Two-nucleon scattering amplitudes at light quark masses from lattice QCD

Abstract

We present a lattice-QCD determination of nucleon-nucleon scattering amplitudes at pion masses of $M_\pi \approx 200$ MeV and $M_\pi \approx 280$ MeV at a single lattice spacing $a \approx 0.064$ fm on two CLS ensembles. The finite-volume energy spectra are extracted from large Hermitian correlation matrices constructed within the distillation framework using an extensive basis of two-nucleon interpolating operators. To reliably relate the finite-volume spectra to the infinite-volume scattering amplitudes, we employ two recently developed formalisms that explicitly account for the long-range interaction generated by one-pion exchange: the plane-wave quantization condition and the relativistic left-hand-cut formalism. We discuss the quark-mass dependence of the nucleon-nucleon scattering lengths, effective ranges, shape parameters and pole positions. At all pion masses considered, our analysis prefers virtual states in both isospin channels by more than $1\sigma$. Comparing also results from our previous calculation at $M_\pi \approx 710$ MeV, we observe that the inverse scattering lengths and binding momenta approach their physical-point phenomenological values monotonically as the pion mass is varied.