[Paper Review] Nucleon form factors with Nf=2 dynamical twisted mass fermions

Constantia Alexandrou, Tomasz Korzec+7 more|arXiv (Cornell University)|Oct 19, 2009

Quantum Chromodynamics and Particle Interactions10 references3 citations

TL;DR

This study computes nucleon electromagnetic and axial form factors using Nf=2 dynamical twisted mass fermions on lattices with spatial sizes of 2.1–2.7 fm and a lattice spacing of ~0.09 fm, covering pion masses from 260–470 MeV. The key result is a chiral extrapolation yielding a physical axial charge of g_A = 1.13(10), consistent with experiment despite large uncertainties due to chiral extrapolation challenges.

ABSTRACT

We present results on the electromagnetic and axial nucleon form factors using two degenerate flavors of twisted mass fermions on lattices of spatial size 2.1 fm and 2.7 fm and a lattice spacing of about 0.09 fm. We consider pion masses in the range of 260-470 MeV. We chirally extrapolate results on the nucleon axial ch arge, the isovector Dirac and Pauli root mean squared radii and magnetic moment to the physical point and co mpare to experiment.

Motivation & Objective

• To compute isovector electromagnetic and axial nucleon form factors using Nf=2 twisted mass fermions on the lattice.
• To perform chiral extrapolation of the nucleon axial charge, magnetic moment, and root mean squared radii to the physical point.
• To assess finite volume effects and compare results with dynamical domain wall fermion simulations.
• To evaluate the consistency of lattice results with experimental data and theoretical expectations from chiral perturbation theory.

Proposed method

• Lattice QCD simulations with two degenerate flavors of twisted mass fermions at a fixed lattice spacing of ~0.09 fm and spatial volumes of 2.1–2.7 fm.
• Use of the tree-level Symanzik improved gauge action and automatic O(a) improvement via tuning the bare quark mass to its critical value.
• Evaluation of nucleon matrix elements via connected three-point functions for the electromagnetic and axial currents.
• Application of the Noether current for electromagnetic form factors (Z_V = 1) and local current for axial current (Z_A = 0.76(1)).
• Chiral extrapolation using one-loop heavy baryon chiral perturbation theory in the small scale expansion.
• Dipole fits to the axial form factor G_A(Q²) and comparison with pion pole dominance predictions for G_p(Q²).

Experimental results

Research questions

• RQ1 How do nucleon electromagnetic and axial form factors computed with Nf=2 twisted mass fermions compare to experimental data?
• RQ2 What is the chiral extrapolation behavior of the nucleon axial charge g_A, and how does it compare to the physical value?
• RQ3 To what extent do the Dirac and Pauli root mean squared radii depend on the pion mass, and how do they compare to chiral perturbation theory predictions?
• RQ4 How do finite volume effects influence the extracted form factors and magnetic moment?
• RQ5 Can the axial form factor G_A(Q²) be described by a dipole form, and does pion pole dominance accurately describe G_p(Q²)?

Key findings

• The nucleon axial charge extrapolated to the physical point is g_A = 1.13(10), consistent with experiment but with a large uncertainty due to chiral extrapolation.
• The Dirac and Pauli root mean squared radii show a weaker dependence on the pion mass than predicted by chiral perturbation theory.
• The isovector magnetic moment and r.m.s. radii exhibit small finite volume effects, indicating reliable results on the current lattice volumes.
• The axial form factor G_A(Q²) is flatter than the experimental dipole form, resulting in a predicted axial mass larger than the physical value.
• The G_p(Q²) form factor is flatter than predicted by pion pole dominance, requiring a larger pole mass than the pion mass.
• Including DWF data in the chiral fit for g_A leads to a significantly different extrapolation curve, highlighting sensitivity to the pion mass range used.