  We present a lattice QCD study of the puzzling positive-parity nucleon
channel, where the Roper resonance $N^*(1440)$ resides in experiment. The study
is based on an ensemble of gauge configurations with $N_f=2+1$ Wilson-clover
fermions with a pion mass of $156$ MeV and lattice size $L=2.9$ fm. We use
several $qqq$ interpolating fields combined with $N\pi$ and $N\sigma$
two-hadron operators in calculating the energy spectrum in the rest frame.
Combining experimental $N\pi$ phase shifts with elastic approximation and the
L\"uscher formalism suggests in the spectrum an additional energy level near
the Roper mass $m_R=1.43$ GeV for our lattice. We do not observe any such
additional energy level, which implies that $N\pi$ elastic scattering alone
does not render a low-lying Roper resonance. The current status indicates that
the $N^*(1440)$ might arise as dynamically generated resonance from coupling to
other channels, most notably the $N\pi\pi$.
