Two nucleon systems atmπ∼450  MeVfrom lattice QCD

Abstract

Nucleon-nucleon systems are studied with lattice quantum chromodynamics at a pion mass of mπ ∼ 450 MeV in three spatial volumes using n f = 2 + 1 flavors of light quarks. At the quark masses employed in this work, the deuteron binding energy is calculated to be B d = 14.4 +3.2 −2.6 MeV, while the dineutron is bound by Bnn = 12.5 +3.0 −5.0 MeV. Over the range of energies that are studied, the S-wave scattering phase shifts calculated in the 1 S0 and 3 S1-3 D1 channels are found to be similar to those in nature, and indicate repulsive short-range components of the interactions, consistent with phenomenological nucleon-nucleon interactions. In both channels, the phase shifts are determined at three energies that lie within the radius of convergence of the effective range expansion, allowing for constraints to be placed on the inverse scattering lengths and effective ranges. The extracted phase shifts allow for matching to nuclear effective field theories, from which low energy counterterms are extracted and issues of convergence are investigated. As part of the analysis, a detailed investigation of the single hadron sector is performed, enabling a precise determination of the violation of the Gell-Mann-Okubo mass relation.

Low-energy theorems for nucleon-nucleon scattering atMπ=450MeV

“…Recently, new results for NN scattering in the 3 S 1 and 1 S 0 channels have been reported by the NPLQCD collaboration at M π ∼ 450 MeV [9]. The calculations were performed for n f = 2 + 1 flavors of light quarks at three lattice volumes of L = 2.8 fm, L = 3.7 fm, and L = 5.6 fm using the lattice spacing of b = 0.12 fm.…”

“…We perform a detailed comparison of our results for these quantities with the ones of Ref. [9] and argue that their determination by means of the effective range approximation is not self-consistent.…”

“…Recently, the NPLQCD collaboration has reported their new results for the S-wave NN observables both in the spin-triplet and the spin-singlet channels at M π = 450 MeV [9]. In particular, they have calculated the values of the deuteron and the dineutron binding energies and the phase shifts in the 3 S 1 and 1 S 0 channels at several values of the center of mass (cms) momenta above threshold.…”

“…Refs. [7][8][9]. To connect these results with experimentally observed quantities corresponding to the physical value of the quark masses one can employ chiral effective field theory (EFT) which is still expected to be applicable at such pion masses [6,[10][11][12][13][14][15][16][17].…”

“…Notice that not only the binding energies but also the NN scattering observables such as the phase shifts and effective range parameters have been calculated on a lattice, see Refs. [9,18,19] for recent analyses of the NN 1 S 0 and 3 S 1 channels by the NPLQCD collaboration at M π 450 and 800 MeV and Ref. [20] for the analysis of the higher partial waves at M π 800 MeV by the CalLat collaboration.…”