Measurement of the Branching Fraction For the Semi-Leptonic Decays $D^{0(+)}\to \ddot{I}{€}^{-(0)}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and Test of Lepton Flavor Universality

Abstract

Using a data sample corresponding to an integrated luminosity of $2.93\mathrm{f}{\mathrm{b}}^{-1}$ taken at a center-of-mass energy of 3.773\,GeV with the BESIII detector operated at the BEPCII collider, we perform an analysis of the semi-leptonic decays $D^{0(+)}\to \ddot{I}{€}^{-(0)}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$. The branching fractions of $D^0\to \ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^{+}\to \ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ are measured to be $(0.272\pm 0.008_{stat.}\pm 0.006_{syst.})\%$ and $(0.350\pm 0.011_{stat.}\pm 0.010_{syst.})\%$, respectively, where the former is of much improved precision compared to previous results and the latter is determined for the first time. Using these results along with previous BESIII measurements of $D^{0(+)}\to \ddot{I}{€}^{-(0)}{e}^{+}\hat{I}{½}_e$, we calculate the branching fraction ratios to be ${\mathcal{R}}^0\equiv {\mathcal{B}}_{D^0\to \ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}/{\mathcal{B}}_{D^0\to \ddot{I}{€}^{-}{e}^{+}\hat{I}{½}_e}=0.922\pm 0.030_{stat.}\pm 0.022_{syst.}$ and ${\mathcal{R}}^{+}\equiv {\mathcal{B}}_{D^{+}\to \ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}/{\mathcal{B}}_{D^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e}=0.964\pm 0.037_{stat.}\pm 0.026_{syst.}$, which are compatible with the theoretical expectation of lepton flavor universality within $1.7\ddot{I}ƒ$ and $0.5\ddot{I}ƒ$, respectively. We also examine the branching fraction ratios in different four-momentum transfer square regions, and find no significant deviations from the standard model predictions.