Observation of $D\to {\bar{K}}_1(1270)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and test of lepton flavor universality with $D\to {\bar{K}}_1(1270){\ell }^{+}\hat{I}{½}_{\ell }$

Abstract

By analyzing 7.93 $\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider, we report the observation of the semimuonic decays of $D^{+}\to {\bar{K}}_1(1270{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^0\to K_1(1270{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ with statistical significances of $12.5\ddot{I}ƒ$ and $6.0\ddot{I}ƒ$, respectively. Their decay branching fractions are determined to be $\mathcal{B}[D^{+}\to {\bar{K}}_1(1270{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]=(2.36\pm 0.20_{-0.27}^{+0.18}\pm 0.48)\times 10^{-3}$ and $\mathcal{B}[D^0\to K_1(1270{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]=(0.78\pm 0.11_{-0.09}^{+0.05}\pm 0.15)\times 10^{-3}$, where the first and second uncertainties are statistical and systematic, respectively, and the third originates from the input branching fraction of ${\bar{K}}_1(1270{)}^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0$ or $K_1(1270{)}^{-}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. Combining our branching fractions with the previous measurements of $\mathcal{B}[D^{+}\to {\bar{K}}_1(1270{)}^0{e}^{+}\hat{I}{½}_e]$ and $\mathcal{B}[D^0\to K_1(1270{)}^{-}{e}^{+}\hat{I}{½}_e]$, we determine the branching fraction ratios to be $\mathcal{B}[D^{+}\to {\bar{K}}_1(1270{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]/\mathcal{B}[D^{+}\to {\bar{K}}_1(1270{)}^0{e}^{+}\hat{I}{½}_e]=1.03\pm 0.14\begin{array}{c}+0.11\\ -0.15\end{array}$ and $\mathcal{B}[D^0\to K_1(1270{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]/\mathcal{B}[D^0\to K_1(1270{)}^{-}{e}^{+}\hat{I}{½}_e]=0.74\pm 0.13\begin{array}{c}+0.08\\ -0.13\end{array}$. Using the branching fractions measured in this work and the world-average lifetimes of the $D^{+}$ and $D^0$ mesons, we determine the semimuonic partial decay width ratio to be $\hat{I}“[D^{+}\to {\bar{K}}_1(1270{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]/\hat{I}“[D^0\to K_1(1270{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼]=1.22\pm 0.10\begin{array}{c}+0.06\\ -0.09\end{array}$, which is consistent with unity as predicted by isospin conservation.

11 pages, 5 figures