The squeeze-out phenomenon of $K^+$ and $K^-$ mesons, i.e. the azimuthal asymmetry of $K^+$ and $K^-$ mesons emitted at midrapidity in heavy ion reactions, is investigated for beam energies of 1-2 A.GeV. It is found that the squeeze-out signal is strongly affected by in-medium potentials of these mesons. The repulsive $K^+$-nucleus potential gives rise to a pronounced out-of-plane emission of $K^+$s at midrapidity. With the $K^+$ potential we reproduce well the experimental data of the $K^+$ azimuthal distribution. It is found that the attractive $K^-$-nucleus potential cancels to a large extent the influence of rescattering and reabsorption of the $K^-$ mesons on the projectile and target residuals (i.e. shadowing). This results in an azimuthally isotropic emission of the midrapidity $K^-$ mesons with transverse momentum up to 0.8 GeV/c. Since it is well accepted that the shadowing alone would lead to a significant out-of-plane preference of particle emission, in particular at high transverse momenta, the disappearance of the out-of-plane preference for the $K^-$ mesons can serve as an unambiguous signal of the attractive $K^-$ potential. We also apply a covariant formalism of the kaon dynamics to the squeeze-out phenomenon. Discrepancies between the theory and the experiments and possible solutions are discussed.
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