Nucleon-Nucleon Scattering Parameters in the Limit of SU(3) Flavor Symmetry

The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L ~ 3.4 fm, 4.5 fm and 6.7 fm, and with a lattice spacing of b ~ 0.145 fm. With determinations of the energies of the two-nucleon systems —both of which contain bound states at these light-quark masses— at rest and moving in the lattice volume, Luscher’s method is used to determine the low-energy phase shift in each channel, from which the scattering length and effective range are obtained. The scattering parameters in the {sup 1}S{sub 0} channel are found to be m{sub π}a{sup ({sup 1}S{sub 0})} = 9.51+/-0.74+/-1.00 and m{sub π}r{sup ({sup 1}S{sub 0})} = 4.76+/-0.37+/-0.40, and in the {sup 3}S{sub 1} channel are m{sub π}a{sup ({sup 3}S{sub 1})} = 7.45+/-0.57+/-0.71 and m{sub π}r{sup ({sup 3}S{sub 1})} = 3.71+/-0.28+/-0.28. These values are consistent with the two-nucleon system exhibiting Wigner’s supermultiplet symmetry, which becomes exact in the limit of large-N{sub c}.