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 $J/ψ$ resonance, we perform the first measurement of the relative phase $ϕ_{γ, 3g}$ between the strong and electromagnetic amplitudes in $J/ψ\to\bar K^0 K^*(892)^0+c.c.$ and $J/ψ\to K^+ K^*(892)^-+c.c.$. Unexpectedly, the phase in the neutral channel is found to be $\sim 150^\circ$, deviating from orthogonality ($90^\circ$) by 4.2$σ$ and from a relative real amplitude (0$^\circ$ or 180$^\circ$) by 10.0$σ$ or 1.6$σ$, respectively. In contrast, the charged channel phase is consistent with $\sim 180^\circ$ within 1$σ$, 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 $J/ψ\to\bar K^0 K^*(892)^0+c.c.$ and $J/ψ\to K^+ K^*(892)^-+c.c.$ are also measured. After subtracting the electromagnetic contribution, the corresponding strong amplitude ratios obey isospin symmetry within $1.8σ$. A search for direct $CP$ violation yields asymmetries consistent with zero.