We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the naïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.
We apply a subtracted dispersion relation formalism with the aim to improve predictions for the two-photon exchange corrections to elastic electron-proton scattering observables at finite momentum transfers. We study the formalism on the elastic contribution, and make a detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables.
We discuss a reformulation of QED in which matter and gauge fields are integrated out explicitly, resulting in a many-body Lorentz covariant theory of 0+1 dimensional worldlines describing super-pairs of spinning charges interacting through Lorentz forces. This provides a powerful, string inspired definition of amplitudes to all loop orders. In particular, one obtains a more general formulation of Wilson loops and lines, with exponentiated dynamical fields and spin precession contributions, and worldline contour averages exactly defined through first quantized path integrals. We discuss in det…
In recent years, different on-shell $\mathbf{3}\to\mathbf{3}$ scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Briceño, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the $B$-matrix representation, derived on the basis of $S$-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Theref…
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -- they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, intro…
In this work, we study the effects of different magnetic field configurations in neutron stars described by a many-body forces formalism (MBF model). The MBF model is a relativistic mean field formalism that takes into account many-body forces by means of a meson field dependence of the nuclear interaction coupling constants. We choose the best parametrization of the model that reproduces nuclear matter properties at saturation and also describes massive neutron stars. We assume matter to be in beta-equilibrium, charge neutral and at zero temperature. Magnetic fields are taken into account bot…
Strong interactions produce a rich spectrum of resonances that decay into three or more hadrons. Understanding their phenomenology requires a theoretical framework to extract parameters fromexperimental data and Lattice QCD simulations of hadron scattering. Two classes of relativistic three-body approaches are currently being pursued: the EFT-based and unitarity-based one. We consider a model of relativistic three-body scattering with an S-wave bound state in the two-body sub-channel using both formalisms. We present and discuss numerical solutions for the multi-hadron scattering amplitudes in…
We developed a novel approach based on a generalization of factorization and nuclear spectral functions, allowing for a consistent treatment of the amplitudes involving one- and two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasi elastic and $Δ$-production peaks. …
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, we examine our scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave functions from the Lippmann--Schwing…
On the equivalence of left-hand-cut and three-body formalisms
Ruhr-Universität Bochum（波鸿鲁尔大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Indiana University（印第安纳大学）
The Alt-Grassberger-Sandhas equations for the five-body eta-4N problem are solved for the case of the driving eta N and NN potentials limited to s-waves. The quasi-particle (Schmidt) method is employed to convert the equations into the effective two-body form. Numerical results are presented for the eta-4He scattering length.
The low-energy scattering of three bosons or distinguishable particles with short-range interactions is characterized by a fundamental parameter, the three-body scattering hypervolume. Its imaginary part is directly related to the three-body recombination rate in a quantum gas consisting of such particles. We derive an analytical formula of it for weak interactions, and perform its first numerical calculations for bosons with a variable nonzero-range potential. For attractive interactions, we identify several three-body resonances at which the three-body scattering hypervolume becomes divergen…
We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel …
Based on the spectator expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculations of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.
In this present work, the scattering state solutions of the Spinless Salpeter equation with the Varshni potential model were investigated. The approximate scattering phase shift, normalization constant, bound state energy, wave number and wave function in the asymptotic region were obtained. The behaviour of the phase shift with the two-body mass index η were discussed and presented.
We consider the many-body system of neutrinos interacting with each other through neutral current weak force. Emerging many-body effects in such a system could play important roles in some astrophysical sites such as the core collapse supernovae. In the literature this many-body system is usually treated within the mean field approximation which is an effective one-body description based on omitting entangled neutrino states. In this paper, we consider the original many-body system in an effective two flavor mixing scenario under the single angle approximation and present a solution without us…
