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

Lattice calculations for A=3,4,6,12 nuclei using chiral effective field theory

We present lattice calculations for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our results were previously summarized in a letter publication. This paper provides full details of the calculations. We include isospin-breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.Comment: 38 pages, 11 figures, final publication versio

NDKNDK, KˉDN\bar{K} DN and NDDˉND\bar{D} molecules

We investigate theoretically baryon systems made of three hadrons which contain one nucleon and one D meson, and in addition another meson, $\bar{D}, K$ or $\bar{K}$. The systems are studied using the Fixed Center Approximation to the Faddeev equations. The study is made assuming scattering of a $K$ or a $\bar{K}$ on a $DN$ cluster, which is known to generate the $\Lambda_c(2595)$, or the scattering of a nucleon on the $D\bar{D}$ cluster, which has been shown to generate a hidden charm resonance named X(3700). We also investigate the configuration of scattering of $N$ on the $KD$ cluster, which is known to generate the $D_{s0}^*(2317)$. In all cases we find bound states, with the $NDK$ system, of exotic nature, more bound than the $\bar{K} DN$.Comment: 9 figure

Lattice effective field theory calculations for A = 3,4,6,12 nuclei

We present lattice results for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our analysis includes isospin-breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.Comment: 4 pages, 4 figures, published version to appear in Phys. Rev. Lett

Spin partners of the Zb(10610)Z_b(10610) and Zb(10650)Z_b(10650) revisited

We study the implications of the heavy-quark spin symmetry for the possible spin partners of the exotic states $Z_b(10610)$ and $Z_b(10650)$ in the spectrum of bottomonium. We formulate and solve numerically the coupled-channel equations for the $Z_b$ states that allow for a dynamical generation of these states as hadronic molecules. The force includes short-range contact terms and the one-pion exchange potential, both treated fully nonperturbatively. The strength of the potential at leading order is fixed completely by the pole positions of the $Z_b$ states such that the mass and the most prominent contributions to the width of the isovector heavy-quark spin partner states $W_{bJ}$ with the quantum numbers $J^{++}$ ($J=0,1,2$) come out as predictions. Since the accuracy of the present experimental data does not allow one to fix the pole positions of the $Z_b$'s reliably enough, we also study the pole trajectories of their spin partner states as functions of the $Z_b$ binding energies. It is shown that, once the heavy-quark spin symmetry is broken by means of the physical $B$ and $B^*$ masses, especially the pion tensor force has a significant impact on the location of the partner states clearly demonstrating the need of a coupled-channel treatment of pion dynamics to understand the spin multiplet pattern of hadronic molecules.Comment: 21 pages, 5 figures, 1 tabl

Ab initio calculation of the Hoyle state

The Hoyle state plays a crucial role in the hydrogen burning of stars heavier than our sun and in the production of carbon and other elements necessary for life. This excited state of the carbon-12 nucleus was postulated by Hoyle [1] as a necessary ingredient for the fusion of three alpha particles to produce carbon at stellar temperatures. Although the Hoyle state was seen experimentally more than a half century ago [2,3], nuclear theorists have not yet uncovered the nature of this state from first principles. In this letter we report the first ab initio calculation of the low-lying states of carbon-12 using supercomputer lattice simulations and a theoretical framework known as effective field theory. In addition to the ground state and excited spin-2 state, we find a resonance at -85(3) MeV with all of the properties of the Hoyle state and in agreement with the experimentally observed energy. These lattice simulations provide insight into the structure of this unique state and new clues as to the amount of fine-tuning needed in nature for the production of carbon in stars.Comment: 4 pp, 3 eps figs, version accepted for publication in Physical Review Letter

Effective short-range interaction for spin-singlet P-wave nucleon-nucleon scattering

Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence that arises can be renormalised using an order-Q^2 counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.Comment: 4 pages, 3 figures (pdf

Spin partners WbJW_{bJ} from the line shapes of the Zb(10610)Z_b(10610) and Zb(10650)Z_b(10650)

In a recent paper Phys.Rev. D98, 074023 (2018), the most up-to-date experimental data for all measured production and decay channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ were analysed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange as well as a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both $Z_b$ states were determined. In this work we employ the same approach to predict in a parameter-free way the pole positions and the line shapes in the elastic and inelastic channels of the (still to be discovered) spin partners of the $Z_b$ states. They are conventionally referred to as $W_{bJ}$'s with the quantum numbers $J^{PC}=J^{++}$ ($J=0,1,2$). It is demonstrated that the results of our most advanced pionful fit, which gives the best $\chi^2/{\rm d.o.f.}$ for the data in the $Z_b$ channels, are consistent with all $W_{bJ}$ states being above-threshold resonances which manifest themselves as well pronounced hump structures in the line shapes. On the contrary, in the pionless approach, all $W_{bJ}$'s are virtual states which can be seen as enhanced threshold cusps in the inelastic line shapes. Since the two above scenarios provide different imprints on the observables, the role of the one-pion exchange in the $B^{(*)}\bar{B}^{(*)}$ systems can be inferred from the once available experimental data directly.Comment: 24 pages, 12 figure

Threshold neutral pion photoproduction off the tri-nucleon to O(q^4)

We calculate electromagnetic neutral pion production off tri-nucleon bound states (3H, 3He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off 3He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole E_{0+}^{pi0 n}.Comment: 17 pages, 5 figures, title changed, final version to appear in EPJA. arXiv admin note: substantial text overlap with arXiv:1103.340

Chiral dynamics in few-nucleon systems

We report on recent progress achieved in calculating various few-nucleon low-energy observables from effective field theory. Our discussion includes scattering and bound states in the 2N, 3N and 4N systems and isospin violating effects in the 2N system. We also establish a link between the nucleon-nucleon potential derived in chiral effective field theory and various modern high-precision potentials.Comment: 12 pp, uses aipproc style files, 4 figures, contribution to the conference on "Mesons and Light Nuclei", Prag, July 2001, to appear in the proceeding