We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the nucleon-nucleon $\left(NN\right)$ data below $290\text{−}\text{MeV}$ lab energy is comparable to the one of phenomenological high-precision potentials. Since $NN$ 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 $NN$ potential reliable up to $290\text{MeV}$. 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 present $\mathit{NN}$ 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 (${\mathrm{N}}^4\mathrm{LO}$). 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 $\pi N$ low-energy constants (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 $\mathit{NN}$ potentials are fit to the world $\mathit{NN}$ data below the pion-production threshold of the year 2016. The potential of the highest order (${\mathrm{N}}^4\mathrm{LO}$) reproduces the world $\mathit{NN}$ data with the outstanding ${\chi }^2$/datum of 1.15, which is the highest precision ever accomplished for any chiral $\mathit{NN}$ potential to date. The $\mathit{NN}$ 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 nonlocal 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 an accurate nucleon–nucleon (NN) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the NN D-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the NN phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral NN potential represents a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations. An important implication of the present work is that the chiral 2π exchange at order four is of crucial interest for future chiral NN potential development

We have performed a coupled channel calculation of the 1++ cc\ifmmode\bar\else\textasciimacron\fi{} sector including qq\ifmmode\bar\else\textasciimacron\fi{} and DD* molecular configurations. The calculation was done within a constituent quark model which successfully describes the meson spectrum, in particular, the cc\ifmmode\bar\else\textasciimacron\fi{} 1-- sector. Two and four-quark configurations are coupled using the P03 model. The elusive X(3872) meson appears as a new state with a high probability for the DD* molecular component. When the mass difference between neutral and charged states is included, a large D0D*0 component is found which dominates for large distances and breaks isospin symmetry in the physical state. The original cc\ifmmode\bar\else\textasciimacron\fi{}(2P13) state acquires a sizable DD* component and can be identified with the X(3940). We study the B$\rightarrow${}K$\pi${}+$\pi${}-J/$\psi${} and B$\rightarrow${}KD0D*0 decays, finding a good agreement with Belle and BABAR experimental data.

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 a better way to determine their properties experimentally.