Spin–orbit force from lattice QCD

We present a first attempt to determine nucleon–nucleon potentials in the parity-odd sector, which appear in the P11, P03, P13, P23–F23 channels, in Nf=2Nf=2 lattice QCD simulations. These potentials are constructed from the Nambu–Bethe–Salpeter wave functions for JP=0−,1− and 2−JP=0−,1− and 2−, which correspond to the A1−, T1− and T2−⊕E− representation of the cubic group, respectively. We have found a large and attractive spin–orbit potential VLS(r)VLS(r) in the isospin-triplet channel, which is qualitatively consistent with the phenomenological determination from the experimental scattering phase shifts. The potentials obtained from lattice QCD are used to calculate the scattering phase shifts in the P11, P03, P13 and P23–F23 channels. The strong attractive spin–orbit force and a weak repulsive central force in spin-triplet P  -wave channels lead to an attraction in the P23 channel, which is related to the P-wave neutron paring in neutron stars.