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Register a new userRelativistic descriptions of few-body systems
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V.A. Karmanov
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A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed.
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We present a work which is meant to inspire the few-body practitioners to venture into the study of new, more exotic, systems and to hadron physicists, working mostly on two-body problems, to move in the direction of studying related few-body systems. For this purpose we devote the discussions in the introduction to show how the input two-body amplitudes can be easily obtained using techniques of the chiral unitary theory, or its extensions to the heavy quark sector. We then briefly explain how these amplitudes can be used to solve the Faddeev equations or a simpler version obtained by treating the three-body scattering as that of a particle on a fixed center. Further, we give some examples of the results obtained by studying systems involving mesons. We have also addressed the field of many meson systems, which is currently almost unexplored, but for which we envisage a bright future. Finally, we give a complete list of works dealing with unconventional few-body systems involving one or several mesons, summarizing in this way the findings on the topic, and providing a motivation for those willing to investigate such systems.
An appropriate framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. The Bakamjian-Thomas construction provides a systematic procedure for implementing interactions in a relativistic invariant way. It leads, however, to problems with cluster separability. It has been known for some time, due to Sokolovs pioneering work, that mass operators with correct cluster properties can be obtained through a series of unitary transformations making use of so-called packing operators. In the present contribution we sketch an explicit construction of packing operators for three-particle systems consisting of distinguishable, spinless particles.
Hadronic composite states are introduced as few-body systems in hadron physics. The $Lambda(1405)$ resonance is a good example of the hadronic few-body systems. It has turned out that $Lambda(1405)$ can be described by hadronic dynamics in a modern technology which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic $bar KN$ composite state of $Lambda(1405)$ is extended to kaonic few-body states. It is concluded that, due to the fact that $K$ and $N$ have similar interaction nature in s-wave $bar K$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like $bar KNN$, $bar KKN$ and $bar KKK$, as well as $Lambda(1405)$ as a $bar KN$ quasibound state and $f_{0}(980)$ and $a_{0}(980)$ as $bar KK$.
A convenient framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. Unlike relativistic quantum field theory, one deals with a fixed, or at least restricted number of degrees of freedom while maintaining relativistic invariance. For systems of interacting particles this is achieved by means of the, so called, Bakamjian-Thomas construction, which is a systematic procedure for implementing interaction terms in the generators of the Poincare group such that their algebra is preserved. Doing relativistic quantum mechanics in this way one, however, faces a problem connected with the physical requirement of cluster separability as soon as one has more than two interacting particles. Cluster separability, or sometimes also termed macroscopic causality, is the property that if a system is subdivided into subsystems which are then separated by a sufficiently large spacelike distance, these subsystems should behave independently. In the present contribution we discuss the problem of cluster separability and sketch the procedure to resolve it.
Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}gtrsim 2,,fm^{-1}$ and small values of ${K}_{CM} lesssim 1.0,,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short range correlation (SRC) picture. When $K_{CM}$ and $k_{rel}$ are both large, the distributions exhibit a strong angle dependence, which is evidence of three-nucleon (3N) SRC. The predicted center-of-mass and angular dependence of 2N and 3N SRC should be observable in two-nucleon knock-out processes $A(e,epN)X$.
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