Measurement of the I=1/2 $K\pi$ $\mathcal{S}$-wave amplitude from Dalitz plot analyses of ${\eta }_c\to K\bar{K}\pi$ in two-photon interactions

We study the processes $\gamma \gamma \to K_S^0{K}^{\pm }{\pi }^{\mp }$ and $\gamma \gamma \to K^+ K^- \pi^0$usingadatasampleof519$fb^{-1}$ recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies at and near the $\mathrm{{\rm Y}}(nS)$ ($n = 2,3,4$)resonances\mathrm{.}Weobserve$\eta_c$ decays to both final states and perform Dalitz plot analyses using a model-independent partial wave analysis technique. This allows a model-independent measurement of the mass-dependence of the $I=1\mathrm{/}2$ $K\pi$ $\mathcal{S}$-wave amplitude and phase. A comparison between the present measurement and those from previous experiments indicates similar behaviour for the phase up to a mass of 1.5 $GeV\mathrm{/}{c}^2$. In contrast, the amplitudes show very marked differences. The data require the presence of a new $a_0(1950)$ resonance with parameters $m=1931\pm 14\pm 22MeV\mathrm{/}{c}^2$ and $\mathrm{\Gamma }=271\pm 22\pm 29MeV$.