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

We study the processes $γγ\to K^0_S K^{\pm}π^{\mp}$ and $γγ\to K^+ K^- π^0$ using a data sample of 519~$fb^{-1}$ 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 $Υ(nS)$ ($n = 2,3,4$) resonances. We observe $η_c$ 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 $I=1/2$ $K π$ $\mathcal{S}$-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 $GeV/c^2$. In contrast, the amplitudes show very marked differences. The data require the presence of a new $a_0(1950)$ resonance with parameters $m=1931 \pm 14 \pm 22 \ MeV/c^2$ and $Γ=271 \pm 22 \pm 29 \ MeV$.

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