Observation of $ D\to {\overline{K}}_{1}(1270){\mu }^{+}{\nu }_{\mu }$ and test of lepton flavor universality with $ D\to {\overline{K}}_{1}(1270){\ell }^{+}{\nu }_{\ell }$

By analyzing $ 7.93\text{}\text{}{\mathrm{fb}}^{-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 {\overline{K}}_{1}(1270{)}^{0}{\mu }^{+}{\nu }_{\mu }$ and $ {D}^{0}\to {K}_{1}(1270{)}^{-}{\mu }^{+}{\nu }_{\mu }$ with statistical significances of $ 12.5\sigma $ and $ 6.0\sigma $, respectively. Their decay branching fractions are determined to be $ \mathcal{B}[{D}^{+}\to {\overline{K}}_{1}(1270{)}^{0}{\mu }^{+}{\nu }_{\mu }]=(2.36\pm 0.2{0}_{-0.27}^{+0.18}\pm 0.48)\times {10}^{-3}$ and $ \mathcal{B}[{D}^{0}\to {K}_{1}(1270{)}^{-}{\mu }^{+}{\nu }_{\mu }]=(0.78\pm 0.1{1}_{-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 $ {\overline{K}}_{1}(1270{)}^{0}\to {K}^{-}{\pi }^{+}{\pi }^{0}$ or $ {K}_{1}(1270{)}^{-}\to {K}^{-}{\pi }^{+}{\pi }^{-}$. Combining our branching fractions with the previous measurements of $ \mathcal{B}[{D}^{+}\to {\overline{K}}_{1}(1270{)}^{0}{e}^{+}{\nu }_{e}]$ and $ \mathcal{B}[{D}^{0}\to {K}_{1}(1270{)}^{-}{e}^{+}{\nu }_{e}]$, we determine the branching fraction ratios to be $ \mathcal{B}[{D}^{+}\to {\overline{K}}_{1}(1270{)}^{0}{\mu }^{+}{\nu }_{\mu }]/\mathcal{B}[{D}^{+}\to {\overline{K}}_{1}(1270{)}^{0}{e}^{+}{\nu }_{e}]=1.03\pm {0.14}_{-0.15}^{+0.11}$ and $ \mathcal{B}[{D}^{0}\to {K}_{1}(1270{)}^{-}{\mu }^{+}{\nu }_{\mu }]/\mathcal{B}[{D}^{0}\to {K}_{1}(1270{)}^{-}{e}^{+}{\nu }_{e}]=0.74\pm {0.13}_{-0.13}^{+0.08}$. 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 $ \mathrm{\Gamma }[{D}^{+}\to {\overline{K}}_{1}(1270{)}^{0}{\mu }^{+}{\nu }_{\mu }]/\phantom{\rule{0ex}{0ex}}\mathrm{\Gamma }[{D}^{0}\to {K}_{1}(1270{)}^{-}{\mu }^{+}{\nu }_{\mu }]=1.22\pm {0.10}_{-0.09}^{+0.06}$, which is consistent with unity as predicted by isospin conservation.