Lattice QCD Calculation of Nucleon Structure
Abstract
It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of stronginteraction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out firstprinciples calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and largescale computer simulation. We started out by calculating the nucleon form factors  electromagnetic, axialvector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermionmore »
 Authors:
 University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
 Publication Date:
 Research Org.:
 University of Kentucky, Lexington, KY (United States). Research Foundation
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1323029
 Report Number(s):
 DOEUKRF84ER40154
TRN: US1700277
 DOE Contract Number:
 FG0284ER40154
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LATTICE FIELD THEORY; D S MESONS; PROTONS; N1440 BARYONS; PIONS; SCALAR MESONS; S QUARKS; CHARMONIUM; D QUARKS; QUANTUM CHROMODYNAMICS; COMPUTERIZED SIMULATION; LEPTONIC DECAY; SPIN; ORBITAL ANGULAR MOMENTUM; CHIRAL SYMMETRY; GLUONS; ELECTROMAGNETIC FORM FACTORS; SIGMA TERMS; MASS; MONTE CARLO METHOD; MEV RANGE; NUCLEONS; STRANGENESS; STRONG INTERACTIONS; SCALARS; MASS SPECTRA; MAGNETIC MOMENTS; PATH INTEGRALS; SUM RULES; APPROXIMATIONS; PARTICLE WIDTHS; RHO770 MESONS; A0980 MESONS; DEGREES OF FREEDOM; PHASE TRANSFORMATIONS; WARD IDENTITY; CORRECTIONS; PARTICLE STRUCTURE; ALGORITHMS; GLUEBALLS; U QUARKS; KENTUCKY; RESEARCH PROGRAMS
Citation Formats
Liu, KehFei, and Draper, Terrence. Lattice QCD Calculation of Nucleon Structure. United States: N. p., 2016.
Web. doi:10.2172/1323029.
Liu, KehFei, & Draper, Terrence. Lattice QCD Calculation of Nucleon Structure. United States. doi:10.2172/1323029.
Liu, KehFei, and Draper, Terrence. 2016.
"Lattice QCD Calculation of Nucleon Structure". United States.
doi:10.2172/1323029. https://www.osti.gov/servlets/purl/1323029.
@article{osti_1323029,
title = {Lattice QCD Calculation of Nucleon Structure},
author = {Liu, KehFei and Draper, Terrence},
abstractNote = {It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of stronginteraction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out firstprinciples calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and largescale computer simulation. We started out by calculating the nucleon form factors  electromagnetic, axialvector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the Ds meson decay constant fDs, the strangeness and charmness, the meson mass decomposition and the strange quark spin from the anomalous Ward identity. Recently, we have started to include multiple lattices with different lattice spacings and different volumes including large lattices at the physical pion mass point. We are getting quite close to being able to calculate the hadron structure at the physical point and to do the continuum and large volume extrapolations, which is our ultimate aim. We have now finished several projects which have included these systematic corrections. They include the leptonic decay width of the ρ, the πN sigma and strange sigma terms, and the strange quark magnetic moment. Over the years, we have also studied hadron spectroscopy with lattice calculations and in phenomenology. These include Roper resonance, pentaquark state, charmonium spectrum, glueballs, scalar mesons a0(1450) and σ(600) and other scalar mesons, and the 1+ meson. In addition, we have employed the canonical approach to explore the firstorder phase transition and the critical point at finite density and finite temperature. We have also discovered a new parton degree of freedom  the connected sea partons, from the pathintegral formulation of the hadronic tensor, which explains the experimentally observed Gottfried sum rule violation. Combining experimental result on the strange parton distribution, the CT10 global fitting results of the total u and d antipartons and the lattice result of the ratio of the momentum fraction of the strange vs that of u or d in the disconnected insertion, we have shown that the connected sea partons can be isolated. In this final technical report, we shall present a few representative highlights that have been achieved in the project.},
doi = {10.2172/1323029},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 8
}

CALCULATION OF THE OPTICAL POTENTIAL WITH THE NUCLEONNUCLEON PHASE SHIFTS IN THE THOMASFERMI APPROXIMATION
The radial dependence of the optical potential for nucleonnucleus scattering is calculated with the help of the empirical nuclear density. The nucleus is approximated locally by the Ferml model. The equation for the scattering in the nuclear medium is solved approximately, and the optical potential is expressed with the help of nucleonnucleon phase shifts. In the numerical computations the SignellMarshak phase shifts are used. The effect of the exclusion principle increases the depth of the real part and decreases the depth of the imaginary part of the optical potential in the center of the nucleus. The radius of the realmore » 
CALCULATION OF THE OPTICAL POTENTIAL WITH THE NUCLEONNUCLEON PHASE SHIFTS IN THE THOMASFERMI APPROXIMATION. PART II
The radial dependence of the optical potential for nucleonnucleus scattering is calculated with the help of the empiri cal nuclear density. The nucleus is approximated locally by the Fermi model. The equation for the scattering in the nuelear medium is solved approximately, and the optical potential is expressed with the help of nucleonnucleon phase shifts. In the numerical computations the latest Yale phase shlfts are used. In comparison with the analogical calculation based on the SignellMarshak phase shifts, the radius and the surface thickness of both the real and the imaginary part of the optical potential practically do not change;more » 
A FIELDTHEORETICAL CALCULATION OF THE ONEPIONEXCHANGE AND TWOPION EXCHANGE CONTRIBUTIONS TO THE PHASESHIFTS WITH HIGHER ANGULAR MOMENTA FOR NUCLEONNUCLEON SCATTERING. Technical Report No. 238
The onepionexchange and twopionexchange parts of the Smatrix for nucleonnucleon scattering are calculated fieldtheoretically. The rescattering of virtual pions by nucleons and the pionpion interaction between virtual pions are taken into account. The Smatrix is then decomposed into the partialwave amplitudes, and the phase shifts are calculated. Numerical evaluations are carried out for the 310Mev protonproton scattering, and the results are compared with the phase shifts obtained by analyzing the experimental data. It is found that, without contribution of the pionpion interaction, the results are far from agreement with experiment because of too strong attraction arising from the contributions ofmore »