Medium effects in proton-induced $K^0$ production at 3.5 GeV

We present the analysis of the inclusive $K^0$ production in $p+p$ and $p+\mathrm{Nb}$ collisions measured with the HADES detector (GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt) at a beam kinetic energy of 3.5 GeV. Data are compared to the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport model. The data suggest the presence of a repulsive momentum-dependent kaon potential as predicted by the chiral perturbation theory (ChPT). For the kaon at rest and at normal nuclear density, the ChPT potential amounts to $\approx 35$ MeV. A detailed tuning of the kaon production cross sections implemented in the model has been carried out to reproduce the experimental data measured in $p+p$ collisions. The uncertainties in the parameters of the model were examined with respect to the sensitivity of the experimental results from $p+\mathrm{Nb}$ collisions to the in-medium kaon potential.

Figure 1

Total specific energy loss in the MDCs versus momentum of the particle. Charged pions are selected with the help of two-dimensional $dE/dx$ cuts (shown by dotted curves).

Figure 2

Invariant mass distribution of ${\pi }^{+}{\pi }^{-}$ pairs in $p+\mathrm{Nb}$ collisions after topological cuts showing a $K_S^0$ signal, characterised by a (extracted by a fit) mass of $M_{K_S^0}=495.2\pm 0.02 \mathrm{MeV}/c^2$ and a width of ${\sigma }_{K_S^0}=7.29\pm 0.05$ $\mathrm{MeV}/c^2$. The number of reconstructed $K_S^0$ amounts to $N_{K_S^0}=(325.0\pm 0.7)\times {10}^3$.

Figure 3

$K_S^0$ transverse momentum spectra in $p+p$ collisions: experimental data (black circles) and GiBUU transport model simulations (dashed curves–original resonance model [30], solid curves–modified resonance model; see text). Systematic uncertainties due to the efficiency correction and absolute normalization are indicated by shaded boxes and red horizontal dashes, respectively.

Figure 4

$K_S^0$ rapidity distribution in $p+p$ collisions (black circles) and GiBUU transport model simulations (dashed curve–original resonance model [30], solid curve–modified resonance model; see text).

Figure 5

Energy dependence of the total cross section of inclusive kaon production (squares–$K^{+}$ [44], triangles–$K^0$ [45]) in proton-proton collisions.

Figure 6

$K_S^0$ transverse momentum spectra in $p+\mathrm{Nb}$ collisions: experimental data (black circles) and GiBUU transport model simulations with (cyan) and without (blue) in-medium ChPT KN potential. The widths of the bands indicate the statistical uncertainties of the simulated data sample. The long-dashed curve shows the total contribution of all $K^0$ production channels excluding $pp$ and $np$ collisions. Major secondary processes are $\Delta N$ reactions (dotted curve), $\pi N$ reactions (hatched area), and the contribution from the charge-exchange reactions $K^{+}N\to K^{0}N\left(\pi \right)$ (dash-dotted curve).

Figure 7

In-medium ChPT kaon potential $U=E^{*}-E$ (in MeV) as a function of the baryonic density and the kaon momentum.

Figure 8

${\chi }^2$ values for different variations of the parameters entering the model. Empty circles–simulations without potential, filled circles–simulations with potential ($\approx 35$ MeV at ${\rho }_B={\rho }_0$). Crosses correspond to the less repulsive potential ($\approx 25$ MeV) and triangles to the more repulsive one ($\approx 45$ MeV). See text and Table 2 for the description of different parameter sets.

Figure 9

$K_S^0$ rapidity distribution in the nucleon-nucleon center-of-mass reference frame for $p+\mathrm{Nb}$ collisions (filled circles) and GiBUU transport model simulations with (cyan) and without (blue) the in-medium ChPT $KN$ potential. The long-dashed curve shows the total contribution of all $K^0$ production channels excluding $pp$ and $np$ collisions. Major secondary processes are $\Delta N$ reactions (dotted curve), $\pi N$ reactions (hatched area), and the contribution from the charge-exchange reactions $K^{+}N\to K^{0}N\left(\pi \right)$ (dash-dotted curve).

Figure 10

Momentum dependence of the nuclear modification factor $R_{\mathrm{Nb}/\mathrm{p}}\left(p\right)\propto {\sigma }_{p\mathrm{Nb}}^{K^0}/{\sigma }_{pp}^{K^0}$. Symbols correspond to the experimental data and bands to GiBUU simulations. Only statistical uncertainties are shown.

Figure 11

Nuclear modification factor $R_{\mathrm{Au}/\mathrm{Nb}}\propto {\sigma }_{p\mathrm{Au}}^{K^{+}}/{\sigma }_{p\mathrm{Nb}}^{K^0}$. Only statistical uncertainties (originating from both HADES and KaoS measurements) are shown.

Figure 12

Nuclear modification factor $R_{\mathrm{Nb}/\mathrm{C}}\left(p\right)\propto {\sigma }_{p\mathrm{Nb}}^{K^0}/{\sigma }_{p\mathrm{C}}^{K^{+}}$.

Figure 13

Ratio of $K^0$ momentum spectra reconstructed in two bins of the polar angle (black circles) and GiBUU transport model simulations with (cyan) and without (blue) repulsive kaon potential.

Figure 14

Pull values [defined by Eq. (7)] for different variations of the parameters entering the model. Empty circles–simulations without potential, filled circles–simulations with potential ($\approx 35$ MeV at ${\rho }_B={\rho }_0$). Crosses correspond to the less repulsive potential ($\approx 25$ MeV) and triangles to the more repulsive one ($\approx 45$ MeV). See text and Table 2 for the description of different parameter sets.