Centrality dependence of subthreshold $\varphi$ meson production in Ni + Ni collisions at $1.9A$ GeV

We analyzed the $\varphi$ meson production in central Ni + Ni collisions at a beam kinetic energy of 1.93A GeV with the FOPI spectrometer and found a production probability per event of $[8.6\pm 1.6\left(\text{stat}\right)\pm 1.5\left(\text{syst}\right)]\times {10}^{-4}$. This new data point allows us for the first time to inspect the centrality dependence of subthreshold $\varphi$ meson production in heavy-ion collisions. The rise of $\varphi$ meson multiplicity per event with mean number of participants can be parametrized by a power function with exponent $\alpha =1.8\pm 0.6$. The ratio of $\varphi$ to $K^{-}$ production yields seems not to depend, within the experimental uncertainties, on the collision centrality, and the average of measured values was found to be $0.36\pm 0.05$.

Figure 1

Identification of charged kaons on the two-dimensional map of FOPI mass parameters: $m_{\text{CDC}}$ (obtained from the CDC) versus $m_{\text{PSB}}$ (from the combination of CDC-PSB data). Rectangles marked by dashed lines delineate the cuts imposed for the selection of $K^{+}$ and $K^{-}$ candidates.

Figure 2

(a) Invariant mass plot of true (solid line) and mixed (scattered points) $K^{+}{K}^{-}$ pairs. The normalization window for the spectrum of mixed pairs is indicated with the arrow. (b) $\varphi$ meson signal obtained after the background subtraction. The solid curve shows the Gaussian distribution fitted within $1.00<M_{\text{inv}}<1.04\text{GeV}/c^2$. (c) A comparison of profiles of experimental (points) and simulated (solid line) $\varphi$ meson signals.

Figure 3

Maps of correction factors for possible unequal efficiencies of matching of CDC tracks with PSB hits between the experimental and simulated data, obtained for (a) ${\pi }^{-}$ tracks, and (b) sum of ${\pi }^{+}$ and proton tracks. Regions in between dashed lines correspond to cuts applied in the $K^{+}{K}^{-}$ analysis.

Figure 4

$\varphi$ meson yield per event at a beam energy of $1.9A$ GeV as a function of number of participant nucleons averaged over the impact parameters. Full circles: data measured at $1.9A$ GeV; open circle: data obtained at $1.756A$ GeV [10] and scaled according to the systematics in [27]; dotted curve: power function fit to the points marked by full circles. See text for details.

Figure 5

(a) Centrality dependence of the $\varphi K^{-}$ ratio at a beam energy of $1.9A$ GeV. The horizontal line and the arrow mark the average value. (b) Centrality dependence of the $\varphi {\pi }^{+}$ ratio. The dotted line shows the fit of the constant function, and the dashed line shows the power function fit. The value of exponent $\alpha$ is the result of the latter fit. See text for details.