Influence of $\varphi$ mesons on negative kaons in Ni + Ni collisions at $1.91A$ GeV beam energy

$\varphi$ and ${\mathrm{K}}^{-}$ mesons from Ni+Ni collisions at the beam energy of $1.91A$ GeV have been measured by the FOPI spectrometer, with a trigger selecting central and semicentral events amounting to 52% of the total cross section. The phase-space distributions, and the total yield of ${\mathrm{K}}^{-}$, as well as the kinetic energy distribution and the total yield of $\varphi$ mesons are presented. The $\varphi /$ ${\mathrm{K}}^{-}$ ratio is found to be $0.44\pm 0.07{\left(\text{stat}\right)}_{-0.10}^{+0.16}\left(\text{syst}\right)$, meaning that about 22% of ${\mathrm{K}}^{-}$ mesons originate from the decays of $\varphi$ mesons, occurring mostly in vacuum. The inverse slopes of direct kaons are up to about 15 MeV larger than the ones extracted within the one-source model, signaling that a considerable share of gap between the slopes of ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ could be explained by the contribution of $\varphi$ mesons to negative kaons.

Figure 1

Particle identification based on relativistic momentum-velocity dependence, with (a) PSB, and (b) MMRPC detectors.

Figure 2

(a) Invariant mass plot of (solid line) true, and (scattered points) mixed ${\mathrm{K}}^{+}{\mathrm{K}}^{-}$ pairs. (b) $\varphi$ meson signal obtained after background subtraction.

Figure 3

Top row: efficiency distribution for (a) ${\mathrm{K}}^{-}$, and (b) $\varphi$ mesons (at $T_{\text{s}}=100\mathrm{MeV},\alpha =0)$. Bottom row: maps of internal efficiency of (c) PSB, and (d) MMRPC detectors, obtained with protons. See text for details.

Figure 4

(a) Transverse momentum distributions of ${\mathrm{K}}^{-}$ for seven rapidity bins in the region $0.34<y_{\text{lab}}<0.89$. Solid (dashed) curves denote the fitted (extrapolated) region. (b) Rapidity distribution of ${\mathrm{K}}^{-}$. Data for $y_{\text{lab}}$ above midrapidity (open circles) are the reflection of measured data points. Boxes indicate systematic errors of points within the selected binning. The dashed and dotted curves correspond to different extrapolation methods. The vertical line indicates the center of mass rapidity $y_{\text{NN}}^{\text{CM}}=0.89$. See text for details.

Figure 5

Kinetic energy distribution of $\varphi$ mesons fitted with Boltzmann-like function, assuming the following input parameters to the efficiency calculation: $T_{\text{s}}=100\mathrm{MeV},\alpha =0$ (see text for details).

Figure 6

Rapidity distribution of $T_{\text{B}}$ (apparent temperatures) for negative kaons within the one-source hypothesis (open squares), and two-source approach $({\mathrm{K}}^{-}$ from $\varphi$ decays: full triangles; direct kaons: open circles). Inverse slope of ${\mathrm{K}}^{+}$ $\left({\mathrm{K}}^{-}\right)$ obtained by the KaoS Collaboration is marked by full circle (square). See text for details.