We present a measurement of the branching fraction for the decay of the neutral B meson into the final state J/psipi(+)pi(-). The data set contains approximately 56x10(6) B (B) over bar pairs produced at the Y(4S) resonance and recorded with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) storage ring. The result of this analysis is B(B-0-->J/psipi(+)pi(-))=(4.6+/-0.7+/-0.6)x10(-5), where the first error is statistical and the second is systematic. In addition, we measure B(B-0-->J/psirho(0))=(1.6+/-0.6+/-0.4)x10(-5).
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