Unexpected large relative strong phase and search for isospin breaking and $CP$ asymmetries in $J/ψ\to K^*(892)\bar K

Abstract

Using a direct scan of 26 energy points near the $J/\ddot{I}ˆ$ resonance, we perform the first measurement of the relative phase $\ddot{I}{•}_{{\hat{I}}^3,3g}$ between the strong and electromagnetic amplitudes in $J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{\ast }(892{)}^0+c.c.$ and $J/\ddot{I}ˆ\to K^{+}{K}^{\ast }(892{)}^{-}+c.c.$. Unexpectedly, the phase in the neutral channel is found to be $\sim 150^{\circ }$, deviating from orthogonality ($90^{\circ }$) by 4.2$\ddot{I}ƒ$ and from a relative real amplitude (0${}^{\circ }$ or 180${}^{\circ }$) by 10.0$\ddot{I}ƒ$ or 1.6$\ddot{I}ƒ$, respectively. In contrast, the charged channel phase is consistent with $\sim 180^{\circ }$ within 1$\ddot{I}ƒ$, exhibiting model-dependent behavior. The corresponding branching fractions are consistent with the world averages but achieve better than twofold improvement in precision. The ratios between the branching fractions of $J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{\ast }(892{)}^0+c.c.$ and $J/\ddot{I}ˆ\to K^{+}{K}^{\ast }(892{)}^{-}+c.c.$ are also measured. After subtracting the electromagnetic contribution, the corresponding strong amplitude ratios obey isospin symmetry within $1.8\ddot{I}ƒ$. A search for direct $CP$ violation yields asymmetries consistent with zero.