We address the issue of bound state in the two-nucleon system in lattice QCD.
Our study is made in the quenched approximation at the lattice spacing of a =
0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. To
distinguish a bound state from an attractive scattering state, we investigate
the volume dependence of the energy difference between the ground state and the
free two-nucleon state by changing the spatial extent of the lattice from 3.1
fm to 12.3 fm. A finite energy difference left in the infinite spatial volume
limit leads us to the conclusion that the measured ground states for not only
spin triplet but also singlet channels are bounded. Furthermore the existence
of the bound state is confirmed by investigating the properties of the energy
for the first excited state obtained by 2x2 diagonalization method. The
scattering lengths for both channels are evaluated by applying the finite
volume formula derived by Luscher to the energy of the first excited states.Comment: 34 pages, 28 figure
