ϕ decay: A relevant source for $K^{-}$ production at energies available at the GSI Schwerionen-Synchrotron (SIS)?

We present phase space distributions and multiplicities of $K^{+}$, $K^{-}$, and ϕ mesons produced in $\mathrm{Ar}+\mathrm{KCl}$ reactions at a kinetic beam energy of 1.756 GeV/nucleon and measured with the HADES spectrometer. The inverse slope parameters and yields of kaons supplement the systematics of previous measurements. The percentage of $K^{-}$ mesons coming from ϕ decay is found to be $18\pm 7\%$.

Figure 1

Particle velocity $\beta$ (top, for the TOF detector) and $\mathit{dE}/\mathit{dx}$ (middle for the TOF detector, bottom for the MDC) as a function of the momentum times the particle's polarity sign for the TOF detector.

Figure 2

Polarity times mass over charge distributions for particle tracks measured in the TOF detector for different cut conditions. The spectrum on top (blue curve) shows the original distribution, whereas the lower two spectra show the effects of the graphical cuts in the TOF $\mathit{dE}/\mathit{dx}$ (green histogram) and additionally the MDC $\mathit{dE}/\mathit{dx}$ (red histogram) distributions, respectively.

Figure 3

Reconstructed mass distributions of $K^{+}$ (top) and $K^{-}$ mesons (bottom) for different phase space regions (left, $0.5<y<0.6$ and $100\hspace{0.5em}\mathrm{MeV}/c^2<m_t<150\hspace{0.5em}\mathrm{MeV}/c^2$; right, $0.4<y<0.5$ and $50\hspace{0.5em}\mathrm{MeV}/c^2<m_t<100\hspace{0.5em}\mathrm{MeV}/c^2$). The solid lines represent combined fits to the signal and background, whereas the dashed lines show the background part only.

Figure 4

Distribution of measured $K^{+}$ (top) and $K^{-}$ (bottom) yields in the TOF detector as a function of the subtracted transverse mass $m_t-m_{K^{\pm }}$ and the laboratory rapidity $y$. The color code refers to the counting rate. The dashed lines indicate the polar angles $\Theta ={15}^{°}$, ${45}^{°}$, and ${85}^{°}$ in the laboratory system. The dotted curves are for constant kaon momentum starting from $p=200$ MeV/$c$ in steps of 200 MeV/$c$. The vertical solid line depicts midrapidity.

Figure 5

Reconstruction efficiency for $K^{+}$ and $K^{-}$ as a function of the transverse mass for different rapidity intervals. The acceptances are not included (see text).

Figure 6

Invariant mass distribution of $K^{+}\text{−}{K}^{-}$ pairs (top). The combinatorial background (shaded area) is obtained by the mixed-event technique. The background-subtracted distribution (bottom) shows a ϕ meson signal (grey area with a Gaussian fit) with a total yield of $168\pm 18$ counts.

Figure 7

Invariant transverse mass spectra of reconstructed $K^{+}$ (left) and $K^{-}$ (right) mesons. For the sake of clarity the spectra are plotted for several laboratory rapidity bins, see legends. The spectra are scaled by the factors as indicated in the plots.

Figure 8

Invariant transverse mass spectrum of reconstructed ϕ mesons for the rapidity range $0.2<y<0.6$.

Figure 9

Rapidity dependence of the inverse slope parameters of $K^{+}$ (top) and $K^{-}$ (bottom) mesons. The full symbols show the measured data, whereas the open ones are reflected data with respect to the c.m. rapidity. The lines represents fits with Eq. (2).

Figure 10

Rapidity density distributions of $K^{+}$ (top) and $K^{-}$ (bottom) mesons. The solid symbols show the measured data, whereas the open ones are reflected data with respect to the c.m. rapidity. The curves represent Gaussian fits to the data. The overlayed dotted lines are simulated isotropic thermal distributions that have been normalized to the data (see text).

Figure 11

$K^{-}/K^{+}$ ratios as a function of the kinetic beam energy for various systems. The present HADES data point is depicted by the solid triangle. KaoS data are from Ref. [15].

Figure 12

$A_{\mathrm{part}}$ dependence of the $K^{-}/K^{+}$ ratio for different beam energies and colliding systems. The solid triangle depicts the present HADES data. The other symbols display KaoS results from Ref. [15]. The dashed lines show the prediction of a thermal model [49, 50] for kinetic beam energies of 1.5, 1.76, and 1.93 GeV/nucleon (from bottom to top).

Figure 13

$\varphi /K^{-}$ ratio as a function of center-of-mass energy $\sqrt{s_{\mathit{NN}}}$. The solid triangle on the left shows the HADES point, whereas the other data points represented by solid triangles refer to results from heavy-ion measurements at higher incident energies [52, 53, 54]. The open circle presents the value measured in $p+p$ at 2.7 GeV [27]. The lines are predictions of a statistical model [49, 50] for four parameters of the correlation radius $R_C$.