Combined analysis of the $K^{+}K^{-}$ interaction using near threshold $pp \to ppK^+K^-$ data

The $K^{+}K^{-}$ final state interaction was investigated based on both the $K^{+}K^{-}$ invariant mass distributions measured at excess energies of Q = 10 and 28 MeV and the near threshold excitation function for the $pp \to ppK^{+}K^{-}$ reaction. The $K^+K^-$ final state enhancement factor was parametrized using the effective range expansion. The effective range of the $K^+K^-$ interaction was estimated to be: $\mathrm{Re}(b_{K^{+}K^{-}}) = -0.1 \pm 0.4_{stat} \pm 0.3_{sys} \mathrm{fm}$ and $\mathrm{Im}(b_{K^{+}K^{-}}) = 1.2^{+0.1_{stat}+0.2_{sys}}_{-0.2_{stat}-0.0_{sys}} \mathrm{fm}$, and the determined real and imaginary parts of the $K^+K^-$ scattering length amount to: $|\mathrm{Re}(a_{K^{+}K^{-}})| = 8.0^{+6.0_{stat}}_{-4.0_{stat}} \mathrm{fm}$ and $\mathrm{Im}(a_{K^{+}K^{-}}) = 0.0^{+20.0_{stat}}_{-5.0_{stat}} \mathrm{fm}$.