Direct evaluation of parton distribution functions of the nucleon from lattice QCD / Aurora Scapellato. Wuppertal, May 2019
Content
Contents
List of Figures
List of Tables
1 Introduction
2 Parton physics
2.1 Elastic scattering
2.2 Inelastic scattering
2.3 Parton Model
2.3.1 OPE analysis and light-cone dominance
2.3.2 Definition of parton distributions
2.3.3 Moments of PDFs and sum rules
2.4 Obtaining parton distributions
3 Lattice QCD and parton physics in Euclidean space
3.1 Introduction to QCD
3.2 Lattice QCD approach
3.3 Standard discretization schemes
3.4 Improved discretization schemes
3.5 Computing observables in lattice QCD
3.6 Quasi-distributions on a Euclidean space-time
4 Nucleon correlation functions on the lattice
4.1 Nucleon field
4.2 Nucleon two-point functions
4.3 Nucleon three-point functions
4.4 Nucleon matrix elements
4.5 Quark propagator
4.6 Smearing techniques
5 Bare matrix elements for quark distribution functions
5.1 Lattice setup
5.1.1 Nf=2 physical point ensemble
5.1.2 Definition of operators
5.1.3 Improvement with momentum smearing
5.1.4 Choosing the optimal setup
5.2 Lattice results at the largest source-sink separation
5.2.1 Matrix elements with stout smearing
5.2.2 Momentum dependence
5.2.3 Unpolarized matrix elements: choice of the Dirac structure
5.3 Lattice results for excited states analysis
5.3.1 The method
5.3.2 Two-point function analysis
5.3.3 Matrix elements for the unpolarized PDFs
5.3.4 Matrix elements for the helicity PDFs
5.3.5 Matrix elements for the transversity PDFs
5.4 Computational cost of simulations
6 Renormalization of matrix elements
6.1 The method
6.2 Lattice results for renormalization functions
6.3 Renormalized matrix elements
6.4 Renormalized matrix elements with stout smearing
7 Physical Quark distributions
7.1 Matching to light-cone PDFs
7.2 Dependence on the pion mass
7.3 Quark unpolarized distributions
7.4 Quark helicity distributions
7.5 Quark transversity distributions
8 Conclusions and Outlook
Bibliography
Appendix A