Study of $\ddot{I}•\to K\bar{K}$ in the amplitude analysis of $D^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+}$

Abstract

We present the first amplitude analysis and branching fraction measurement of $D^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+}$ decay. The analysis uses a dataset corresponding to an integrated luminosity of 20.3~$\mathrm{f}{\mathrm{b}}^{-1}$, which was recorded at a center-of-mass energy 3.773~GeV by the BESIII detector. The measured branching fraction is $\mathcal{B}(D^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+})=(5.780\pm 0.085\pm 0.052)\times 10^{-3}$, where the first uncertainty is statistical and the second is systematic. Using the known value of $\mathcal{B}(D^{+}\to \ddot{I}•\ddot{I}{€}^{+},\ddot{I}•\to K^{+}{K}^{-})$, we determine the relative branching fraction between $\ddot{I}•\to K_S^0{K}_L^0$ and $\ddot{I}•\to K^{+}{K}^{-}$ to be $\mathcal{B}(D^{+}\to \ddot{I}•\ddot{I}{€}^{+},\ddot{I}•\to K_S^0{K}_L^0)/\mathcal{B}(D^{+}\to \ddot{I}•\ddot{I}{€}^{+},\ddot{I}•\to K^{+}{K}^{-})=0.628\pm 0.022\pm 0.015\pm 0.017$, where the third uncertainty is related to $\mathcal{B}(D^{+}\to \ddot{I}•\ddot{I}{€}^{+},\ddot{I}•\to K^{+}{K}^{-})$. This result is significantly lower than the previous world average and is consistent with the isospin expectation for the $\ddot{I}•$ meson's coupling to charged and neutral kaon pairs.