[Paper Review] Improved positivity bound for Deep Inelastic Scattering on transversely polarized nucleon

Jacques Soffer, Oleg Teryaev|ArXiv.org|Jun 22, 1999

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper improves the positivity bound for the transverse asymmetry $A_2$ in deep inelastic scattering on transversely polarized nucleons by exploiting the fact that the spin-3/2 state of the photon-nucleon system does not contribute to interference. The refined bound is particularly effective when the longitudinal asymmetry is small or negative, such as at low $x$ or in the neutron case, providing a tighter constraint on $A_2$ without relying on specific dynamical models.

ABSTRACT

The positivity bound for the transverse asymmetry $A_2$ may be improved by making use of the fact, that the state of a photon and a nucleon with total spin 3/2, does not participate to the interference. The bound is therefore useful in the case of a longitudinal asymmetry small (say, at low $x$) or negative (like in the neuteron case).

Motivation & Objective

• To refine the positivity bound for the transverse asymmetry $A_2$ in deep inelastic scattering on transversely polarized nucleons.
• To address the limitation of standard positivity bounds when the longitudinal asymmetry is small or negative, as in the case of neutrons or at low $x$.
• To exploit the non-participation of the spin-3/2 photon-nucleon state in interference to tighten the bound on $A_2$.
• To provide a model-independent constraint on $A_2$ that remains valid under conditions where traditional bounds become weak.

Proposed method

• The analysis uses the fact that the total spin-3/2 state of the photon-nucleon system does not contribute to the interference term in the scattering amplitude.
• By excluding the spin-3/2 component, the positivity condition on the spin-density matrix is modified, leading to a tighter bound on $A_2$.
• The method relies on general principles of quantum mechanics and unitarity, without assuming specific dynamical models of parton distributions.
• The improved bound is derived from the positivity of the spin-density matrix, considering the absence of the spin-3/2 contribution in the interference channel.
• The bound is applied to cases where the longitudinal asymmetry is small or negative, such as at low Bjorken-$x$ or for the neutron.
• The derivation is formal and model-independent, valid for any spin-1/2 nucleon target.

Experimental results

Research questions

• RQ1 Can the standard positivity bound for $A_2$ be improved in cases where the longitudinal asymmetry is small or negative?
• RQ2 How does the exclusion of the spin-3/2 photon-nucleon state affect the bound on $A_2$?
• RQ3 Is there a model-independent way to tighten the positivity constraint on $A_2$ in deep inelastic scattering on transversely polarized nucleons?
• RQ4 Does the improved bound remain effective for the neutron or at low $x$, where the longitudinal asymmetry is small or negative?
• RQ5 Can the non-participation of the spin-3/2 state be used to derive a physically meaningful and tighter bound on $A_2$?

Key findings

• The positivity bound for $A_2$ is improved by excluding the spin-3/2 photon-nucleon state, which does not contribute to interference.
• The improved bound is particularly effective when the longitudinal asymmetry is small or negative, such as at low $x$ or in the neutron case.
• The bound remains valid and tighter than standard positivity bounds under these conditions without requiring dynamical assumptions.
• The method is model-independent and based solely on unitarity and the structure of the spin-density matrix.
• The result provides a more robust constraint on $A_2$ in experimental analyses where the longitudinal asymmetry is poorly constrained.
• The improvement is significant in kinematic regions where standard bounds are weak, enhancing the reliability of $A_2$ extraction from data.