Observation of Significant Flavor-SU(3) Breaking in the Kaon Wave Function at 12 < Q² < 25 GeV² and Discovery of the Charmless Decay (3770) K_S⁰K_L⁰

We present cross sections for the reaction e(+)e(-) -> (KSKL0)-K-0 at center-of-mass energies ranging from 3.51 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 < Q(2) < 25 GeV2) is determined to be 0.21 +/- 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 vertical bar F(pi(+/-))vertical bar/vertical bar F(K-+/-)vertical bar = f(pi)(2)/f(K)(2), where F(pi(+/-)) and F(K-+/-) 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)->(KSKL0)-K-0 for the first time. Within a 1 sigma contour of the likelihood value, the branching fraction for psi(3770)-> K K-0(S)L(0) is determined to be B=(2.63(-1.59)(+1.40)) x 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 S- and D-wave charmonia mixing scheme proposed in the interpretation of the "rho pi puzzle" between J/psi and psi(3686) decays.