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

Abstract

We study the processes ${\hat{I}}^3{\hat{I}}^3\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }$ and ${\hat{I}}^3{\hat{I}}^3\to K^{+}{K}^{-}\ddot{I}{€}^0$ using a data sample of 519~$f{b}^{-1}$ 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 $\hat{I}\yen (nS)$ ($n=2,3,4$) resonances. We observe $\hat{I}{\cdot }_c$ 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 $I=1/2$ $K\ddot{I}€$ $\mathcal{S}$-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 $m=1931\pm 14\pm 22MeV/c^2$ and $\hat{I}“=271\pm 22\pm 29MeV$.

20 pages, 14 postscript figures, Submitted to Phys. Rev. D