Test of lepton universality and measurement of the form factors of D⁰ K^* (892) ^-^+_

We report a first study of the semileptonic decay D⁰ K^-⁰^+_ by analyzing an e^+e^- annihilation data sample of 7. 9~fb^-1 collected at the center-of-mass energy of 3. 773 GeV with the BESIII detector. The absolute branching fraction of D⁰ K^-⁰^+_ is measured for the first time to be (0. 729 0. 014 ₒₓ₀ₓ 0. 011 ₒₘₒₓ) \%. Based on an amplitude analysis, the S- wave contribution is determined to be (5. 76 0. 35 ₒₓ₀ₓ 0. 29 ₒₘₒₓ) \% of the total decay rate in addition to the dominated K^* (892) ^- component. The branching fraction of D⁰ K^* (892) ^-^+_ is given to be (2. 062 0. 039 ₒₓ₀ₓ 0. 032 ₒₘₒₓ) \%, which improves the precision of the world average by a factor of 5. Combining with the world average of B (D⁰ K^* (892) ^-e^+ₑ), the ratio of the branching fractions obtained is B (D⁰ K^{* (892) ^-^+_) }{ B (D⁰ K^* (892) ^-e^+ₑ) } = 0. 960. 08, in agreement with lepton flavor universality. Furthermore, assuming single-pole dominance parameterization, the most precise hadronic form factor ratios for D⁰ K^* (892) ^- ^+_ are extracted to be rₕ=V (0) /A₁ (0) =1. 37 0. 09 ₒₓ₀ₓ 0. 03 ₒₘₒₓ and r₂=A₂ (0) /A₁ (0) =0. 76 0. 06 ₒₓ₀ₓ 0. 02 ₒₘₒₓ.