Three-Particle Physics and Dispersion Relation Theory

The following sections are included:

• Preface

• Contents

The following sections are included:

• Non-relativistic three-nucleon and three-quark systems

• Dispersion relation technique for three particle systems

• References

The following sections are included:

• Analytical properties of four-point amplitudes

• Dispersion relation N/D-method and ansatz of separable interactions

• Instantaneous interaction and spectral integral equation for two-body systems

• Appendix A. Angular momentum operators

• Appendix B: The ππ scattering amplitude near the twopion thresholds, π⁺π^- and π⁰π⁰

• Appendix C: Four-pole fit of the ππ(00⁺⁺) wave in the region M_ππ < 900 MeV

• References

The following sections are included:

• Three-body system in terms of separable interactions: analytic continuation of the four-point scattering amplitude to the decay region

• Non-relativistic approach and transition of two-particle spectral integral to the three-particle one

• Consideration of amplitudes in terms of a three-particle spectral integral

• Three-particle composite systems, their wave functions and form factors

• Equation for an amplitude in the case of instantaneous interactions in the final state

• Conclusion

• Appendix A. Example: loop diagram with G^L=G^R=1

• Appendix B. Phase space for n-particle state

• Appendix C. Feynman diagram technique and evolution of systems in the positive time-direction

• Appendix D. Coordinate representation for nonrelativistic three-particle wave function

• References

The following sections are included:

• Introduction

• Non-resonance interaction of the produced particles

• The production of three particles near the threshold when two particles interact strongly

• Decay amplitude for K → 3π and pion interaction

• Equation for the three-nucleon amplitude

• Appendix A. Landau rules for finding the singularities of the diagram

• Appendix B. Anomalous thresholds and final state interaction

• Appendix C. Homogeneous Skornyakov–Ter-Martirosyan equation

• Appendix D. Coordinates and observables in the threebody problem

• References

The following sections are included:

• Boson propagators

• Propagators of fermions

• Spectral integral equations for the coupled three-meson decay channels in annihilation at rest

• Conclusion

• References

The following sections are included:

• The K-Matrix and D-Matrix Techniques

• Meson-meson scattering

• Partial wave analysis of baryon spectra in the frameworks of K-matrix and D-matrix methods

• References

The following sections are included:

• Introduction

• Meson–nucleon collisions at high energies: peripheral two-meson production in terms of reggeon exchanges

• Results of the fit

• Summary for isoscalar resonances

• Appendix A. D-matrix technique in the two-meson production reactions

• Appendix B. Elements of the reggeon exchange technique in the two-meson production reactions

• Appendix C. Cross sections for the reactions πN → ππN, KKN, ηηN

• Appendix D. Status of trajectories on (J, M²) plane

• Appendix E. Assignment of Mesons to Nonets

• References

The following sections are included:

• Diquarks and reduction of baryon states

• Baryons as quark–diquark systems

• The setting of states with L = 0 and the SU(6) symmetry

• The setting of baryons with L > 0 as states

• Version with and overlapping and states

• Conclusion

• Appendix A. Spectral integral equations for pure and systems

• Appendix B. Group theoretical description. Symmetrical basis in the three-body problem

• References

The dispersion technique allows us to construct analytic and unitary amplitudes which is a necessary condition to study strong interaction physics (i.e. the physics of hadrons). Working in the framework of this approach one can be sure that causality is fulfilled in the considered processes, and there exists a complete set of states one can work with…