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

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 +νμ)=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+νμ)/Γ(D +→K̄0μ+νμ)=0. 594±0.043±0.033 and the ratio Γ(D+→K̄ 0μ+νμ)/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+) νμ,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)%.