Analysis of the D⁺→K^-π⁺e ⁺ν_e decay channel

Using 347.5fb^-1 of data recorded by the BABAR detector at the PEP-II electron-positron collider, 244×103 signal events for the D ⁺→K^-π⁺e⁺ν_e decay channel are analyzed. This decay mode is dominated by the K̄(892)0 contribution. We determine the K^̄*(892)0 parameters: mK(892)0=(895.4±0.2±0.2)MeV/c2, ΓK ^*(892)00=(46.5±0.3±0.2)MeV/c2, and the Blatt-Weisskopf parameter r_BW=2.1±0.5±0.5(GeV/c) ^-1, where the first uncertainty comes from statistics and the second from systematic uncertainties. We also measure the parameters defining the corresponding hadronic form factors at q2=0 (r_V=V(0)A ₁(0)=1.463±0.017±0.031, r₂=A ₂(0)A₁(0)=0.801±0.020±0.020) and the value of the axial-vector pole mass parametrizing the q2 variation of A₁ and A₂: m_A=(2.63±0.10±0.13)GeV/c2. The S-wave fraction is equal to (5.79±0.16±0.15)%. Other signal components correspond to fractions below 1%. Using the D⁺→K ^-π⁺π⁺ channel as a normalization, we measure the D⁺ semileptonic branching fraction: B(D ⁺→K^-π⁺e⁺ν_e)= (4.00±0.03±0.04±0.09)×10^-2, where the third uncertainty comes from external inputs. We then obtain the value of the hadronic form factor A₁ at q2=0: A₁(0)=0.6200±0. 0056±0.0065±0.0071. Fixing the P-wave parameters, we measure the phase of the S wave for several values of the Kπ mass. These results confirm those obtained with Kπ production at small momentum transfer in fixed target experiments.