Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD

We present results of the first fully dynamical lattice QCD determination of nucleon-nucleon scattering lengths in the ${}^{1}S_0$ channel and ${}^{3}S_1-{}^{3}D_1$ coupled channels. The calculations are performed with domain-wall valence quarks on the MILC staggered configurations with a lattice spacing of $b=0.125\mathrm{fm}$ in the isospin-symmetric limit, and in the absence of electromagnetic interactions.

Figure 1

The logarithm of the ratio of correlation functions in the ${}^{1}S_0$ channel ($G^{10}$) as a function of time slice. Each has been offset vertically for display purposes. The dotted lines correspond to the fit function at the central values of the fit parameters.

Figure 2

The logarithm of the ratio of correlation functions in the ${}^{3}S_1-{}^{3}D_1$ coupled channels ($G^{01}$) as a function of time slice. Each has been offset vertically for display purposes. The dotted lines correspond to the fit function at the central values of the fit parameters.

Figure 3

Allowed regions for the scattering length in the ${}^{1}S_0$ channel as a function of the pion mass. The experimental value of the scattering length and NDA have been used to constrain the extrapolation in both BBSvK and W power countings at NLO.

Figure 4

Allowed regions for the $s$-wave scattering length in the ${}^{3}S_1-{}^{3}D_1$ coupled channels as a function of the pion mass. The experimental value of the scattering length and NDA have been used to constrain the extrapolation in BBSvK power counting at NLO. (W counting gives a similar result.)