Nuclear axial current operators to fourth order in chiral effective field theory

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.Comment: 72 pages, 21 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

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

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

The magnetic moment of the \rho-meson

The magnetic moment of the \rho-meson is calculated in the framework of a low-energy effective field theory of the strong interactions. We find that the complex-valued strong interaction corrections to the gyromagnetic ratio are small leading to a value close to the real leading tree level result, g_\rho = 2. This is in a reasonably good agreement with the available lattice QCD calculations for this quantity.Comment: 10 pages, 4 figure

Isospin-violating nucleon-nucleon forces using the method of unitary transformation

Recently, we have derived the leading and subleading isospin-breaking three-nucleon forces using the method of unitary transformation. In the present work we extend this analysis and consider the corresponding two-nucleon forces using the same approach. Certain contributions to the isospin-violating one- and two-pion-exchange potential have already been discussed by various groups within the effective field theory framework. Our findings agree with the previously obtained results. In addition, we present the expressions for the subleading charge-symmetry-breaking two-pion exchange potential which were not considered before. These corrections turn out to be numerically important. Together with the three-nucleon force results presented in our previous work, the results of the present study specify completely isospin-violating nuclear forces up to the order $q^5/\Lambda^5$, where $q$ ($\Lambda$) denotes the soft (hard) scale.Comment: 25 pages, 12 figure

Complex-mass renormalization in hadronic EFT: applicability at two-loop order

We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting.Comment: 8 pages, 2 figures, version accepted for publication in EPJ

Subleading contributions to the chiral three-nucleon force II: Short-range terms and relativistic corrections

We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.Comment: 14 pages, 4 figure