Pion Nucleon Scattering. Part 2: Methods and Results of Phenomenological Analyses

Front Matter....Pages -
2.0 Introduction....Pages 1-3
2.1.1 General remarks on partial wave and amplitude analyses....Pages 4-5
2.1.3 Inelastic partial wave analysis - the continuum ambiguity....Pages 5-7
2.1.4 Classification of partial wave analyses....Pages 7-8
2.1.5 The SACLAY and CERN phase shift analyses....Pages 8-9
2.1.6 The analysis LONDON 73 (“CBC”)....Pages 9-9
2.1.7 The Karlsruhe-Helsinki analyses KH 78 and KH 80....Pages 10-14
2.1.8 The analysis LENINGRAD 78 and the SIN analyses....Pages 14-14
2.1.9 The Carnegie-Mellon-Berkeley analysis (CMU-LBL 79)....Pages 15-18
2.1.10 New energy-dependent analyses....Pages 18-20
2.1.11 BARRELETs method....Pages 20-23
2.1.12 The analysis HENDRY 80....Pages 23-24
2.1.13 (pi-)p scattering near the eta-production threshold....Pages 24-25
2.1.14 The tail of high partial waves....Pages 25-27
2.1.15 Amplitude analyses without dispersion constraints....Pages 27-31
2.1.16 Amplitude analyses with dispersion constraints....Pages 31-32
2.1.17 Electromagnetic corrections....Pages 32-36
2.2.1 pi N forward amplitudes from total cross sections and dispersion relations....Pages 36-39
2.2.2 pi N partial wave amplitudes....Pages 55-55
Fig. 2.2.1 - 33....Pages 56-71
Table 2.2.2.1: KH 78 analysis....Pages 72-85
Table 2.2.2.2 - 3: KH 80 analysis....Pages 86-93
Table 2.2.2.4 - 5: CMU-LBL and SIN analyses....Pages 93-101
2.2.3 Invariant amplitudes....Pages 102-102
0.00 - 0.76 GeV/c....Pages 103-112
0.78 - 6.00 GeV/c....Pages 113-123
Table 2.2.3.2: Below threshold....Pages 124-128
2.2.4 s-channel helicity amplitudes....Pages 128-128
Table 2.2.3.3: At fixed scattering angle....Pages 129-144
2.3.1 Differential cross sections....Pages 148-148
Fig. 3.1.1 - 4....Pages 149-150
Table 2.3.1.2: Decomposition in the presence of Coulomb effects....Pages 151-153
Table 2.3.1.1: Reconstructed from the KH solution....Pages 154-163
Table 2.3.1.3: Legendre expansion....Pages 164-167
Part 1....Pages 168-182
Part 2....Pages 183-198
2.4.1.1 The notion of a resonance....Pages 198-202
2.4.1.2 Parametrizations of resonances....Pages 202-204
2.4.1.3 Results for the parameters of nucleon resonances....Pages 204-214
2.4.1.4 Nucleon resonances in other reactions than pi N -> pi N....Pages 214-216
2.4.1.5 Models for nucleon resonances....Pages 216-220
2.4.1.6 Degeneracy of the complex pole positions....Pages 221-222
2.4.2 Meson-nucleon coupling constants....Pages 222-228
2.4.3 Zero trajectories....Pages 229-237
2.4.4 The saturation of isospin bounds....Pages 238-242
2.4.5 Invariant amplitudes in the unphysical region and near threshold....Pages 242-244
Fig. 4.6.1 - 2....Pages 244-246
Table 2.4.6.1: Partial wave amplitudes....Pages 247-264
2.4.6.2 pi pi-scattering phase shifts....Pages 265-268
2.4.6.3 Extrapolation of pi pi N anti-N partial waves to t > 0....Pages 268-272
2.4.7 Low energy expansions....Pages 273-285
2.5.1 Low-energy models for the pion-nucleon system....Pages 285-301
2.5.2 Electromagnetic nucleon and pion form factors....Pages 301-310
2.5.3 Two-pion exchange in nucleon-nucleon scattering....Pages 310-313
2.5.4 anti-N N <-> pi pi amplitudes at t > 4m{2}....Pages 313-314
2.6.2 The Coulomb interference region....Pages 314-321
2.6.3 Diffraction scattering: fits to the data and amplitude analysis....Pages 321-321
2.6.3.1 The shape of the diffraction peak....Pages 322-326
2.6.3.2 The momentum dependence of (C+) and of the slope of Im(C+)....Pages 326-328
2.6.3.3 The partial wave decomposition of the diffraction peak....Pages 328-330
2.6.3.4 The inelastic overlap function....Pages 330-331
2.6.3.5 A high energy approximation of the impact parameter formalism....Pages 331-333
2.6.3.6 pp-scattering amplitudes in the ISR range....Pages 333-335
2.6.3.7 Elastic scattering at large t....Pages 335-337
2.6.3.8 The isospin even s-channel helicity flip amplitude....Pages 337-339
2.6.4.1 The CHOU-YANG model....Pages 339-344
2.6.4.2 The CHENG-WU model....Pages 344-345
2.6.4.3 Geometrical scaling....Pages 345-347
2.6.4.4 The VAN HOVE model for the inelastic overlap function....Pages 347-348
2.6.4.5 Other s-channel models....Pages 348-349
2.6.4.7 General remarks on t-channel models....Pages 349-350
2.6.4.8 HARARIs dual absorptive model....Pages 350-351
2.6.4.9 Recent work on Regge pole phenomenology....Pages 351-353
2.6.4.10 LIPKINS two-component pomeron....Pages 353-353
2.6.4.11 Diffraction in electromagnetic processes....Pages 354-356
2.6.4.12 The transition to the wide-angle region....Pages 356-357
2.6.4.13 Theoretical papers on diffraction scattering....Pages 358-358
2.6.5 Near-forward charge-exchange scattering....Pages 359-375
2.6.6 Wide-angle scattering....Pages 376-382
2.6.7 Near-backward scattering....Pages 382-396
2.6.8 Total elastic and charge-exchange cross sections....Pages 396-400
2.6.9 Survey index for the experimental data in the near-backward u-range....Pages 401-404
A - I....Pages 405-414
J - Z....Pages 415-423
Addendum: A - S....Pages 423-423
A - C....Pages 424-437
C - H....Pages 438-451
H - N....Pages 452-465
N - Z....Pages 466-477
Addendum: A - S....Pages 477-477
3.3 List of pion-nucleon scattering experiments....Pages 478-479
1 Kinematics....Pages 480-487
2 Scattering amplitudes....Pages 487-499
3 Expansions of scattering amplitudes....Pages 500-514
4 Measurable quantities....Pages 514-519
5 Unitarity....Pages 519-525
6.1 Behaviour of invariant amplitudes under symmetry operations....Pages 525-527
6.2 The MANDELSTAM representation....Pages 527-533
6.3 Fixed-t dispersion relations....Pages 533-537
6.4 Forward dispersion relations....Pages 537-541
6.6 Fixed-u and fixed-s dispersion relations....Pages 542-543
6.7 Hyperbolic dispersion relations....Pages 543-545
6.8 Fixed center-of-mass angle dispersion relations....Pages 545-547
6.10 Fixed-nu dispersion relations....Pages 548-548
7 Analytic properties of partial wave amplitudes....Pages 549-560
8 Low energy models....Pages 561-569
9 Regge models....Pages 569-578
10 Isospin bounds....Pages 578-580
11 Electromagnetic nucleon and pion form factors....Pages 580-587
12 References....Pages 588-593
Subject index....Pages 594-601