Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD

TL;DR

This paper reports the first lattice QCD calculation of higher partial-wave nucleon-nucleon scattering phase shifts, employing novel methods and the Luscher formalism in the SU(3)-flavor limit at high quark masses.

Contribution

It introduces new lattice techniques for calculating l > 0 scattering phase shifts and applies them to nucleon-nucleon interactions in a novel computational setup.

Findings

First lattice QCD results for l > 0 nucleon-nucleon phase shifts.

Validation of the Luscher formalism for higher partial waves.

Finite-volume spectra successfully mapped to phase shifts.

Abstract

We present a determination of nucleon-nucleon scattering phase shifts for l >= 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For l > 0, this is the first lattice QCD calculation using the Luscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to m_pi = m_K ~ 800 MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V ~ (3.5 fm)^3 and V ~ (4.6 fm)^3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.