Measurements of charmless hadronic b{yields}s penguin decays in the {pi}{sup +}{pi}{sup -}K{sup +}{pi}{sup -} final state and first observation of B{sup 0}{yields}{rho}{sup 0}K{sup +}{pi}{sup -}

We report measurements of charmless hadronic B{sup 0} decays into the {pi}{sup +}{pi}{sup -}K{sup +}{pi}{sup -} final state. The analysis uses a sample of 657x10{sup 6} BB pairs collected with the Belle detector at the KEKB asymmetric-energy e{sup +}e{sup -} collider at the resonance. The decay B{sup 0}{yields}{rho}{sup 0}K{sup +}{pi}{sup -} is observed for the first time; the significance is 5.0{sigma} and the corresponding partial branching fraction for M{sub K{pi}} is an element of (0.75,1.20) GeV/c{sup 2} is [2.8{+-}0.5(stat){+-}0.5(syst)]x10{sup -6}. We also obtain the first evidence for B{sup 0}{yields}f{sub 0}(980)K{sup +}{pi}{sup -} with 3.5{sigma} significance and for B{sup 0}{yields}{pi}{sup +}{pi}{sup -}K*{sup 0} with 4.5{sigma} significance. For the two-body decays B{sup 0}{yields}{rho}{sup 0}K*{sup 0} and B{sup 0}{yields}f{sub 0}(980)K*{sup 0}, the significances are 2.7{sigma} and 2.5{sigma}, respectively, and the upper limits on the branching fractions are 3.4x10{sup -6} and 2.2x10{sup -6} at 90% confidence level.