Proton-proton fusion in lattice effective field theory

The proton-proton fusion rate is calculated at low energy in a lattice effective field theory (EFT) formulation. The strong and the Coulomb interactions are treated non-perturbatively at leading order in the EFT. The lattice results are shown to accurately describe the low energy cross section within the validity of the theory at energies relevant to solar physics. In prior work in the literature, Coulomb effects were generally not included in non-perturbative lattice calculations. Work presented here is of general interest in nuclear lattice EFT calculations that involve Coulomb effects at low energy. It complements recent developments of the adiabatic projection method for lattice calculations of nuclear reactions.Comment: 11 pages, 2 figure

Chiral perturbation theory for the Wilson lattice action

We extend chiral perturbation theory to include linear dependence on the lattice spacing $a$ for the Wilson action. The perturbation theory is written as a double expansion in the small quark mass $m_q$ and lattice spacing $a$. We present formulae for the mass and decay constant of a flavor-non-singlet meson in this scheme to order $a$ and $m_q^2$. The extension to the partially quenched theory is also described.Comment: 9 pages LaTeX2

Adiabatic projection method for scattering and reactions on the lattice

We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s-wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work.Comment: 17 pages, 4 figures, version to appear in Eur. Phys. J.