We present the first nucleon-nucleon potential at next-tonext-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to nextto-leading order of the isospin-violation scheme. The accuracy for the reproduction of the N N data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since N N potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable N N potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.

We analyze the results by chiral N N models for the two-nucleon system and calculate the predictions for the nucleon vector analyzing power of elastic nucleon-deuteron (N d) scattering, A y , by these models. Our conclusion is that a quantitative chiral two-nucleon potential does not resolve the N d A y puzzle (when only two-body forces are included).PACS numbers: 21.30.+y, 21.45.+v, 25.10.+s, 27.10+h The term A y puzzle refers to the inability to explain the nucleon vector analyzing power A y in elastic nucleon-deuteron (Nd) scattering below 30 MeV laboratory energy for the incident nucleon by means of three-body calculations in which only two-nucleon forces are applied. The problem showed up as soon as it was possible to conduct three-body continuum calculations with realistic NN potentials. The first such calculation was performed by Stolk and Tjon [1] in 1978 using the Reid soft-core potential [2], and the first calculations with (a separable representation of) the Paris potential [3] were conducted by the Graz-Osaka group in 1987 [4]; in both cases, the A y predictions showed the characteristic problem. Finally, the 'puzzle' became proverbial when rigorous three-nucleon continuum Faddeev calculations using realistic forces were started on a large scale [5]. Over the years, many measurements and calculations of Nd A y were performed (including the pd reaction that involves the Coulomb force [6]) which all confirmed that the problem was real (see Ref.[7] for a review): For energies below 20 MeV, the A y is predicted about 30% too small in the angular region around 120 deg center-of-mass angle where the maximum occurs.There have been many attempts to solve the problem. Already in the very early stages of three-body continuum calculations, when only schematic NN potentials were applied, it was noticed that the Nd A y predictions depend very sensitively on the strength of the input NN potential in the triplet P waves [8,9]-a sensitivity that was confirmed in later calculations using realistic forces [10]. Based upon this experience, Wita la and Glöckle [11] showed in 1991 that small changes in those 3 P wave potentials could remove the discrepancy. This finding gave rise to systematic investigations of the question whether the small variations of the low-energy phase shifts of, particularly, those triplet P waves necessary to explain the Nd A y are consistent with the NN data base. While Tornow and coworkers [12] suggest that the low-energy NN data may leave some lattitude in the NN 3 P waves that could * On leave from University of Salamanca, Spain. Another important observation has been that conventional three-nucleon forces (when added to a realistic two-nucleon potential) change the predictions for Nd A y only slightly and do not improve them [14,6]. Therefore, the general perception in the community has shifted towards the believe that the A y puzzle is the 'smoking gun' for new types of three-nucleon forces [15][16][17][18] or new physics [19].However, very recently, there has been an apparent indicatio...

We present N N potentials through five orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-next-to-leading order (N 4 LO). The construction may be perceived as consistent in the sense that the same power counting scheme as well as the same cutoff procedures are applied in all orders. Moreover, the long-range parts of these potentials are fixed by the very accurate πN LECs as determined in the Roy-Steiner equations analysis by Hoferichter, Ruiz de Elvira and coworkers. In fact, the uncertainties of these LECs are so small that a variation within the errors leads to effects that are essentially negligible, reducing the error budget of predictions considerably. The N N potentials are fit to the world N N data below pion-production threshold of the year of 2016. The potential of the highest order (N 4 LO) reproduces the world N N data with the outstanding χ 2 /datum of 1.15, which is the highest precision ever accomplished for any chiral N N potential to date. The N N potentials presented may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the consistent order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our family of potentials is non-local and, generally, of soft character. This feature is reflected in the fact that the predictions for the triton binding energy (from two-body forces only) converges to about 8.1 MeV at the highest orders. This leaves room for three-nucleon-force contributions of moderate size.

We present the two-and three-pion exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N 4 LO, fifth order) of chiral effective field theory, and calculate nucleon-nucleon scattering in peripheral partial waves with L ≥ 3 using low-energy constants that were extracted from πN analysis at fourth order. While the net three-pion exchange contribution is moderate, the two-pion exchanges turn out to be sizeable and prevailingly repulsive, thus, compensating the excessive attraction characteristic for NNLO and N 3 LO. As a result, the N 4 LO predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception of the 1 F3 wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the N N interaction.

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We revisit the bottomonium spectrum motivated by the recently exciting experimental progress in the observation of new bottomonium states, both conventional and unconventional. Our framework is a nonrelativistic constituent quark model which has been applied to a wide range of hadronic observables from the light to the heavy quark sector and thus the model parameters are completely constrained. Beyond the spectrum, we provide a large number of electromagnetic, strong and hadronic decays in order to discuss the quark content of the bottomonium states and give more insights about the better way to determine their properties experimentally.Comment: 23 pages, 17 tables, 1 figur

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