Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD

Abstract

We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross-section of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.