First Observation of $D^{0(+)}\to \bar{K}\ddot{I}‰e^{+}\hat{I}{½}_e$ and Determination of the Branching Fraction of ${\bar{K}}_1(1270)\to \bar{K}\ddot{I}‰$

Abstract

Using 20.3~fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector, we report the first observation of the semileptonic decays \mbox{$D^0\to K^{-}\ddot{I}‰e^{+}\hat{I}{½}_e$} and \mbox{$D^{+}\to K_S^0\ddot{I}‰e^{+}\hat{I}{½}_e$} with significances of $8.0\ddot{I}ƒ$ and $5.8\ddot{I}ƒ$, respectively. Their decay branching fractions are measured to be $\mathcal{B}(D^0\to K^{-}\ddot{I}‰e^{+}\hat{I}{½}_e)=(9.4_{-1.8}^{+2.0}\pm 0.6)\times 10^{-5}$ and $\mathcal{B}(D^{+}\to K_S^0\ddot{I}‰e^{+}\hat{I}{½}_e)=(8.0_{-2.1}^{+2.4}\pm 0.7)\times 10^{-5}$. Combining with the latest measurements of $D^{0(+)}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-(0)}{e}^{+}\hat{I}{½}_e$ and assuming ${\bar{K}}_1(1270)$ to be the sole mediating resonance in all processes, the branching ratios are determined to be $\frac{\hat{I}“(K_1(1270{)}^{-}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-})}{\hat{I}“(K_1(1270{)}^{-}\to K^{-}\ddot{I}‰)}=3.4_{-0.7}^{+0.8}\pm 0.3$ and $\frac{\hat{I}“({\bar{K}}_1(1270{)}^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0)}{\hat{I}“({\bar{K}}_1(1270{)}^0\to {\bar{K}}^0\ddot{I}‰)}=7.9_{-2.1}^{+2.4}\pm 0.7$. The combined branching fraction is determined to be $\mathcal{B}({\bar{K}}_1(1270)\to \bar{K}\ddot{I}‰)=(8.4\pm 1.4\pm 0.5)\%$, which is the most precise measurement from a collider experiment. Furthermore, %based on the $\bar{K}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ invariant mass spectra, for the first time based on a single vector-pseudoscalar decay channel, the ${\bar{K}}_1(1270)$ mass is measured to be $(1336\pm 9\pm 2)$~MeV/$c^2$, providing unique experimental support for the two-pole structure of the ${\bar{K}}_1(1270)$ resonance. The first uncertainties are statistical, and the second are systematic.