Observation of significant flavor-SU(3) breaking in the kaon wave function at $12{\mathrm{GeV}}^2<Q^2<25{\mathrm{GeV}}^2$ and discovery of the charmless decay $\ddot{I}ˆ(3770)\to K_S^0{K}_L^0$

Abstract

We present cross sections for the reaction $e^{+}{e}^{-}\to K_S^0{K}_L^0$ at center-of-mass energies ranging from 3.51 GeV to 4.95 GeV using data samples collected in the BESIII experiment, corresponding to a total integrated luminosity of 26.5 fb${}^{-1}$. The ratio of neutral-to-charged kaon form factors at large momentum transfers ($12{\mathrm{GeV}}^2<Q^2<25{\mathrm{GeV}}^2$) is determined to be $0.21\pm 0.01$, which indicates a small but significant effect of flavor-SU(3) breaking in the kaon wave function, and consequently excludes the possibility that flavor-SU(3) breaking is the primary reason for the strong experimental violation of the pQCD prediction $|F(\ddot{I}{€}^{\pm })|/|F(K^{\pm })|=f_{\ddot{I}}^2€/f_K^2$, where $F(\ddot{I}{€}^{\pm })$ and $F(K^{\pm })$ are the form factors, and $f_{\ddot{I}}€$ and $f_K$ are the decay constants of charged pions and kaons, respectively. We also observe a significant signal for the charmless decay $\ddot{I}ˆ(3770)\to K_S^0{K}_L^0$ for the first time. Within a $1\ddot{I}ƒ$ contour of the likelihood value, the the branching fraction for $\ddot{I}ˆ(3770)\to K_S^0{K}_L^0$ is determined to be $\mathcal{B}=(2.63_{-1.59}^{+1.40})\times 10^{-5}$, and the relative phase between the continuum and $\ddot{I}ˆ(3770)$ amplitudes is $\ddot{I}•=(-0.39_{-0.10}^{+0.05})\ddot{I}€$. The branching fraction is in good agreement with the $\mathcal{S}$- and $\mathcal{D}$-wave charmonia mixing scheme proposed in the interpretation of the "$\ddot{I}\ddot{I}€$ puzzle" between $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ decays.

18 pages, 56 figures