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Title: 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 strong-interaction 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 first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, 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 » 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 D s meson decay constant f Ds, 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 a 0(1450) and σ(600) and other scalar mesons, and the 1 -+ meson. In addition, we have employed the canonical approach to explore the first-order 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 path-integral 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 anti-partons 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.« less

Authors:
 [1];  [1]
  1. 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) (SC-26)
OSTI Identifier:
1323029
Report Number(s):
DOE-UKRF-84ER40154
TRN: US1700277
DOE Contract Number:
FG02-84ER40154
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; N-1440 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; RHO-770 MESONS; A0-980 MESONS; DEGREES OF FREEDOM; PHASE TRANSFORMATIONS; WARD IDENTITY; CORRECTIONS; PARTICLE STRUCTURE; ALGORITHMS; GLUEBALLS; U QUARKS; KENTUCKY; RESEARCH PROGRAMS

Citation Formats

Liu, Keh-Fei, and Draper, Terrence. Lattice QCD Calculation of Nucleon Structure. United States: N. p., 2016. Web. doi:10.2172/1323029.
Liu, Keh-Fei, & Draper, Terrence. Lattice QCD Calculation of Nucleon Structure. United States. doi:10.2172/1323029.
Liu, Keh-Fei, 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, Keh-Fei 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 strong-interaction 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 first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, 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 first-order 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 path-integral 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 anti-partons 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
}

Technical Report:

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  • 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 Ferml model. The equation for the scattering in the nuclear medium is solved approximately, and the optical potential is expressed with the help of nucleon-nucleon phase shifts. In the numerical computations the Signell-Marshak 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 » part is practically equal to the radius of the density distribution, whereas the radius of the imaginary part is slightly bigger. The results are compared with the experimental estimates of the optical potential. (auth)« less
  • 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 nucleon-nucleon phase shifts. In the numerical computations the latest Yale phase shlfts are used. In comparison with the analogical calculation based on the Signell-Marshak 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 » the depths of the optical potential increase- a little (less than 8%, i.e., less than 2 Mev) for the imaginary part and up to 35%, i.e., up to 15 Mev, for the real part-in the center of the nucleus. (auth)« less
  • The one-pion-exchange and two-pion-exchange parts of the S-matrix for nucleon-nucleon scattering are calculated field-theoretically. The rescattering of virtual pions by nucleons and the pion-pion interaction between virtual pions are taken into account. The S-matrix is then decomposed into the partial-wave amplitudes, and the phase shifts are calculated. Numerical evaluations are carried out for the 310-Mev proton-proton scattering, and the results are compared with the phase shifts obtained by analyzing the experimental data. It is found that, without contribution of the pion-pion interaction, the results are far from agreement with experiment because of too strong attraction arising from the contributions ofmore » the two-pion-exchange part, but the contribution of the pion- pion resonance in the I = J = 1 state improves the results considerably by largely cancelling the attraction. It is, however, also found that definite discrepancies still remain between the theory and the experiments, and this suggests that some unknown effects must play important roles in determining the nuclear force in the region of the internucleon distance around the Compton wave length of the pion. (auth)« less