Observation of $D\to \bar{K}_{1}(1270)μ^+ν_μ$ and test of lepton flavor universality with $D\to \bar{K}_1(1270) \ell^{+} ν_{\ell}$

Abstract

By analyzing 7.93 $\rm fb^{-1}$ 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 $D^+\to \bar K_1(1270)^0μ^+ν_μ$ and $D^0\to K_1(1270)^-μ^+ν_μ$ with statistical significances of $12.5σ$ and $6.0σ$, respectively. Their decay branching fractions are determined to be ${\mathcal B}[D^{+}\to \bar{K}_1(1270)^0 μ^{+}ν_μ]=(2.36\pm0.20^{+0.18}_{-0.27}\pm 0.48)\times10^{-3}$ and ${\mathcal B}[D^{0}\to K_1(1270)^{-} μ^{+}ν_μ]=(0.78\pm0.11^{+0.05}_{-0.09}\pm 0.15)\times10^{-3}$, where the first and second uncertainties are statistical and systematic, respectively, and the third originates from the input branching fraction of $\bar K_{1}(1270)^0\to K^- π^+π^0$ or $K_1(1270)^-\to K^-π^+π^-$. Combining our branching fractions with the previous measurements of ${\mathcal B}[D^+\to \bar K_1(1270)^0e^+ν_{e}]$ and ${\mathcal B}[D^0\to K_1(1270)^-e^+ν_{e}]$, we determine the branching fraction ratios to be ${\mathcal B}[D^+\to \bar K_1(1270)^0μ^+ν_μ]/{\mathcal B}[D^+\to \bar K_1(1270)^0e^+ν_{e}]=1.03 \pm 0.14 \substack{+0.11\\-0.15}$ and ${\mathcal B}[D^0\to K_1(1270)^-μ^+ν_μ]/{\mathcal B}[D^0\to K_1(1270)^-e^+ν_{e}]=0.74\pm 0.13 \substack{+0.08\\-0.13}$. 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 $Γ[D^+\to \bar K_1(1270)^0 μ^+ν_μ]/Γ[D^0\to K_1(1270)^- μ^+ν_μ]=1.22\pm 0.10\substack{+0.06\\-0.09}$, which is consistent with unity as predicted by isospin conservation.