Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi><mml:mo>π</mml:mo><mml:mtext> </mml:mtext><mml:mi mathvariant="script">S</mml:mi></mml:math>-wave amplitude from Dalitz plot analyses of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>η</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>π</mml:mi></mml:math>in two-photon interactions

We study the processes $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{K}_{S}^{0}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ and $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ using a data sample of $519\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded with the BABAR detector operating at the SLAC PEP-II asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider at center-of-mass energies at and near the $\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=2$, 3, 4) resonances. We observe ${\ensuremath{\eta}}_{c}$ 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 $I=1/2$ $K\ensuremath{\pi}\text{ }\mathcal{S}$-wave amplitude and phase. A comparison between the present measurement and those from previous experiments indicates similar behavior for the phase up to a mass of $1.5\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. In contrast, the amplitudes show very marked differences. The data require the presence of a new ${a}_{0}(1950)$ resonance with parameters $m=1931\ifmmode\pm\else\textpm\fi{}14\ifmmode\pm\else\textpm\fi{}22\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and $\mathrm{\ensuremath{\Gamma}}=271\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}29\text{ }\text{ }\mathrm{MeV}$.