Measurement of the ratio of the vector to pseudoscalar charm semileptonic decay rate Γ (D⁺ → K̄ *⁰μ⁺ν_μ)/Γ (D⁺ → K̄⁰μ⁺ν_μ)

Using a high statistics sample of photo-produced charm particles from the FOCUS experiment at Fermilab, we report on the measurement of the ratio of semileptonic rates Γ(D⁺→Kπμ⁺ν _μ)/Γ(D⁺→K̄⁰μ ⁺ν_μ)=0.625±0.045±0.034. Allowing for the Kπ S-wave interference measured in [J.M. Link, et al., FOCUS Collaboration, Phys. Lett. B 544 (2002) 89], we extract the vector to pseudoscalar ratio Γ(D⁺→K̄ *⁰μ⁺ν_μ)/Γ(D ⁺→K̄⁰μ⁺ν_μ)=0. 594±0.043±0.033 and the ratio Γ(D⁺→K̄ ⁰μ⁺ν_μ)/Γ(D⁺→ K^-π⁺π⁺)=1.019±0.076±0.065. Our results show a lower ratio for Γ(D→K*ℓν)/ Γ(D→Kℓν) than has been reported recently and indicate the current world average branching fractions for the decays D ⁺→K̄⁰(μ⁺,e⁺) ν_μ,e are low. Using the world average B(D⁺→ K^-π⁺π⁺) [K. Hagiwara, et al., Particle Data Group Collaboration, Phys. Rev. D 66 (2002) 010001, and 2003 partial update for edition 2004 (http://pdg.lbl.gov)] we extract B(D⁺→K̄ ⁰μ⁺ν)=(9.27±0.69±0.59±0.61)%.