Measuring $ψ′′→KS0KL0as a test of theS- andD-wave mixing of charmonia

Abstract

Adding to the long standing ``$\ensuremath{\rho}\ensuremath{\pi}$ puzzle'' in ${\ensuremath{\psi}}^{\ensuremath{'}}$ and $J/\ensuremath{\psi}$ decays, recently BEijing Spectrometer (BES) reported $\mathcal{B}({\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})$ which is enhanced relative to the perturbative QCD (pQCD) ``12% rule'' expectation from $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})$. If the enhancement is due to the mixing of the $S$- and $D$-wave charmonium states as in the $\ensuremath{\rho}\ensuremath{\pi}$ case, the newly measured $\mathcal{B}({\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})$ gives a constraint on $\mathcal{B}({\ensuremath{\psi}}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})$. It serves as a good test for the scenario of the $S$- and $D$-wave mixing in the ${\ensuremath{\psi}}^{\ensuremath{'}}$ and ${\ensuremath{\psi}}^{\ensuremath{'}\ensuremath{'}}$.