Chiral soliton models for baryons / H. Weigel.

Format:

Book

Author/Creator:

Weigel, H. (Herbert)

Series:

Lecture notes in physics 0075-8450 ; 743.

Lecture notes in physics, 0075-8450 ; 743

Language:

English

Subjects (All):

Baryons.

Particles (Nuclear physics)--Chirality.

Particles (Nuclear physics).

Solitons.

Physical Description:

ix, 274 pages : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2008]

Summary:

This comprehensive research monograph introduces and reviews the concept of chiral soliton models for baryons.

In these models, baryons emerge as (topological) defects of the chiral field. This concept is thoroughly explained and its applications shed light on a number of bayron properties, ranging from static properties via nucleon resonances and deep inelastic scattering to even heavy ion collisions. As far as possible, the theoretical investigations are confronted with experiment. Conceived to bridge the gap between advanced graduate textbooks and the research literature, this volume also features a number of appendices to help nonspecialist readers to follow in more detail some of those discussions that are basic to the soliton picture for baryons.

Contents:

1 Introduction and Motivation 1

References 4

2 Quark Flavor Interaction 5

2.1 Chiral Symmetry 5

2.2 Dynamical Breaking of Chiral Symmetry 6

2.3 The Nambu-Jona-Lasinio Model 8

2.4 Gradient Expansion 15

2.5 PCAC 19

2.6 Relation to Instanton Effects 21

2.7 Final Note on Chiral Quark Models 24

References 24

3 Self-consistent Soliton 27

3.1 Static Energy Functional 27

3.2 Method 31

3.3 Soliton Solutions in NJL-Type Models 35

3.3.1 Pseudoscalar Fields 35

3.3.2 Vector and Axial-Vector Fields 38

3.3.3 Remark on the w Field 39

3.3.4 Comments on Scalar Fields 40

References 41

4 The Skyrme Model 43

4.1 Large-NC Considerations 43

4.2 Baryons in Large-NC QCD 47

4.3 A Simple Soliton 51

4.4 Skyrme Model Soliton 53

4.5 Equations of Motion and Wess-Zumino Term 55

4.6 Topological Structures 58

4.7 Vector Interactions 60

References 64

5 Soliton Quantization in Flavor SU(2) 65

5.1 Collective Coordinates 65

5.2 Quantization of the SU(N) Rigid Top 67

5.3 Nucleon and Δ States 71

5.4 Nucleon Static Properties 73

5.5 Quantization in Vector Meson Models 79

5.6 Quantization in Chiral Quark Models 81

References 83

6 Soliton Quantization in Flavor SU(3) 85

6.1 Baryon States in the Non-relativistic Quark Model 85

6.2 Quantization of the Soliton in the Flavor Symmetric Case 86

6.3 Flavor Symmetry Breaking 92

6.4 Diagonalization with Flavor Symmetry Breaking 96

6.5 Beyond the Classical Hedgehog Solution 98

6.6 Bound State Approach 100

6.7 Baryons with a Heavy Valence Quark 105

6.8 Brief Summary on Soliton Quantization 110

References 111

7 Baryon Properties 113

7.1 Electromagnetic Properties 114

7.2 Relativistic Corrections 119

7.3 Axial Charges and Hyperon Decays 120

7.4 Proton Spin Puzzle 125

7.5 Strangeness in the Nucleon 129

7.6 Neutron-Proton Mass Difference 131

7.7 Nucleon Structure Functions 134

References 143

8 Meson-Baryon Scattering in Chiral Soliton Models 147

8.1 Adiabatic Approximation 148

8.2 S-Wave Scattering 153

8.3 P-Wave Scattering and the Yukawa Problem 156

8.4 Photoproduction 160

8.5 Non-harmonic Excitations 167

8.6 Estimate of Quantum Corrections in Soliton Models 171

References 178

9 Exotic Baryons 181

9.1 Exotic Flavor Structure and Spectrum 182

9.2 Spectrum and Mixing Mechanisms 185

9.3 The Myth of the Narrow Pentaquark 190

9.4 Rigid Rotator at Arbitrary NC 193

9.5 Solution to the Yukawa Problem 197

9.6 Skyrme Model Results for the Pentaquark Width 203

References 204

10 Multi-baryon Systems in the Skyrme Model 207

10.1 Static Configurations with B ≥ 2 207

10.2 Product Ansatz 211

10.3 Nucleon-Nucleon Potential 212

10.4 Towards Dense Matter 217

10.5 An Application to Heavy Ion Collisions 220

10.6 The H-dibaryon 225

References 229

Epilogue 231

A Chiral Properties of Quark Bilinears 233

Reference 235

B Functional Techniques 237

C Baryon Current and Wess-Zumino Term 243

C.1 Gradient Expansion of the Fermion Determinant with a Baryon Source 243

C.2 Gauging the Wess-Zumino Term 246

C.3 Wess-Zumino Term in the Bound State Approach 249

C.4 π0 Decay 250

References 252

D SU(3) Euler Angles 253

References 258

E Matrix Elements of Momentum Eigenstates 259

E.1 Momentum Eigenstates from Collective Coordinates 259

E.2 Relativistic Recoil Corrections 261

References 263

Recoupling Coefficients in Adiabatic Scattering 265

F.1 Adiabatic Recoupling Coefficients 265

F.2 Jost Function for Intrinsic Fluctuations 267

References 270.

Notes:

Includes bibliographical references and index.

ISBN:

3540754350

9783540754350

OCLC:

173721146