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Three-Particle Physics and Dispersion Relation Theory

Three-Particle Physics and Dispersion Relation TheoryTitoloThree-Particle Physics and Dispersion Relation Theory
AutoreAnisovich, A. V. ; Anisovich, V. V. ; Matveev, M. A.
Prezzo
€ 73,66   Spedizioni gratuite in Italia
(Prezzo € 77,54)
CategoriaScience: Physics - Nuclear
Science: Physics - Atomic & Molecular
Science: Physics - Mathematical & Computational
RilegaturaHardcover
Dati344 p.
Anno2013
EditoreWorld Scientific Publishing Company
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Prefacev
1 Introduction
1
1.1 Non-relativistic three-nucleon and three-quark systems
1
1.1.1 Description of three-nucleon systems
2
1.1.2 Three-quark systems
3
1.2 Dispersion relation technique for three particle systems
4
1.2.1 Elements of the dispersion relation technique for two-particle systems
5
1.2.2 Interconnection of three particle decay amplitudes and two-particle scattering ones in hadron physics
6
1.2.3 Quark-gluon language for processes in regions I, III and IV
10
1.2.4 Spectral integral equation for three particles
11
1.2.5 Isobar models
12
1.2.6 Quark-diquark model for baryons and group-theory approach
19
2 Elements of Dispersion Relation Technique for Two-Body Scattering Reactions
25
2.1 Analytical properties of four-point amplitudes
25
2.1.1 Mandelstam planes for four-point amplitudes
26
2.1.2 Bethe-Salpeter equations in the momentum representation
29
2.2 Dispersion relation TV/D-method and ansatz of separable interactions
34
2.2.1 N/D-method for the one-channel scattering amplitude of spinless particles
34
2.2.2 Scattering amplitude and energy non-conservation in the spectral integral representation
37
2.2.3 Composite system wave function and its form factors
39
2.2.4 Scattering amplitude with multivertex representation of separable interaction
42
2.3 Instantaneous interaction and spectral integral equation for two-body systems
45
2.3.1 Instantaneous interaction
45
2.3.2 Spectral integral equation for a composite system
47
2.4 Appendix A. Angular momentum operators
52
2.4.1 Projection operators and denominators of the boson propagators
55
2.4.2 Useful relations for Zαμ1"...μn and Xv2... vn (n-1)
56
2.5 Appendix B: The π π scattering amplitude near the two-pion thresholds, π+ π- and π0π0
58
2.6 Appendix C: Four-pole fit of the π π(00++) wave in the region Mπ π < 900 MeV
59
3 Spectral Integral Equation for the Decay of a Spinless Particle
63
3.1 Three-body system in terms of separable interactions: analytic continuation of the four-point scattering amplitude to the decay region
64
3.1.1 Final state two-particle S-wave interactions
65
3.1.2 General case: rescatterings of outgoing particles, PiPj → PiPj, with arbitrary angular momenta
71
3.2 Non-relativistic approach and transition of two-particle spectral integral to the three-particle one
77
3.2.1 Non-relativistic approach
78
3.2.2 Threshold limit constraint
80
3.2.3 Transition of the two-particle spectral integral representation amplitude to the three-particle spectral integral
81
3.3 Consideration of amplitudes in terms of a three-particle spectral integral
84
3.3.1 Kinematics of the outgoing particles in the c.m. system
86
3.3.2 Calculation of the block B(0)13-12(s, S12)
86
3.4 Three-particle composite systems, their wave functions and form factors
87
3.4.1 Vertex and wave function
88
3.4.2 Three particle composite system form factor
89
3.5 Equation for an amplitude in the case of instantaneous interactions in the final state
90
3.6 Conclusion
91
3.7 Appendix A. Example: loop diagram with GL = GR = 1
92
3.8 Appendix B. Phase space for n-particle state
92
3.9 Appendix C. Feynman diagram technique and evolution of systems in the positive time-direction
93
3.9.1 The Feynman diagram technique and non-relativistic three particle systems
94
3.10 Appendix D. Coordinate representation for non-relativistic three-particle wave function
97
4 Non-relativistic Three-Body Amplitude
101
4.1 Introduction
101
4.1.1 Kinematics
101
4.1.2 Basic principles for selecting the diagrams
103
4.2 Non-resonance interaction of the produced particles
106
4.2.1 The structure of the amplitude with a total angular momentum J = 0
106
4.2.2 Production of three particles in a state with J = 1
120
4.3 The production of three particles near the threshold when two particles interact strongly
123
4.3.1 The production of three spinless particles
124
4.4 Decay amplitude for K → 3π and pion interaction
126
4.4.1 The dispersion relation for the decay amplitude
126
4.4.2 Pion spectra and decay ratios in K → πππ within taking into account mass differences of kaons and pions
130
4.4.3 Transformation of the dispersion relation for the K → π π π amplitude to a single integral equation
134
4.5 Equation for the three-nucleon amplitude
137
4.5.1 Method of extraction of the leading singularities
138
4.5.2 Helium-3/tritium wave function
145
4.6 Appendix A. Landau rules for finding the singularities of the diagram
150
4.7 Appendix B. Anomalous thresholds and final state interaction
153
4.8 Appendix C. Homogeneous Skornyakov-Ter-Martirosyan equation
158
4.9 Appendix D. Coordinates and observables in the three-body problem
159
4.9.1 Choice of coordinates and group theory properties
159
4.9.2 Parametrization of a complex sphere
162
4.9.3 The Laplace operator
163
4.9.4 Calculation of the generators Lik and Bik
165
4.9.5 The cubic operator Ω
168
4.9.6 Solution of the eigenvalue problem
170
5 Propagators of Spin Particles and Relativistic Spectral Integral Equations
173
5.1 Boson propagators
174
5.1.1 Projection operators and denominators of the boson propagators
174
5.2 Propagators of fermions
176
5.2.1 The classification of the baryon states
176
5.2.2 Spin-1/2 wave functions
177
5.2.3 Spin-3/2 wave functions
179
5.3 Spectral integral equations for the coupled three-meson decay channels in pp (JPG = 0-+) annihilation at rest
182
5.3.1 The S-P-D-wave meson rescatterings
183
5.3.2 Equations with inclusion of resonance production
188
5.3.3 The coupled decay channels pp(IJPC = 10-+) → π0π0π0, ηηη0, KKπ0
189
5.4 Conclusion
194
6 Isobar model and partial wave analysis. D-matrix method
197
6.1 The if-Matrix and D-Matrix Techniques
198
6.1.1 K-matrix approach
198
6.1.2 Spectral integral equation for the If-matrix amplitude
200
6.1.3 D-matrix approach
201
6.2 Meson-meson scattering
204
6.2.1 K-matrix fit
204
6.2.2 D-matrix fit
207
6.3 Partial wave analysis of baryon spectra in the frameworks of K-matrix and D-matrix methods
209
6.3.1 Pion and photo induced reactions
212
7 Reggeon-Exchange Technique
217
7.1 Introduction
217
7.2 Meson-nucleon collisions at high energies: peripheral two-meson production in terms of reggeon exchanges
219
7.2.1 K-matrix and D-matrix approaches
220
7.2.2 Reggeized pion-exchange trajectories for the waves JPG = 0++, 1--, 2++, 3--, 4++
223
7.2.3 Amplitudes with aj-trajectory exchanges
227
7.2.4 π-p → KK n reaction with exchange by ρ-meson trajectories
233
7.3 Results of the fit
237
7.3.1 The ƒ0(1300) state
239
7.4 Summary for isoscalar resonances
243
7.4.1 Isoscalar-scalar sector
243
7.4.2 Isoscalar-tensor sector
244
7.4.3 Isoscalar sector JPC = 4++
244
7.5 Appendix A. D-matrix technique in the two-meson production reactions
245
7.5.1 D-matrix in one-channel and two-channel cases
245
7.6 Appendix B. Elements of the reggeon exchange technique in the two-meson production reactions
247
7.6.1 Angular momentum operators for two-meson systems
248
7.6.2 Reggeized pion exchanges
249
7.7 Appendix C. Cross sections for the reactions π N → π πN, KKN, ηηN
256
7.7.1 The CERN-Munich approach
257
7.7.2 GAMS, VES, and BNL approaches
258
7.8 Appendix D. Status of trajectories on (J, M2) plane
259
7.8.1 Kaon trajectories on (J, M2) plane
261
7.9 Appendix E. Assignment of Mesons to Nonets
262
8 Searching for the Quark-Diquark Systematics of Baryons
267
8.1 Diquarks and reduction of baryon states
267
8.2 Baryons as quark-diquark systems
271
8.2.1 S'-wave diquarks and baryons
271
8.2.2 Wave functions of quark-diquark systems with L = 0
272
8.2.3 Wave functions of quark-diquark systems with L ≠ 0
277
8.2.4 Quarks and diquarks in baryons
279
8.3 The setting of states with L = 0 and the SU(6) symmetry
282
8.3.1 Baryon spectra for the excited states
283
8.3.2 The setting of (L=0) states
284
8.4 The setting of baryons with L > 0 as (qD11, qD00) states
285
8.4.1 The setting of N(J+) states at MD00 ≠ MD11 and L ≥2
288
8.4.2 The setting of the N(J~) states at MD00 ≠ MD11
289
8.4.3 The setting of Δ(J+) states at MD00 ≠ MD11 and L ≥ 2
290
8.4.4 The setting of Δ(J-) states at MD00 MD11
291
8.4.5 Overlapping of baryon resonances
292
8.5 Version with MD00 = Md11 and overlapping qD00(S = 1/2) and qD11(S =1/2) states
296
8.6 Conclusion
297
8.7 Appendix A. Spectral integral equations for pure qD00 and qD11 systems
299
8.7.1 Confinement singularities
299
8.7.2 The qD00 systems
300
8.7.3 Spectral integral equations for qD\ systems with I= 3/2
303
8.8 Appendix B. Group theoretical description. Symmetrical basis in the three-body problem
307
8.8.1 Group theoretical properties. Parametrization
309
8.8.2 Basis functions
311
8.8.3 Transformation coefficients ⟨j1j2|j1j2⟨φKJM
313
8.8.4 Applying ⟨j1j2|j1j2⟨Φ KLM to the three-body problem
318
8.8.5 The d-function of the 0(6) group
319
9 Conclusion
323

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