Hadronic Physics from Lattice QCD

✍ Scribed by Anthony M. Green

• Publisher: World Scientific
• Year: 2004
• Tongue: English
• Leaves: 385
• Category: Library

✦ Synopsis

• Several of the authors give elementary introductions that lead to some duplication. This we believe is a positive feature since each author presents a different viewpoint emphasizing the particular topic of that chapter - The topics chosen are the closest Lattice QCD comes to more conventional particle and nuclear physics - The numerical results presented in the various chapters are most up-to-date

✦ Table of Contents

Preface
Contents
Chapter 1 Meson and Baryon Spectroscopy on a Lattice
1.1 Introduction
1.2 Basic Lattice Gauge Theory
1.3 Systematic Errors
1.3.1 Unquenching
1.3.2 Lattice spacing errors
1.3.3 Quark mass dependence
1.3.4 Finite size effects
1.4 An Analysis of Some Lattice Data
1.5 Parameter Values of Lattice QCD Calculations
1.6 The Masses of Light Mesons
1.6.1 P-wave mesons and higher excitations
1.7 The Masses of Light Baryons
1.7.1 Excited baryon states
1.8 Electromagnetic Effects
1.9 Insight from Lattice QCD Calculations
1.10 What Lattice QCD Is Not Good at
1.11 Conclusions
Acknowledgements
Appendix: Technical Details
Bibliography
Chapter 2
Exotics
2.1 Introduction
2.2 Glueballs and Scalar Mesons
2.2.1 Glueballs in quenched QCD
2.2.2 Scalar mesons in quenched QCD
2.2.3 Scalar mesons in full QCD
2.2.4 Experimental evidence for scalar mesons
2.3 Hybrid Mesons
2.3.1 Heavy quark hybrid mesons
2.3.2 Hybrid meson decays
2.3.3 Light quark hybrid mesons
2.4 Hadronic Molecules
2.5 Conclusions and Outlook
Acknowledgements
Bibliography
Chapter 3
Two Quark Potentials
3.1 Motivation
3.2 The Static QCD Potential
3.2.1 Wilson loops
3.2.2 Exact results
3.2.3 Strong coupling expansions
3.2.4 String picture
3.2.5 The potential in perturbation theory
3.3 Quark-Antiquark Potentials between Non-Static Quarks
3.3.1 Radial form of V(QQ)
3.3.2 Comparison with the form of V(NN)
3.4 Conclusions
Acknowledgements
Bibliography
Chapter 4
Interactions between Lattice Hadrons
4.1 Introductory Overview on Goals, Strategies, Methods
4.1.1 Modeling nuclear forces
4.1.2 The lattice QCD perspective
4.1.3 Short and long term goals for lattice QCD
4.1.4 Probing the lattice
4.1.5 Finite-size methods
4.1.6 Residual interaction
4.1.7 Use of improved actions
4.2 A Simple U(1) Lattice Model in 2+1 Dimensions
4.2.1 Lattice action
4.2.2 Meson fields
4.2.3 Correlation matrices
4.2.4 Correlation matrix for noninteracting mesons
4.2.5 Computation with random sources
4.3 Effective Residual Interaction
4.3.1 Perturbative definition
4.3.2 Effective interaction for composite operators
4.3.3 Lattice symmetries
4.3.4 Truncated momentum basis
4.3.5 Adiabatic approximation
4.3.6 Analysis on a periodic lattice
4.4 Current State of QCD in 3+1 Dimensions
4.4.1 Scattering lengths for and N systems
4.4.2 Static N Š N and N Š N potentials
4.4.3 Heavy-light meson-meson systems
4.4.4 Momentum-space work on the – system
4.4.5 Coordinate-space work on the – system
4.5 Conclusion and Outlook
Acknowledgements
Appendix A: Remarks on Staggered Fields
Appendix B: Improved Lattice Actions
B.1: A scalar example
B.2: Improvement of a pure gauge theory
B.3: Improvement of a fermionic action
B.4: More on highly improved actions
B.5: Clover leaf fermion action
Bibliography
Chapter 5
Bridges from Lattice QCD to
Nuclear Physics
5.1 Introduction
5.1.1 Numerical treatment of QCD
5.1.2 Effective Field/Potential Theories
5.2 What Is Meant by “A Bridge”?
5.2.1 A simple example of a bridge
5.2.2 Are there bridges other than VQQ?
5.3 The Energies of Four Static Quarks (QQQQ)
5.3.1 Quark descriptions of hadron-hadron interactions
5.3.2 The role of lattice QCD
5.4 (QQ) and [(QQ)(QQ)] Configurations
5.4.1 Lattice calculations with (QQ) configurations
5.4.2 Lattice calculations with [(QQ)(QQ)] configurations
5.4.3 Lattice parameters and finite size/scaling check
5.5 Potential Model Description of the Lattice Data
5.5.1 Unmodified two-body approach
5.5.2 The effect of multiquark interactions
5.5.3 A compromise for the overlap factor f
5.5.4 The effect of two-gluon exchange
5.5.5 Parametrizations of the gluon-field overlap factor f
5.6 More Complicated [(QQ)(QQ)] Geometries
5.6.1 Tetrahedral configurations on a lattice
5.6.2 QCD in two dimensions (1+1)
5.7 Extensions of the 2 × 2 f-Model
5.8 Heavy-Light Mesons (Qq)
5.8.1 Bottom (B)-mesons
5.8.2 Lattice parameters
5.8.3 Maximal Variance Reduction (MVR)
5.8.4 Energies of heavy-light mesons (Qq)
5.9 Charge and Matter Distributions of Heavy-Light Mesons
(Qq)
5.9.1 Three-point correlation functions C3
5.9.2 Analysis of C3
5.9.3 Fits to the radial forms
5.9.4 Sum rules
5.10 The B – B System as a [(Qq)(Qq)] Configuration
5.10.1 Lattice calculation of the [(Qq)(Qq)] system
5.10.2 Extension of the f-model to the [(Qq)(Qq)] system
5.11 The B – B System as a [(Qq)(Qq)] Configuration
5.12 Conclusions and the Future
Acknowledgements
Appendix A: Extensions of the f-Model from 2 × 2 to 6 × 6
A.1: The 3 × 3 extension of the unmodified two-body approach of Subsec. 5.5.1
A.2: The 3 × 3 extension of the f-model of Subsec. 5.5.2
A.3: The 6 × 6 extension of the f-model of Subsec. 5.5.2
Appendix B: Extension of the f-Model to [(Qq)(Qq)] Systems
Bibliography