Improved measurements of D⁰ K^-^+_ and D^+ K⁰^+_

Using 7. 93 fb^-1 of e^+e^- collision data collected at the center-of-mass energy of 3. 773 GeV with the BESIII detector, we measure the absolute branching fractions of D⁰ K^-e^+ₑ, D⁰ K^-^+_, D^+ K⁰e^+ₑ, and D^+ K⁰^+_ to be (3. 5090. 009 ₒₓ₀ₓ. 0. 013 ₒₘₒₓ. ) \%, (3. 4080. 011 ₒₓ₀ₓ. 0. 013 ₒₘₒₓ. ) \%, (8. 8560. 039 ₒₓ₀ₓ. 0. 078 ₒₘₒₓ. ) \%, and (8. 6610. 046 ₒₓ₀ₓ. 0. 080 ₒₘₒₓ. ) \%, respectively. By performing a simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor fK_+ (0) and the modulus of the c s CKM matrix element |V₂ₒ| is determined to be fK_+ (0) |V₂ₒ|=0. 71620. 0011 ₒₓ₀ₓ. 0. 0012 ₒₘₒₓ. . Taking the value of |V₂ₒ|=0. 973490. 00016 from the standard model global fit or that of fK_+ (0) =0. 74520. 0031 from the LQCD calculation as input, we derive the results fK_+ (0) =0. 73570. 0011 ₒₓ₀ₓ. 0. 0012 ₒₘₒₓ. and |V₂ₒ|=0. 96110. 0015 ₒₓ₀ₓ. 0. 0016 ₒₘₒₓ. 0. 0040 ₋ₐ₂₃.