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 ¹P₁, ³P₀, ³P₁, ³P₂–³F₂ channels, in N_f=2 lattice QCD simulations. These potentials are constructed from the Nambu–Bethe–Salpeter wave functions for J^P=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 V_LS(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 ¹P₁, ³P₀, ³P₁ and ³P₂–³F₂ 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 ³P₂ channel, which is related to the P-wave neutron paring in neutron stars