Relativistic Few-Body Physics

I discuss different formulations of the relativistic few-body problem with an emphasis on how they are related. I first discuss the implications of some of the differences with non-relativistic quantum mechanics. Then I point out that the principle of special relativity in quantum mechanics implies that the quantum theory has a Poincaré symmetry, which is realized by a unitary representation of the Poincaré group. This representation can always be decomposed into direct integrals of irreducible representations and the different formulations differ only in how these irreducible representations are realized. I discuss how these representations appear in different formulations of relativistic quantum mechanics and discuss some applications in each of these frameworks.     

Few-Body Aspects of Hypernuclear Physics

Recent development in the study of the structure of light Λ and double Λ hypernuclei is reviewed from the view point of few-body problems and interactions between the constituent particles. In the study the present author and collaborators employed Gaussian expansion method for few-body calculations; the method has been applied to many kinds of few-body systems in the fields of nuclear physics and exotic atomic/molecular physics. We reviewed the following subjects studied using the method: (1) Precise three- and four-body calculations of ${^7_{\Lambda}{\rm He}}$ , ${^7_{\Lambda}{\rm Li}}$ , ${^7_{\Lambda}{\rm Be}}$ , ${^8_{\Lambda}{\rm Li}}$ , ${^8_{\Lambda}{\rm Be}}$ , ${^9_{\Lambda}{\rm Be}}$ , ${^{10}_{\Lambda}{\rm Be}}$ , ${^{10}_{\Lambda}{\rm B}}$ and ${^{13}_{\Lambda}{\rm C}}$ provide important information on the spin structure of the underlying Λ N interaction by comparing the calculated results with the recent experimental data by γ-ray hypernuclear spectroscopy. (2) The Λ-Σ coupling effect was investigated in ${^4_{\Lambda}{\rm H}}$ and ${^4_{\Lambda}{\rm He}}$ on the basis of the N?+?N?+?N?+?Λ (Σ) four-body model. (3) A systematic study of double-Λ hypernuclei and the Λ Λ interaction, based on the NAGARA event data ( ${^6_{\Lambda\Lambda}{\rm He}}$ ), was performed within the α +?x?+?Λ +?Λ cluster model (x = n, p, d, t,³He and α) and α +?α +?n?+?Λ +?Λ cluster model, (4) The Demachi-Yanagi event was interpreted as observation of the 2⁺ state of ${^{10}_{\Lambda \Lambda}{\rm Be}}$ , (5) The Hida event was interpreted as observation of the ground state of ${^{11}_{\Lambda \Lambda}{\rm Be}}$ .     

Experimental Activities in Few-Body Physics

Understanding the few-nucleon system remains one of the challenges in modern nuclear and hadron physics. Observables in few-nucleon scattering processes are sensitive probes to study the two and many-body interactions between nucleons in nuclei. In the past decades, several facilities provided a large data base to study in detail the three-nucleon interactions below the pion-production threshold by exploiting polarized proton and deuteron beams and large-acceptance detectors. Only since recently, the four-nucleon scattering process at intermediate energies has been explored. In addition, there is a focus to collect data in the hyperon-nucleon sector, thereby providing access to understand the more general baryon-baryon interaction. In this contribution, some recent results in the few-nucleon sector are discussed together with some of the preliminary results from a pioneering and exclusive study of the four-nucleon scattering process. Furthermore, this paper discusses the experimental activities in the hyperon sector, in particular, the perspectives of the hyperon program of PANDA.     

Nuclear Few-Body Physics at FAIR

The FAIR facility, to be constructed at the GSI site in Darmstadt, will be addressing a wealth of outstanding questions within the realm of subatomic, atomic and plasma physics through a combination of novel accelerators, storage rings and innovative experimental set-ups. One of the key installations is the fragment separator Super-FRS that will be able to deliver an unprecedented range of radioactive ion beams (RIBs) in the energy range of 0?C1.5?GeV/u to the envisaged experiments collected within the NuSTAR collaboration. This will in particular permit new experimental investigations of nuclear few-body systems at extreme isospins, also reaching beyond the drip-lines, using the NuSTAR-R³B set-up. The outcome of pilot experiments on unbound systems are reported, as well as crucial detector upgrades.     

Few-Body Physics in a Many-Body World

The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three or more bodies brings about complications but also a host of interesting phenomena. In recent years, the cooling and trapping of atoms and molecules has shown great promise to provide a highly controllable environment to study few-body physics. However, as is true for many systems where few-body effects play an important role the few-body states are not isolated from their many-body environment. An interesting question then becomes if or (more precisely) when we should consider few-body states as effectively isolated and when we have to take the coupling to the environment into account. Using some simple, yet non-trivial, examples I will try to suggest possible approaches to this line of research.     

Panel Session on the Future of Few-Body Physics

During the 22nd European Few-Body Conference, a session was devoted to a panel discussion on the future of few-body physics. The panel members were Charlotte Elster, Jaume Carbonell, Evgeny Epelbaum, Nasser Kalantar-Nayestanaki, and Jean-Marc Richard. The session was chaired by Ben Bakker. After presentations by the panel members, several topics were discussed with the audience. The conclusions of this discussion are presented in this paper.     

Relativistic Covariance of Light-Front Few-Body Systems in Hadron Physics

We study the light-front covariance of a vector-meson decay constant using a manifestly covariant fermion field theory model in (3 + 1) dimensions. The light-front zero-mode issues are analyzed in terms of polarization vectors and method of identifying the zero-mode operator and of obtaining the light-front covariant decay constant is discussed.     

Stochastic Variational Approach to Few-Body Problems in Condensed Matter Physics

The stochastic variational method is a powerful approach to solve few-body problems. The application of the stochastic variational approach to few-body problems in condensed matter physics is presented. The examples include calculation of energy spectra of atoms in magnetic field, confined atoms and trapped Fermi gases.     

The Few-Body Approximation in Nuclear,Atomic, and Molecular Physics

The quantum theory of few-body scattering based on Faddeev-Yakubovsky integral and differential equa¬tions is applied to calculations of various processes (elastic, inelastic, atom exchange, and dissociative) in nuclear, atomic, and molecular physics. Analytical solutions of these equations are presented for various limiting cases. The methods used for solving the integral and differential systems of equations are discussed.     

Few-Body Physics in Chiral Effective Field Theory: Recent Developments

Chiral effective field theory provides a systematic tool to study few-nucleon dynamics based on the approximate and spontaneously broken chiral symmetry of QCD. I discuss applications of this method to nuclear forces and few-nucleon dynamics. Various related topics including recent advances in nuclear lattice simulations are also addressed.     

Deeply virtual compton scattering from the neutron with CLAS and CLAS12

Generalised Parton Distributions (GPDs) offer an insight into the three-dimensional structure of the nucleon and its internal dynamics, relating the longitudinal momentum of quarks to their transverse position. A very effective means of accessing GPDs is via measurements of cross-sections and polarisation-asymmetries in Deeply Virtual Compton Scattering (DVCS). In particular, the beam-spin asymmetry (BSA) in DVCS from the neutron is especially sensitive to angular momentum of the up- and down-quarks, and its measurement therefore has potential to shed important light on the puzzle of nucleon spin. We present a preliminary extraction of BSA from a recent experiment using a 6 GeV electron beam and the CLAS detector at Jefferson Laboratory and introduce the Central Neutron Detector to be integrated with CLAS12 for the exclusive measurement of neutron DVCS at 11 GeV, made possible by the Jefferson Lab upgrade.     

Large Few-Body Systems

Signatures of large few-body systems were recently observed in experiments with ultracold gases. This paper presents a brief introductory review of related theoretical concepts and recent experimental advances.     

The spin program with CLAS at JLab

We report on the status of an extensive program to study the scattering of longitudinally polarized electrons from longitudinally polarized NH₃ and ND₃ targets using the CLAS detector at JLab. The data span a range inQ ² from 0.05–4.5 (GeV/c)² and a range inW, the γ^* N invariant mass, up to about 3 GeV. With the excellent particle identification available with the CLA, both inclusive and exclusive scattering can be studied. The experimental techniques are reviewed and some preliminary results are presented. This paper focuses on extraction of the spin structure functiongg ₁ for the proton and the deuteron.