  Interpretation of CP violation measurements using charmonium decays, in both
the B0 and Bs systems, can be subject to changes due to "penguin" type
diagrams. These effects can be investigated using measurements of the
Cabibbo-suppressed B0->J/\psi pi+pi- decays. The final state composition of
this channel is investigated 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 is performed using both the invariant mass spectra and the decay
angular distributions. An improved measurement of the B0->J/\psi pi+pi-
branching fraction of (3.97 +/-0.09+/- 0.11 +/- 0.16)x10^{-5} is reported where
the first uncertainty is statistical, the second is systematic and the third is
due to the uncertainty of the branching fraction of the decay B- -> J/\psi K-
used as a normalization channel. In the J/\psi pi+pi- final state significant
production of f0(500) and rho(770) resonances is found, both of which can be
used for CP violation studies. In contrast evidence for the f0(980) resonance
is not found, thus establishing the first upper limit on the branching fraction
product B(B0->J/\psi f0(980) x B(f0(980)-> pi+ pi-) < 1.1x10^{-6}, leading to
an upper limit on the absolute value of the mixing angle of the f0(980)$ with
the f0(500) of <31 degrees, both at 90% confidence level.
