Systematic errors in extracting nucleon properties from lattice QCD

TL;DR

The paper addresses systematic errors in lattice QCD extractions of nucleon form factors, highlighting excited-state contamination as a key source of mismatch with experiment. It compares the standard plateau method with a summation approach for three-point functions, applying them to isovector currents to extract $F_1(q^2)$, $F_2(q^2)$ and $G_A(q^2)$ across CLS ensembles. The summation method yields linear dependence on the sink-time parameter and reduces excited-state effects, with preliminary results showing partial agreement with experiment for $F_2(q^2)$ and no consistent downward trend in $g_A$ at light pion masses; however, statistical uncertainties remain larger and improvements are planned. The work provides a viable path toward more reliable nucleon structure calculations on the lattice, with plans to explore multiple lattice spacings, smaller pion masses, and full axial form factors.

Abstract

Form factors of the nucleon have been extracted from experiment with high precision. However, lattice calculations have failed so far to reproduce the observed dependence of form factors on the momentum transfer. We have embarked on a program to thoroughly investigate systematic effects in lattice calculation of the required three-point correlation functions. Here we focus on the possible contamination from higher excited states and present a method which is designed to suppress them. Its effectiveness is tested for several baryonic matrix elements, different lattice sizes and pion masses.

Figures (6)

• Figure 1: Examples for the standard method for $V_0$ and $g_A$
• Figure 2: The summation method for $V_0$ and different momenta
• Figure 3: Examples for the standard method and the summation method for $V_0$ and $g_A$
• Figure 4: Preliminary results for the Dirac and the Pauli form factors extracted with the summation method.
• Figure 5: Preliminary results for the axial charge extracted with the summation method.