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We present results of the first fully dynamical lattice QCD determination of nucleon-nucleon scattering lengths in the 1S0 channel and 3S1 - 3D1 coupled channels. The calculations are performed with domain-wall valence quarks on the MILC staggered configurations with a lattice spacing of b = 0.125 fm in the isospin-symmetric limit, and in the absence of electromagnetic interactions.

The binding energies of a range of nuclei and hypernuclei with atomic number A ≤ 4 and strangeness |s| ≤ 2, including the deuteron, di-neutron, H-dibaryon, 3 He, ΛΛ He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange-quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n f = 3 dynamical light quarks using an isotropic clover discretization of the quark action in three lattice volumes of spatial extent L ∼ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ∼ 0.145 fm.2

The two-nucleon sector is near an infrared fixed point of QCD and as a result the S-wave scattering lengths are unnaturally large compared to the effective ranges and shape parameters. It is usually assumed that a lattice QCD simulation of the two-nucleon sector will require a lattice that is much larger than the scattering lengths in order to extract quantitative information. In this paper we point out that this does not have to be the case: lattice QCD simulations on much smaller lattices will produce rigorous results for nuclear physics.One of the central goals of nuclear physics is to make rigorous predictions for both elastic and inelastic processes in multi-nucleon systems directly from QCD. The only presently-available technique to achieve this goal is lattice QCD, where space-time is discretized and QCD Green functions are evaluated in Euclidean space. Unfortunately, at present, the variety of processes that can be addressed with lattice QCD is quite limited. The currently-available computational power restricts not only the sizes of lattices that can be utilized, but also the lattice spacings and quark masses that can be simulated. Moreover, the Maiani-Testa theorem [1] precludes determination of scattering amplitudes away from kinematic thresholds from Euclidean-space Green functions at infinite volume. However, by generalizing a result from non-relativistic quantum mechanics [2] to quantum field theory, Lüscher [3,4] realized that one can access 2 → 2 scattering amplitudes from lattice simulations performed at finite volume. Significant progress has been made using this finite-volume technique to determine the low-energy ππ phase shifts directly from QCD, e.g. Ref. [5]. However, only one lattice QCD calculation of the nucleon-nucleon (NN) scattering lengths [6] has been attempted, and it was a quenched simulation with heavy pions 1 .When contemplating computing nuclear observables with lattice QCD one naively assumes that the lattice must be much larger than the systems being simulated, so that the systems on the lattice resemble those at infinite-volume. This would mean, for instance, that when computing the rate for the simplest inelastic nuclear process, np → dγ, which near threshold involves radiative capture from the 1 S 0 channel, a lattice of size L ≫ |a ( 1 S 0 ) |, |a ( 3 S 1 ) | is required, where a ( 1 S 0 ) and a ( 3 S 1 ) are the 1 S 0 and 3 S 1 NN scattering lengths, respectively. Given that a ( 1 S 0 ) = −23.714 fm, such a calculation would have to await a future in which computational power is sufficient to handle volumes of this size. Fortunately, as we will see, this argument is not correct.There is a sizable separation of length scales in nuclear physics, due to the fact that nature has chosen to be very near an infrared fixed point of QCD [8,9,10]. As a result, the scattering lengths in both S−wave channels are unnaturally-large compared to all typical strong-interaction length scales, including the range of the nuclear potential which is determined by the pion Compton wavelength. P...