Phenomenology of the $ppK^+K^-$ system near threshold

In this article studies of the near threshold $pp\to ppK^+K^-$ reaction conducted with the COSY-11 and the ANKE detectors are reviewed. In particular recent investigations on the $K^+K^-$ final state interaction are revisited taking into account updated cross sections of the COSY-11 experiment. These studies resulted in the new value of $K^+K^-$ effective range amounting to: $\mathrm{Re}(b_{K^{+}K^{-}}) = -0.2^{+0.8_{stat}~+0.4_{sys}}_{-0.6_{stat}~-0.4_{sys}}~\mathrm{fm}$ and $\mathrm{Im}(b_{K^{+}K^{-}}) = 1.2^{~+0.5_{stat}~+0.3_{sys}}_{~-0.3_{stat}~-0.3_{sys}}~\mathrm{fm}$. The determined real and imaginary parts of the $K^+K^-$ scattering length were estimated to be: $\left|\mathrm{Re}(a_{K^{+}K^{-}})\right| = 10^{~+17_{stat}}_{~-10_{stat}}~\mathrm{fm}$ and $\mathrm{Im}(a_{K^{+}K^{-}}) = 0^{~+37_{stat}}_{~-10_{stat}}~\mathrm{fm}$.