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E-raamat: Lattice QCD for Nuclear Physics

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  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Physics 889
  • Ilmumisaeg: 21-Nov-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319080222
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Lattice QCD for Nuclear PhysicsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Physics 889
  • Ilmumisaeg: 21-Nov-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319080222
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With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter.Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun and many new observables will be calculated at the new computational facilities.The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice disc

retizations, hadron spectroscopy and structure, many-body systems, together with more topical lectures in nuclear physics aimed a providing a broad phenomenological background. Exercises to encourage hands-on experience with parallel computing and data analysis are included.

Lattice QCD: a Brief Introduction.- Lattice Methods for Hadron Spectroscopy.- Hadron Structure on the Lattice.- Chiral Perturbation Theory.- Nuclear Physics From Lattice QCD.- High Temperature and Density in Lattice QCD.- References.
1 Lattice QCD: A Brief Introduction 1(34)
H.B. Meyer
1.1 Introduction and Scope
1(1)
1.2 The Lattice Formulation of Quantum Field Theory
2(12)
1.2.1 Scalar Field Theory
2(3)
1.2.2 Fermions
5(5)
1.2.3 Gauge Fields
10(2)
1.2.4 Lattice QCD
12(2)
1.3 The Approach to the Continuum and Renormalization
14(7)
1.3.1 The Weak-Coupling Expansion
15(2)
1.3.2 The Renormalization Group
17(2)
1.3.3 The Continuum Limit and Universality
19(1)
1.3.4 Improvement
20(1)
1.4 Observables
21(6)
1.4.1 The Wilson Loop and Its Interpretation
21(3)
1.4.2 Hadron Spectroscopy
24(2)
1.4.3 Spontaneous Chiral Symmetry Breaking and Low-Energy Constants
26(1)
1.5 Theory Topics for the Lattice Practitioner
27(5)
1.5.1 Ward Identities
27(2)
1.5.2 Chiral Symmetry on the Lattice
29(2)
1.5.3 Topology of the Gauge Field
31(1)
1.5.4 Recursive Finite-Size Technique: Linking Vastly Different Length Scales
31(1)
1.6 Importance Sampling Monte-Carlo Methods: Basic Ideas
32(2)
1.7 Outlook
34(1)
2 Lattice Methods for Hadron Spectroscopy 35(34)
Sinead M. Ryan
2.1 Introduction
35(8)
2.1.1 Notation and Basics
36(2)
2.1.2 Current and Future Experiments
38(1)
2.1.3 Lattice Hadron Spectroscopy
39(2)
2.1.4 Correlators in a Euclidean Field Theory
41(2)
2.2 Some New (and Old) Ideas for Making Measurements
43(9)
2.2.1 Smearing
44(1)
2.2.2 All to All Propagators
45(2)
2.2.3 Distillation
47(4)
2.2.4 Interim Summary
51(1)
2.3 Lattice Symmetries and Classifying States
52(2)
2.3.1 Connecting Lattice and Continuum Groups
53(1)
2.4 Building Operators and Extracting Energies
54(9)
2.4.1 Constructing Good Operators
56(2)
2.4.2 Fitting Data to Extract Energies
58(5)
2.4.3 A Lattice Error Budget
63(1)
2.5 Current Challenges
63(4)
2.5.1 Resonances and Scattering States
63(4)
2.6 Summary
67(2)
3 Hadron Structure on the Lattice 69(38)
K.U. Can
A. Kusno
E.V. Mastropas
J.M. Zanotti
3.1 Introduction
69(1)
3.2 Experimental Probes
70(13)
3.2.1 Elastic e-p Scattering
70(5)
3.2.2 Deep-Inelastic Scattering
75(6)
3.2.3 Neutron Beta Decay
81(2)
3.3 Determining Matrix Elements on the Lattice
83(22)
3.3.1 Lattice Three-Point Functions
84(4)
3.3.2 Extracting Matrix Elements
88(6)
3.3.3 Moments of Structure Functions
94(5)
3.3.4 Generalised Parton Distributions
99(6)
3.4 Summary
105(2)
4 Chiral Perturbation Theory 107(46)
Brian C. Tiburzi
4.1 Introductory Remarks
107(2)
4.2 The Chiral Lagrangian
109(12)
4.2.1 Symmetries and Symmetry Breaking
109(3)
4.2.2 Chiral Dynamics
112(3)
4.2.3 Leading Order and Beyond
115(3)
4.2.4 External Fields
118(3)
4.3 Applications Tailored to Lattice QCD
121(10)
4.3.1 Partially Quenched QCD
121(3)
4.3.2 Effects of Finite Volume
124(5)
4.3.3 Lattice Discretization Effects
129(2)
4.4 Including the Nucleon
131(10)
4.4.1 Heavy Fermions
132(2)
4.4.2 Heavy-Nucleon XPT
134(2)
4.4.3 Quark-Mass Dependence of the Nucleon
136(2)
4.4.4 Beyond Leading Order
138(3)
4.5 Issues of Convergence
141(11)
4.5.1 Including Strange Mesons
142(2)
4.5.2 Including Strange Baryons
144(3)
4.5.3 Excluding Strangeness
147(3)
4.5.4 Not-So-Heavy Baryons
150(2)
4.6 Final Remarks
152(1)
5 Nuclear Physics from Lattice QCD 153(42)
William Detmold
5.1 Introduction
153(1)
5.2 Approaching Nuclear Physics in Lattice QCD
154(2)
5.3 Two-Hadron Systems
156(19)
5.3.1 Scattering Information from Finite Volume Energy Eigenvalues
156(7)
5.3.2 Boosted Systems, Asymmetric Systems, and Systems with Unequal Masses
163(1)
5.3.3 Resonances
164(2)
5.3.4 Bound Systems
166(1)
5.3.5 Lattice Wavefunctions and Potentials
167(4)
5.3.6 Numerical Investigations
171(4)
5.4 Multi-Hadron Systems: Theoretical Framework
175(3)
5.4.1 Three-Body Systems
176(1)
5.4.2 Many-Meson Systems: Threshold Expansion
176(2)
5.4.3 Many Baryon Systems
178(1)
5.5 Multi-Hadron Systems: Contraction Methods
178(5)
5.5.1 Mesonic Systems
179(2)
5.5.2 Baryonic Systems
181(2)
5.6 Many Meson Systems
183(3)
5.7 Nuclei and Hypernuclei
186(4)
5.8 Current Issues and Future Challenges
190(3)
5.8.1 Statistical Precision
190(1)
5.8.2 Beyond Spectroscopy
191(1)
5.8.3 How Large Is a Large Volume?
192(1)
5.8.4 Spectral Gaps, Large Volumes and the Approach to the Chiral Limit
192(1)
5.8.5 Electroweak Effects
193(1)
Conclusions
193(2)
6 High Temperature and Density in Lattice QCD 195(40)
Carleton DeTar
6.1 Introduction
195(3)
6.1.1 Why Study High T and High Density QCD?
195(1)
6.1.2 Phenomenology of the Quark-Gluon Plasma
196(2)
6.2 Lattice QCD at Strong Coupling
198(9)
6.2.1 Partition Function
198(1)
6.2.2 Wilson Action and Noether Current
199(1)
6.2.3 External Point Current
200(1)
6.2.4 Gauge Theory at Strong Coupling, High T
201(1)
6.2.5 Chemical Potential
202(1)
6.2.6 Fermions at Strong Coupling, Large Mass, High T
203(2)
6.2.7 Three-Dimensional Flux-Tube Model of QCD
205(2)
6.3 Signals for Deconfinement
207(8)
6.3.1 Free Energy of a Static Charge
207(1)
6.3.2 Free Energy of a Pair of Static Charges
208(2)
6.3.3 Strange Quark Number Susceptibility
210(1)
6.3.4 Dimensional Reduction
211(2)
6.3.5 Hadrons in the Thermal Medium
213(2)
6.4 Signals for Chiral Symmetry
215(10)
6.4.1 Chiral Effective Theory and Symmetry Restoration
216(2)
6.4.2 Signals of Chiral Symmetry Restoration
218(4)
6.4.3 Universality and Critical Behavior
222(3)
6.5 Equation of State
225(6)
6.5.1 Models at Low and High Temperature
225(1)
6.5.2 Equation of State at Zero Density
226(3)
6.5.3 Equation of State at Nonzero Density
229(2)
6.5.4 Charm Quark Contribution
231(1)
6.6 Fluctuations of Conserved Charges
231(1)
Conclusions
232(3)
References 235
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