Observation of significant flavor-SU(3) breaking in the kaon wave function at $12~{\rm GeV}^2<Q^2<25~{\rm GeV}^2$ and discovery of the charmless decay $ψ(3770)\to K_S^0K_L^0$

Abstract: We present cross sections for the reaction $e^+e^-\to K_S^0K_L^0$ 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 ($12~{\rm GeV}^2<Q^2<25~{\rm GeV}^2$) 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 $|F(\pi^{\pm})|/|F(K^{\pm})|=f^2_{\pi}/f^2_{K}$, where $F(\pi^{\pm})$ and $F(K^{\pm})$ are the form factors, and $f_{\pi}$ and $f_{K}$ are the decay constants of charged pions and kaons, respectively. We also observe a significant signal for the charmless decay $\psi(3770)\to K_S^0K_L^0$ for the first time. Within a $1\sigma$ contour of the likelihood value, the the branching fraction for $\psi(3770)\to K_S^0K_L^0$ is determined to be ${\cal B}=(2.63_{-1.59}^{+1.40})\times 10^{-5}$, and the relative phase between the continuum and $\psi(3770)$ amplitudes is $\phi=(-0.39_{-0.10}^{+0.05})\pi$. The branching fraction is in good agreement with the $\mathcal{S}$- and $\mathcal{D}$-wave charmonia mixing scheme proposed in the interpretation of the "$\rho\pi$ puzzle" between $J/\psi$ and $\psi(3686)$ decays.