Nucleon form factors and structure functions

TL;DR

This study uses $N_f=2$ non-perturbatively improved Clover lattice QCD to compute nucleon structure observables, focusing on the lowest moments of PDFs and electromagnetic form factors in the region $m_ ext{PS} o 170$–270 MeV. It combines advanced simulation techniques, RI$^ ext{'}$-MOM renormalization, and SSE/ChEFT fits to analyze finite-size and chiral-mimetic mass dependencies, comparing with phenomenology wherever possible. Key findings include significant finite-size effects in $g_A$ that persist after correction, a larger-than-phenomenology trend for several $v_2$/a1 moments, and radii that rise with decreasing $m_ ext{PS}$ in line with chiral EFT expectations, though discrepancies with experiment remain. Overall, the work demonstrates both the promise and the ongoing challenges of extracting nucleon structure from lattice QCD, emphasizing the need for finer control of systematics and broader quark-mass coverage.

Abstract

We give an update on our ongoing efforts to compute the nucleon's form factors and moments of structure functions using Nf=2 flavours of non-perturbatively improved Clover fermions. We focus on new results obtained on gauge configurations where the pseudo-scalar meson mass is in the range of 170-270 MeV. We will compare our results with various estimates obtained from chiral effective theories since we have some overlap with the quark mass region where results from such theories are believed to be applicable.

Figures (6)

• Figure 1: The left panel shows the simulation points in the $m_\mathrm{PS}^2$ vs. $m_\mathrm{PS} L$ plane. In the right panel dashed lines show the lattice spacing and box sizes for which simulations have been performed. In both figures the continuous lines show where $m_\mathrm{PS} L=3$.
• Figure 2: The left panel shows $g_\mathrm{A}$ as a function of $m_\mathrm{PS}^2$. The open and filled diamonds show the lattice results before and after correction of finite size effects, respectively. The star indicates the experimental result. The line shows a fit to the data as described in the text. The right panel shows the relative finite size effects determined on the lattice (symbols) and obtained from a fit to an expression from ChEFT.
• Figure 3: The left panel shows $g_\mathrm{A}/f_\mathrm{PS}$ as a function of $m_\mathrm{PS}^2$. The right panel shows our results for $g_\mathrm{T}^{\overline{\mathrm{MS}}}$ at a scale $\mu=2\,\hbox{GeV}$.
• Figure 4: The left and right panel show results for the second moment of the iso-vector and iso-scalar unpolarized PDFs, respectively, as a function of $m_\mathrm{PS}^2$. The solid lines show the fits to an expression from ChEFT.
• Figure 5: The left panel shows the results for the second of the polarized PDFs as a function of $m_\mathrm{PS}^2$. In the right panel the results for the Dirac form factor radius $r_1$ are plotted. The dashed lines show results from ChEFT as described in the text.