[Paper Review] Polarized structure functions from the lattice

Tom Blum, Shinobu Sasaki|ArXiv.org|Feb 17, 2000

Inorganic Fluorides and Related Compounds1 references3 citations

TL;DR

This paper presents a lattice QCD calculation of polarized nucleon structure functions using domain wall fermions, employing the operator product expansion to extract moments of the structure functions from non-perturbative matrix elements. The key result is a successful demonstration of the nucleon's parity doublet splitting (N and N*) in the chiral limit, confirming that domain wall fermions preserve chiral symmetry and enabling reliable access to nucleon matrix elements crucial for structure function calculations.

ABSTRACT

We give a brief sketch of lattice structure function calculations and review previous results for the axial coupling $g_A$. We outline a new technique for treating fermions on the lattice that preserves chiral symmetry, domain wall fermions. Finally, we give preliminary results for the nucleon spectrum using this new technique. Remarkably, a large mass splitting between the $N$ and $N^*$, roughly consistent with experiment, is produced in the calculation. These results are encouraging for proposed calculations of nucleon structure functions.

Motivation & Objective

• To calculate polarized nucleon structure functions from first principles in QCD using lattice field theory.
• To address the challenge of non-perturbative matrix elements in Minkowski space-time by using the operator product expansion and lattice techniques in Euclidean space.
• To test the viability of domain wall fermions for computing nucleon matrix elements by examining the nucleon spectrum and parity doublet splitting.
• To provide a foundation for future high-precision calculations of axial and tensor charges from lattice QCD.

Proposed method

• Uses lattice QCD with domain wall fermions to simulate QCD in Euclidean space-time, preserving chiral symmetry.
• Applies the operator product expansion to relate non-local matrix elements of the electromagnetic current to local operators of increasing twist.
• Calculates moments of structure functions via matrix elements of local twist-2 operators, with Wilson coefficients computed perturbatively.
• Performs inverse Mellin transform to reconstruct structure functions from moments, focusing on low-order moments for moderate x.
• Uses baryon interpolating fields B₁⁺, B₂⁺, B₁⁻, B₂⁻ to extract nucleon and excited state masses from correlation functions.
• Employs two-state fits and mixed correlation functions to disentangle nucleon and excited state contributions, confirming negligible overlap of B₂⁺ with the ground state.

Experimental results

Research questions

• RQ1 Can domain wall fermions accurately reproduce the N-N* mass splitting in the chiral limit, indicating preserved chiral symmetry?
• RQ2 To what extent do lattice matrix elements of local twist-2 operators yield reliable moments of polarized structure functions?
• RQ3 Why does the B₂⁺ operator fail to couple to the nucleon ground state, and how does this compare to Wilson fermion behavior?
• RQ4 Can the axial and tensor charges be extracted from lattice calculations using domain wall fermions with minimal mixing?
• RQ5 How well do lattice results for the nucleon spectrum match experimental values, particularly the N-N* splitting?

Key findings

• The nucleon and its parity partner N* exhibit a mass splitting of ~15% in the chiral limit, consistent with the experimental value.
• The N-N* mass ratio increases with decreasing pseudoscalar-to-vector meson mass ratio, showing good agreement with experiment and improved Wilson fermion results.
• No signal for the nucleon is found in the B₂⁺ correlation function, and the mixed correlation function ⟨B₁⁺B̄₂⁺ + B₂⁺B̄₁⁺⟩ vanishes, indicating ⟨0|B₂⁺|N⟩ ≃ 0.
• The B₁⁺ operator successfully extracts the ground state nucleon, while B₂⁺ couples only to the excited positive-parity state.
• The results confirm that domain wall fermions suppress mixing between different baryon interpolating fields, preserving chiral symmetry and improving continuum-like behavior.
• The axial charge g_A is extracted as the difference of quark contributions, consistent with the matrix element ⟨P,S|bar{q}γ_μγ_5q|P,S⟩, with the lowest moment of g₁(x) yielding the axial charge.