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

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

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

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

Role of the total isospin 3/2 component in three-nucleon reactions

We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin T=3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the 1S0 state with isospin T=3/2. For neutron-deuteron elastic scattering the T=3/2 contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called "2/3-1/3" rule.Comment: 24 pages, 8 figures, 3 Table

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal versio

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

Einfluss des Anbausystems auf Ertrag und Gesundheit von Winterweizen

In a long-term trial in central Switzerland, yield and health of winter wheat was examined under organic, extensive and intensive management. In the organic cropping system, soil was ploughed and fertilised with cattle dung. In the extensive system, soil was cultivated ploughless and dung was supplemented by mineral fertiliser. Herbicides were used, but no growth regulators or fungicides. In the intensive system, soil was ploughed and manure was based on cattle dung and mineral fertiliser with 20 % more nitrogen than in the extensive system. For plant protection, herbicides, growth regulators and fungicides were used. In the period from 2004 to 2007, average winter wheat yields of the intensive and the extensive crop management system exceeded those of the organic production by 21.3 % and 5.5 % respectively. This was probably due to the higher level of fertilisation and plant protection. In 2007, a year with frequent rain during the summer, the infestation of grains with Microdochium nivale and Fusarium graminearum was lowest in the organic wheat. In consequence, its germination capacity was higher and the deoxynivalenol content was lower compared with the other systems. The increased grain infestation with F. graminearum and the higher deoxynivalenol content of wheat grains in the extensive system can be explained by the ploughless tillage, with straw from the previous maize crop remaining on the soil surface