Study of the K⁺π⁺π^- final state in B⁺→J/ψK⁺π⁺π^- and B⁺→ψ^′K⁺π⁺π ^-

Using 535×106 B-meson pairs collected by the Belle detector at the KEKB e⁺e^- collider, we measure branching fractions of (7.16±0.10(stat)±0.60(syst)×10^-4 for B ⁺→J/ψK⁺π⁺π^- and (4.31±0.20(stat)±0.50(syst))×10^-4 for B ⁺→ψ^′K⁺π⁺π ^-. We perform amplitude analyses to determine the resonant structure of the K⁺π⁺π^- final state in B ⁺→J/ψK⁺π⁺π^- and B⁺→ψ^′K⁺π⁺π ^- and find that the K₁(1270) is a prominent component of both decay modes. There is significant interference among the different intermediate states, which leads, in particular, to a striking distortion of the ρ line shape due to the ω. Based on the results of the fit to the B⁺→J/ψK⁺π⁺π^- data, the relative decay fractions of the K₁(1270) to Kρ, Kω, and K^*(892)π are consistent with previous measurements, but the decay fraction to K0*(1430) is significantly smaller. Finally, by floating the mass and width of the K₁(1270) in an additional fit of the B⁺→J/ψK⁺π⁺π^- data, we measure a mass of (1248.1±3.3(stat)±1.4(syst))MeV/c2 and a width of (119.5±5.2(stat)±6.7(syst))MeV/c2 for the K ₁(1270).