K+ and K- potentials in hadronic matter are observable quantities

The comparison of $K^+$ and $K^-$ spectra at low transverse momentum in light symmetric heavy ion reactions at energies around 2 AGeV allows for a direct experimental determination of the strength of the $K^+$ as well as of t he $K^-$ nucleus potential. Other little known or unknown input quantities like the production or rescattering cross sections of $K^+$ and $K^-$ mesons do not spoil this signal. This result, obtained by simulations of these reactio ns with the Isospin Quantum Molecular Dynamics (IQMD) model, may solve the longstanding question of the behaviour of the $K^-$ in hadronic matter and especially whether a $K^-$ condensate can be formed in heavy ion collisions.

How to determine experimentally the K+ nucleus potential and the K+ N rescattering cross section in a hadronic environment?

Comparing K+ spectra at low transverse momenta for different symmetric collision systems at beam energies around 1 AGeV allows for a direct determination of both the strength of the K+ nucleus potential as well as of the K+N rescattering cross section in a hadronic environment. Other little known or unknown quantities which enter the K+ dynamics, like the production cross sections of K+ mesons or the hadronic equation of state, do not spoil this signal as they cancel by using ratios of spectra. This procedure is based on transport model calculations using the Isospin Quantum Molecular Dynamics (IQMD) model which describes the available data quantitatively.