[Paper Review] On the Oscillations of the Tensor Spin Structure Function

А.В. Ефремов, Oleg Teryaev|ArXiv.org|Oct 31, 1999

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This paper investigates the oscillatory behavior of the quark tensor spin structure function in the context of deep inelastic scattering, demonstrating that its oscillations—driven by Lorentz covariance and factorization—lead to a vanishing first moment, which supports the extraction of the neutron's g₁ structure function from deuteron data with minimal nuclear effects. The zero second moment for the singlet component further implies that deviations from zero directly signal gluonic contributions.

ABSTRACT

The smallness of the deuteron tensor spin structure function is the necessary condition to extract neutron $g_1$ function neglecting the nuclear effects. The oscillating behavior of the quark tensor spin structure function leading to the zero first moment is shown to be the straightforward consequence of the factorization property and Lorentz covariance. For the singlet contribution the momentum conservation leads to the zero second moment also. The deviations from zero directly measure the gluon contribution.

Motivation & Objective

• To understand the origin of the smallness of the deuteron tensor spin structure function.
• To analyze the oscillatory behavior of the quark tensor spin structure function in the framework of quantum field theory.
• To establish that the vanishing first moment is a consequence of factorization and Lorentz covariance.
• To examine the role of momentum conservation in enforcing a zero second moment for the singlet component.
• To link deviations from zero moments to the gluon contribution in the nucleon structure.

Proposed method

• Utilizes the factorization property of the twist-2 matrix elements in deep inelastic scattering.
• Applies Lorentz covariance to derive constraints on the tensor spin structure function.
• Analyzes the momentum-space behavior of the tensor structure function, showing oscillatory patterns.
• Considers the singlet combination of quark distributions and applies momentum sum rules.
• Derives the vanishing of the first moment from the antisymmetric nature of the tensor structure function under certain transformations.
• Uses the second moment sum rule to show that momentum conservation forces the second moment to vanish for the singlet component.

Experimental results

Research questions

• RQ1 Why is the deuteron tensor spin structure function small, and how does this enable extraction of the neutron g₁ function?
• RQ2 What dynamical principles lead to the oscillatory behavior of the quark tensor spin structure function?
• RQ3 How do factorization and Lorentz covariance constrain the first moment of the tensor structure function?
• RQ4 Why does the singlet component of the tensor structure function have a vanishing second moment?
• RQ5 In what way do deviations from zero moments signal the presence of gluonic contributions?

Key findings

• The oscillatory behavior of the quark tensor spin structure function leads directly to a zero first moment, consistent with factorization and Lorentz covariance.
• The vanishing of the first moment is not accidental but a consequence of fundamental symmetries in the parton model.
• For the singlet combination, momentum conservation enforces a zero second moment of the tensor structure function.
• Deviations from zero in the first or second moments are direct indicators of gluon contributions to the nucleon spin structure.
• The smallness of the deuteron tensor structure function is thus a natural consequence of these symmetry and conservation constraints.
• The results provide a theoretical foundation for using the deuteron as a proxy to extract neutron spin structure functions with reduced nuclear effects.