Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer (i.e. more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ~40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions.Comment: 57 pages, 17 figures, 19 table

Precision nucleon-nucleon potential at fifth order in the chiral expansion

We present a nucleon-nucleon potential at fifth order in chiral effective field theory. We find a substantial improvement in the description of nucleon-nucleon phase shifts as compared to the fourth-order results of Ref. [E. Epelbaum, H. Krebs, U.-G. Mei{\ss}ner, arXiv:1412.0142 [nucl-th]]. This provides clear evidence of the corresponding two-pion exchange contributions with all low-energy constants being determined from pion-nucleon scattering. The fifth-order corrections to nucleon-nucleon observables appear to be of a natural size which confirms the good convergence of the chiral expansion for nuclear forces. Furthermore, the obtained results provide strong support for the novel way of quantifying the theoretical uncertainty due to the truncation of the chiral expansion proposed in Ref. [E. Epelbaum, H. Krebs, U.-G. Mei{\ss}ner, arXiv:1412.0142 [nucl-th]]. Our work opens up new perspectives for precision ab initio calculations in few- and many-nucleon systems and is especially relevant for ongoing efforts towards a quantitative understanding the structure of the three-nucleon force in the framework of chiral effective field theory.Comment: 5 pages, 4 figures, 3 table

Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order

We present improved nucleon-nucleon potentials derived in chiral effective field theory up to next-to-next-to-next-to-leading order. We argue that the nonlocal momentum-space regulator employed in the two-nucleon potentials of Refs. [E. Epelbaum, W. Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005) 362], [D.R. Entem, R. Machleidt, Phys. Rev. C68 (2003) 041001] is not the most efficient choice, in particular since it affects the long-range part of the interaction. We are able to significantly reduce finite-cutoff artefacts by using an appropriate regularization in coordinate space which maintains the analytic structure of the amplitude. The new potentials do not require the additional spectral function regularization employed in Ref. [E. Epelbaum, W. Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005) 362] to cut off the short-range components of the two-pion exchange and make use of the low-energy constants c_i and d_i determined from pion-nucleon scattering without any fine tuning. We discuss in detail the construction of the new potentials and convergence of the chiral expansion for two-nucleon observables. We also introduce a new procedure for estimating the theoretical uncertainty from the truncation of the chiral expansion that replaces previous reliance on cutoff variation.Comment: 34 pages, 13 figures, 7 table

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

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

New insights into the spin structure of the nucleon

We analyze the low-energy spin structure of the nucleon in a covariant effective field theory with explicit spin-3/2 degrees of freedom to third order in the small scale expansion. Using the available data on the strong and electromagnetic width of the Delta-resonance, we give parameter-free predictions for various spin-polarizabilities and moments of spin structure functions. We find an improved description of the nucleon spin structure at finite photon virtualities for some observables and point out the necessity of a fourth order calculation.Comment: 13 pages, 6 figure

Efficient calculation of chiral three-nucleon forces up to N3LO for ab initio studies

We present a novel framework to decompose three-nucleon forces in a momentum space partial-wave basis. The new approach is computationally much more efficient than previous methods and opens the way to ab initio studies of few-nucleon scattering processes, nuclei and nuclear matter based on higher-order chiral 3N forces. We use the new framework to calculate matrix elements of chiral three-nucleon forces at N2LO and N3LO in large basis spaces and carry out benchmark calculations for neutron matter and symmetric nuclear matter. We also study the size of the individual three-nucleon force contributions for $^3$H. For nonlocal regulators, we find that the sub-leading terms, which have been neglected in most calculations so far, provide important contributions. All matrix elements are calculated and stored in a user-friendly way, such that values of low-energy constants as well as the form of regulator functions can be chosen freely.Comment: 10 pages, 4 figure

The reaction pi N -> pi pi N in chiral effective field theory with explicit Delta(1232) degrees of freedom

The reaction pi N -> pi pi N is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit Delta(1232) degrees of freedom. Using total cross section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit Delta degrees of freedom is given.Comment: 30 pages, 13 figure

On-shell consistency of the Rarita-Schwinger field formulation

We prove that any bilinear coupling of a massive spin-3/2 field can be brought into a gauge invariant form suggested by Pascalutsa by means of a non-linear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit Delta (1232) isobar degrees of freedom are discussed.Comment: 9 pages, 1 figur

Design, Fabrication and Test of Composite Curved Frames for Helicopter Fuselage Structure

Aspects of curved beam effects and their importance in designing composite frame structures are discussed. The curved beam effect induces radial flange loadings which in turn causes flange curling. This curling increases the axial flange stresses and induces transverse bending. These effects are more important in composite structures due to their general inability to redistribute stresses by general yielding, such as in metal structures. A detailed finite element analysis was conducted and used in the design of composite curved frame specimens. Five specimens were statically tested and compared with predicted and test strains. The curved frame effects must be accurately accounted for to avoid premature fracture; finite element methods can accurately predict most of the stresses and no elastic relief from curved beam effects occurred in the composite frames tested. Finite element studies are presented for comparative curved beam effects on composite and metal frames