The decay Bs->J/psipi+pi- can be exploited to study CP violation. A detailed understanding of its structure is imperative in order to optimize its usefulness. An analysis of this three-body final state is performed using a 1.0/fb sample of data produced in 7 TeV pp collisions at the LHC and collected by the LHCb experiment. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. The pi+pi- system is shown to be dominantly in an S-wave state, and the CP-odd fraction in this Bs decay is shown to be greater than 0.977 at 95% confidence level. In addition, we report the first measurement of the J/psipi+pi- branching fraction relative to J/psiphi of (19.79 +/- 0.47 +/- 0.52)%.
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