Influence of $\varphi$ mesons on negative kaons in Ni+Ni collisions at 1.91A GeV beam energy

$\varphi$ and K${}^{-}$ mesons from Ni+Ni collisions at the beam energy of 1.91A GeV have been measured by the FOPI spectrometer, with a trigger selecting central and semi-central events amounting to 51% of the total cross section. The phase space distributions, and the total yield of K${}^{-}$, as well as the kinetic energy distribution and the total yield of $\varphi$ mesons are presented. The $\varphi$\K${}^{-}$ ratio is found to be $0.44 \pm 0.07($\text{stat}$) ^{+0.18}_{-0.12} ($\text{syst}$)$,meaningthatabout22$^-$ mesons originate from the decays of $\varphi$ mesons, occurring mostly in vacuum. The inverse slopes of direct kaons are up to about 15 MeV larger than the ones extracted within the one-source model, signalling that a considerable share of gap between the slopes of K${}^{+}$ and K${}^{-}$ could be explained by the contribution of $\varphi$ mesons to negative kaons.