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

Abstract 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 + → K π μ + ν μ ) / Γ ( D + → K ¯ 0 μ + 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 + → K ¯ * 0 μ + ν μ ) / Γ ( D + → K ¯ 0 μ + ν μ ) = 0.594 ± 0.043 ± 0.033 and the ratio Γ ( D + → K ¯ 0 μ + ν μ ) / Γ ( D + → K − π + π + ) = 1.019 ± 0.076 ± 0.065 . Our results show a lower ratio for Γ ( D → K * l ν ) / Γ ( D → K l ν ) than has been reported recently and indicate the current world average branching fractions for the decays D + → K ¯ 0 ( 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 + → K ¯ 0 μ + ν ) = ( 9.27 ± 0.69 ± 0.59 ± 0.61 ) % .