Two-nucleon scattering: merging chiral effective field theory with dispersion relations

We consider two-nucleon scattering close to threshold. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes calculated in a relativistic formulation of chiral perturbation theory. The constraints set by unitarity are used in order to stabilize the extrapolation. Neutron-proton phase shifts are analyzed up to laboratory energies $T_{{\rm lab}}\simeq250$ MeV based on the next-to-next-to-next-to-leading order expression for the subthreshold amplitudes. We find a reasonably accurate description of the empirical S- and P-waves and a good convergence of our approach. These results support the assumption that the subthreshold nucleon-nucleon scattering amplitude may be computed perturbatively by means of the chiral expansion. The intricate soft scales that govern the low-energy nucleon-nucleon scattering are generated dynamically via a controlled analytic continuation.Comment: 10 pages, 5 figures, version accepted for publication, a more detailed discussion of the results is adde

Two-nucleon scattering: merging chiral effective field theory with dispersion relations

We consider two-nucleon scattering close to threshold. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes calculated in a relativistic formulation of chiral perturbation theory. The constraints set by unitarity are used in order to stabilize the extrapolation. Neutron-proton phase shifts are analyzed up to laboratory energies $T_{{\rm lab}}\simeq250$ MeV based on the next-to-next-to-next-to-leading order expression for the subthreshold amplitudes. We find a reasonably accurate description of the empirical S- and P-waves and a good convergence of our approach. These results support the assumption that the subthreshold nucleon-nucleon scattering amplitude may be computed perturbatively by means of the chiral expansion. The intricate soft scales that govern the low-energy nucleon-nucleon scattering are generated dynamically via a controlled analytic continuation.Comment: 10 pages, 5 figures, version accepted for publication, a more detailed discussion of the results is adde

Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory

We calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave decomposition. Deuteron form factors are extracted by applying the Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation function of deuteron interpolating fields and the electromagnetic current operator. Numerical results of a leading-order calculation with removed cutoff regularization agree well with experimental data.Comment: 9 pages, 2 figure

Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion

We confirm the claim of Ref. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] that 20 operators are sufficient to represent the most general local isospin-invariant three-nucleon force and derive explicit relations between the two sets of operators suggested in Refs. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] and [H. Krebs, A.M. Gasparyan, E. Epelbaum, Phys.Rev. C87 (2013) 5, 054007]. We use the set of 20 operators to discuss the chiral expansion of the long- and intermediate-range parts of the three-nucleon force up to next-to-next-to-next-to-next-to-leading order in the standard formulation without explicit Delta(1232) degrees of freedom. We also address implications of the large-N_c expansion in QCD for the size of the various three-nucleon force contributions.Comment: 15 pages, 6 figure

Isospin-breaking two-nucleon force with explicit Delta-excitations

We study the leading isospin-breaking contributions to the two-nucleon two-pion exchange potential due to explicit Delta degrees of freedom in chiral effective field theory. In particular, we find important contributions due to the delta mass splittings to the charge symmetry breaking potential that act opposite to the effects induced by the nucleon mass splitting.Comment: 10 pages, 4 figure

Lattice methods and the nuclear few- and many-body problem

We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.Comment: 20 pages, 3 figures, Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Lattice calculations for A=3,4,6,12 nuclei using chiral effective field theory

We present lattice calculations for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our results were previously summarized in a letter publication. This paper provides full details of the calculations. We include isospin-breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.Comment: 38 pages, 11 figures, final publication versio

How (not) to renormalize integral equations with singular potentials in effective field theory

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.Comment: 12 pages, 5 figure

Chiral Expansion, Renormalization and the Nuclear Force

The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.Comment: Talk at International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos-Sao Paulo (Brasil), 21-26 August 200