Spectral ratio: an observable to determine $K^{+}$ nucleus potential and $K^{+}$ N scattering cross section

Here we aim to show that the ratio of the momentum spectra of $K^{+}$ at small transverse momentum measured for symmetric systems of different sizes can be such an observable.

$K^{+}$ and $K^{-}$ potentials in hadronic matter can be observed

We aim to show that K+ and K- spectra at low transverse momentum measured in light symmetric systems at around 2AGeV depend strongly on the K potential. The ratio of the spectra can allow therefore for a direct determination of the strength of the K+ as well as that of the K- potential in a hadronic environment.

In-medium effects on $K^{+}$ and $K^{-}$ spectra in lighter systems

We aim to explore the in-medium effects on the transverse momentum ($p_{T}$) spectra of $K^{+}$ and $K^{-}$ in lighter mass system $^{12}C+^{12}C$.

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.