First Measurement of the Decay Dynamics in the Semileptonic Transition of the $D^{+(0)}$ into the Axial-vector Meson ${\bar{K}}_1(1270)$

Abstract

Using $e^{+}{e}^{-}$ data taken at the center-of-mass energy of 3.773 GeV with the BESIII detector, corresponding to an integrated luminosity of 20.3 fb${}^{-1}$, we report the first measurement of the decay dynamics of the semileptonic decays $D^{+(0)}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{0(-)}{e}^{+}\hat{I}{½}_e$. The amplitude analysis gives the hadronic form factors of the semileptonic $D$ transitions into the axial-vector meson ${\bar{K}}_1(1270)$ to be $r_A=(-11.2\pm 1.0_{\mathrm{stat}}\pm 0.9_{\mathrm{syst}})\times 10^{-2}$ and $r_V=(-4.3\pm 1.0_{\mathrm{stat}}\pm 2.5_{\mathrm{syst}})\times 10^{-2}$. This is the first in the semileptonic decays of heavy mesons into axial-vector mesons. The angular analysis yields an up-down asymmetry ${\mathcal{A}}_{ud}^{\prime }=0.01\pm 0.11$, which is consistent with the Standard Model prediction. In addition, the branching fractions of $D^{+}\to {\bar{K}}_1(1270{)}^0{e}^{+}\hat{I}{½}_e$ and $D^0\to K_1(1270{)}^{-}{e}^{+}\hat{I}{½}_e$ are determined with improved precision to be $(2.27\pm 0.11_{\mathrm{stat}}\pm 0.07_{\mathrm{syst}}\pm 0.07_{\mathrm{input}})\times 10^{-3}$ and $(1.02\pm 0.06_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}}\pm 0.03_{\mathrm{input}})\times 10^{-3}$, respectively. No significant signals of $D^{+}\to {\bar{K}}_1(1400{)}^0{e}^{+}\hat{I}{½}_e$ and $D^0\to K_1(1400{)}^{-}{e}^{+}\hat{I}{½}_e$ are observed and their branching fraction upper limits are set as $1.4\times 10^{-4}$ and $0.7\times 10^{-4}$ at 90\% confidence level, respectively.

15 pages, 6 figures, submitted to PRL