Low-energy theorems for nucleon-nucleon scattering at Mπ=450M_{\pi}=450 MeV

We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of $M_\pi\simeq 450$ MeV obtained by the NPLQCD collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^3S_1$ and $^1S_0$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation

Two-nucleon scattering: merging chiral effective field theory with dispersion relations

We consider two-nucleon scattering close to threshold. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes calculated in a relativistic formulation of chiral perturbation theory. The constraints set by unitarity are used in order to stabilize the extrapolation. Neutron-proton phase shifts are analyzed up to laboratory energies $T_{{\rm lab}}\simeq250$ MeV based on the next-to-next-to-next-to-leading order expression for the subthreshold amplitudes. We find a reasonably accurate description of the empirical S- and P-waves and a good convergence of our approach. These results support the assumption that the subthreshold nucleon-nucleon scattering amplitude may be computed perturbatively by means of the chiral expansion. The intricate soft scales that govern the low-energy nucleon-nucleon scattering are generated dynamically via a controlled analytic continuation.Comment: 10 pages, 5 figures, version accepted for publication, a more detailed discussion of the results is adde

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

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

Binding energy of the X(3872)X(3872) at unphysical pion masses

Chiral extrapolation of the $X(3872)$ binding energy is investigated using the modified Weinberg formulation of chiral effective field theory for the $D \bar{D}^*$ scattering. Given its explicit renormalisability, this approach is particularly useful to explore the interplay of the long- and short-range $D \bar{D}^*$ forces in the $X(3872)$ from studying the light-quark (pion) mass dependence of its binding energy. In particular, the parameter-free leading-order calculation shows that the $X$-pole disappears for unphysical large pion masses. On the other hand, without contradicting the naive dimensional analysis, the higher-order pion-mass-dependent contact interaction can change the slope of the binding energy at the physical point yielding the opposite scenario of a stronger bound $X$ at pion masses larger than its physical value. An important role of the pion dynamics and of the 3-body $D\bar{D}\pi$ effects for chiral extrapolations of the $X$-pole is emphasised. The results of the present study should be of practical value for the lattice simulations since they provide a non-trivial connection between lattice points at unphysical pion masses and the physical world.Comment: 24 pages, 4 figure

On-shell consistency of the Rarita-Schwinger field formulation

We prove that any bilinear coupling of a massive spin-3/2 field can be brought into a gauge invariant form suggested by Pascalutsa by means of a non-linear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit Delta (1232) isobar degrees of freedom are discussed.Comment: 9 pages, 1 figur

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

Nucleon-deuteron capture with chiral potentials

Present day chiral nucleon-nucleon potentials up to N3LO and three nucleon forces at N2LO are used to analyze nucleon-deuteron radiative capture at deuteron lab energies below E_d= 100 MeV. The differential cross section and the deuteron analyzing powers A_y(d) and A_{yy} are presented and compared to data. The theoretical predictions are obtained in the momentum-space Faddeev approach using the nuclear electromagnetic current operator with exchange currents introduced via the Siegert theorem. The chiral forces provide the same quality of data description as a combination of the two-nucleon AV18 and the three-nucleon Urbana IX interactions. However, the different parametrizations of the chiral potentials lead to broad bands of predictions.Comment: 20 pages, 12 ps figure