0.2<y<0.7$ in inelastic $p+p$ collisions at 158 GeV$/c$ incident momentum. Only statistical errors are shown; the overall systematic error of normalization is 9$\%$. Curves show results of fits with the exponential function Eq. (3).

Figure 12

Rapidity distributions for $K^{*}{\left(892\right)}^0$ (a) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b) integrated over $p_T<1.5$ GeV$/c$ in inelastic $p+p$ collisions at 158 GeV$/c$ incident momentum. Only statistical errors are shown; the overall systematic error of normalization is 9$\%$. Curves show fits with a Gaussian function centered at midrapidity $y=0$ (${\chi }^2$ per degree of freedom 1.1 and 1.4, respectively).

Figure 13

(a) Yields per wounded nucleon $K^{*}{\left(892\right)}^0$$/\langle N_W\rangle$ (dots) and ${\overline{K}}^{*}{\left(892\right)}^0$$/\langle N_W\rangle$ (squares) versus size of the collision system. (b) Ratios $\langle K^{*}{\left(892\right)}^0\rangle$$/\langle K^{+}\rangle$ (dots) and $\langle {\overline{K}}^{*}{\left(892\right)}^0\rangle$$/\langle K^{-}\rangle$ (squares) versus size of the collision system ($p+p$, $\mathrm{C}+\mathrm{C}$, $\mathrm{Si}+\mathrm{Si}$, and $\mathrm{Pb}+\mathrm{Pb}$ collisions). Total kaon yields were taken from Refs. [2, 18, 23] and appropriately scaled by $\langle N_W\rangle$. For evaluating error bars the quadratic sums of statistical and systematic errors were used.

Figure 14

Predictions of the UrQMD model version 1.3p1 [28] for the 23.5$\%$ most central $\mathrm{Pb}+\mathrm{Pb}$ collisions at 158$A$ GeV: distributions of rapidity (a),(b) and transverse momentum $p_T$ (c,d) in the rapidity interval $0.43<y<1.78$ of $K^{*}{\left(892\right)}^0$ (a),(c) and ${\overline{K}}^{*}{\left(892\right)}^0$ (b),(d). The curves show the successive reduction of yields owing to various interaction mechanisms of the $K^{*}{\left(892\right)}^0$ and ${\overline{K}}^{*}{\left(892\right)}^0$ and their decay daughters in the fireball (see text). Note that the final results show the yield predictions for the $K^{+}{\pi }^{-}$ and $K^{-}{\pi }^{+}$ decay channels, respectively. The curves in Figs. 8 and 9 were obtained by scaling these by 3/2.

Figure 15

(a) Ratio of measured total yields of $K^{*}{\left(892\right)}^0$ (dots) and ${\overline{K}}^{*}{\left(892\right)}^0$ (squares) to statistical HGM predictions [12] versus the size of the collision system ($p+p$, $\mathrm{C}+\mathrm{C}$, $\mathrm{Si}+\mathrm{Si}$, and $\mathrm{Pb}+\mathrm{Pb}$ collisions). (b) Ratio of measured yield in central $\mathrm{Pb}+\mathrm{Pb}$ collisions to the statistical HGM prediction for $K^{*}{\left(892\right)}^0$ (dot), ${\overline{K}}^{*}{\left(892\right)}^0$ (square), $\phi$ meson [27], and preliminary measurement of $\Lambda \left(1520\right)$ [32] versus the lifetime $\tau$ of the resonance state. For evaluating error bars the quadratic sums of statistical and systematic errors were used.