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Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions

LHPC Collaboration, Jonathan D. Bratt, Robert G. Edwards, Michael Engelhardt, Philipp Hagler, Huey-Wen Lin, Mei-Feng Lin, Harvey B. Meyer, Bernhard Musch, John W. Negele, Kostas Orginos, Andrew V. Pochinsky, Massimiliano Procura, David G. Richards, Wolfram Schroers, Sergey N. Syritsyn

TL;DR

The paper investigates nucleon structure using a 2+1 flavor mixed-action lattice QCD approach, advancing high-statistics measurements of vector/axial form factors, GPD moments, and the quark spin decomposition. It leverages several chiral EFT schemes (SSE and BChPT) to perform simultaneous and regime-specific extrapolations in m_π and Q^2, contrasted with phenomenology. Key findings include nucleon radii smaller than experiment at accessible pion masses, a near-phenomenological g_A but with finite-volume and chiral-range caveats, and a surprising near-cancellation of quark orbital angular momentum contributing to the proton spin. The work also emphasizes the importance of error correlations, finite-volume studies, and renormalization in extracting reliable hadron-structure observables from lattice QCD, outlining clear paths toward lighter masses and inclusion of disconnected diagrams for more definitive comparisons with experiment. Overall, the study demonstrates both the promise and current limitations of mixed-action lattice calculations in resolving the spin and spatial structure of the nucleon.

Abstract

We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.

Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions

TL;DR

The paper investigates nucleon structure using a 2+1 flavor mixed-action lattice QCD approach, advancing high-statistics measurements of vector/axial form factors, GPD moments, and the quark spin decomposition. It leverages several chiral EFT schemes (SSE and BChPT) to perform simultaneous and regime-specific extrapolations in m_π and Q^2, contrasted with phenomenology. Key findings include nucleon radii smaller than experiment at accessible pion masses, a near-phenomenological g_A but with finite-volume and chiral-range caveats, and a surprising near-cancellation of quark orbital angular momentum contributing to the proton spin. The work also emphasizes the importance of error correlations, finite-volume studies, and renormalization in extracting reliable hadron-structure observables from lattice QCD, outlining clear paths toward lighter masses and inclusion of disconnected diagrams for more definitive comparisons with experiment. Overall, the study demonstrates both the promise and current limitations of mixed-action lattice calculations in resolving the spin and spatial structure of the nucleon.

Abstract

We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.

Paper Structure

This paper contains 44 sections, 72 equations, 47 figures, 43 tables.

Table of Contents

  1. Introduction
  2. Overview of physical observables
  3. New lattice calculations
  4. Improved statistics
  5. Tests for systematic errors
  6. Super jackknife analysis and error correlation
  7. Renormalization of lattice operators
  8. Finite-volume effects
  9. Results
  10. The axial charge
  11. Electromagnetic form factors
  12. Isovector Dirac form factor $F_1^v(Q^2)$
  13. Dipole fits to isovector $F_1^v(Q^2)$
  14. SSE fits to isovector $\langle r_1^2\rangle$
  15. BChPT fits to isovector $\langle r_1^2\rangle$
  16. ...and 29 more sections

Figures (47)

  • Figure 1: Layout of smeared nucleon sources (stars) and coherent, fixed momentum sinks (vertical lines) on our lattices: (left) even configurations; (right) odd configurations.
  • Figure 2: Comparison of coherent sink technique and two source-sink separations with our previous calculation. The observables are the axial charge, $g_A$ in the left panel, see Sec. \ref{['sec:gA']}, and the isovector charge radius, $a^{-2}\langle r_1^2\rangle$ in the right panel, see Sec. \ref{['sec:form-factors']}.
  • Figure 3: Comparison of two separations on two volumes for the isovector axial charge, $g_A$. This plot shows the resulting plateau plot, i.e. $g_A(T)$ as a function of the location of the operator insertion at fixed source-sink separation.
  • Figure 4: Comparison of bootstrap (left panels) and super jackknife (right panels) resampling plans for chiral fits to the nucleon axial charge, $g_A$. The upper two plots show fits to the lowest three masses, the lower two show fits to the lowest four masses.
  • Figure 5: Mass plateau at $am=0.010$ on the $20^3$ and the $28^3$ lattices. The band corresponds to Eq. (\ref{['eq:c2pt-fit-func']}).
  • ...and 42 more figures