Kaon pair production in proton-nucleus collisions at 2.83 GeV kinetic energy

The production of non-$\varphi K^{+}{K}^{-}$ pairs by protons at 2.83 GeV kinetic energy on C, Cu, Ag, and Au targets has been investigated by using the COSY-ANKE magnetic spectrometer. The $K^{-}$ momentum dependence of the differential cross section has been measured for laboratory polar angles ${\theta }_{K^{\pm }}\le {12}^{\circ }$ over the 0.2–0.9 GeV/$c$ range. The comparison of the data with detailed model calculations indicates an attractive $K^{-}$-nucleus potential of about $-60$ MeV at normal nuclear matter density at a mean momentum of 0.5 GeV/$c$. However, this approach has difficulty in reproducing the smallness of the observed cross sections at low-$K^{-}$ momenta.

Figure 1

Time-of-flight difference between the stop counters in the negative and positive detection systems for the carbon target. The left and right peaks contain the $K^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ events, respectively.

Figure 2

Invariant mass $\left(\mathit{IM}\right)$ distribution for $K^{+}{K}^{-}$ pairs produced in $p$-C collisions at 2.83 GeV beam energy. The vertical line indicates the cut $\mathit{IM}\le 1.005$ GeV/$c^2$ used for the separation of the non-$\varphi$ and $\varphi$-rich regions.

Figure 3

Double-differential cross sections for the production of nonresonant $K^{+}{K}^{-}$ pairs in the ANKE acceptance in the collisions of 2.83 GeV protons with (a) C, (b) Cu, (c) Ag, and (d) Au targets as functions of the $K^{-}$ laboratory momentum. The experimental data, which are taken from from Table 1, are averaged over small kaon angles, ${\theta }_{K^{\pm }}\le {12}^{\circ }$, and over $K^{+}$ momenta in the range $200\le p_{K^{+}}\le 600$ MeV/$c$. The curves represent, from the bottom to top, model calculations [44] for $K^{-}$ potential depths $U=0$ MeV (long dashed), $-60$ MeV (dot long dashed), $-126$ MeV (short dashed), and $-180$ MeV (dot short dashed), respectively. The solid lines are simple spline functions through the experimental data points.

Figure 4

Ratio of the measured integrated cross section for nonresonant $K^{+}{K}^{-}$ pair production on a given nucleus $A$ to the corresponding cross sections, calculated within the adopted model and supposing four values for the $K^{-}$ potential depth at nuclear matter density: $U=0$ MeV, $-60$ MeV, $-126$ MeV, and $-180$ MeV. The curve represents a third-order polynomial fit of all ratios presented in the figure, with the shaded band indicating the $1\sigma$ confidence interval. The pair of vertical dotted lines corresponds to the regions where the ratio is unity within the errors given by the third-order fit. The color code is identical to that shown explicitly in Fig. 3.

Figure 5

Ratios of the measured and calculated double-differential cross sections for nonresonant $K^{+}{K}^{-}$ pair production off (a) Au, (b) Ag, and (c) Cu targets presented in Fig. 3, to the measured and calculated ones for the C target, given also in the same figure as functions of the $K^{-}$ laboratory momentum. The color code and the notation of the curves are the same as those in Fig. 3.