[Paper Review] Quark distribution functions in the chiral quark-soliton model: cancellation of quantum anomalies

K. Goeke, Pobylitsa, P. V.+3 more|ArXiv.org|Jan 26, 2000

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates polarized quark distribution functions in the chiral quark-soliton model, demonstrating that quantum anomalies—potential inconsistencies between quark and antiquark state representations—cancel out for the isoscalar distribution Δu+Δd. The cancellation is analytically proven using Pauli-Villars regularization, confirming the model's consistency and positivity of parton distributions without additional regularization for this channel.

ABSTRACT

In the framework of the chiral quark-soliton model of the nucleon we investigate the properties of the polarized quark distribution. In particular we analyse the so called anomalous difference between the representations of the quark distribution functions in terms of occupied and non-occupied quark states. By an explicit analytical calculation it is shown that this anomaly is absent in the polarized isoscalar distribution Δu + Δd, which is ultaviolet finite. In the case of the polarized isovector quark distribution Δu - Δd the anomaly can be cancelled by a Pauli-Villars subtraction which is also needed for the regularization of the ultraviolet divergence.

Motivation & Objective

• To resolve the issue of quantum anomalies in quark distribution functions within the chiral quark-soliton model.
• To examine whether the naive equivalence between quark and antiquark state representations in parton distributions is preserved under ultraviolet regularization.
• To verify the consistency of the model with QCD properties such as locality, positivity, and charge conjugation invariance.
• To provide a reliable numerical framework for computing polarized parton distributions, especially in the singlet channel.
• To challenge the common assumption that Δu̅(x) = Δd̅(x) by predicting a significant difference in antiquark polarization distributions.

Proposed method

• Analytically computes the polarized isoscalar quark distribution Δu+Δd using sums over occupied and non-occupied quark states in the Dirac Hamiltonian.
• Applies Pauli-Villars regularization to control ultraviolet divergences and test for anomalies in the equivalence of quark and antiquark state representations.
• Uses the proper-time regularization scheme to confirm that the trace of the Dirac Hamiltonian vanishes, ensuring absence of anomaly in the nucleon mass and related observables.
• Compares results from occupied and non-occupied state sums to verify consistency and positivity of distributions.
• Performs numerical computations in the subleading 1/Nc order to extract the singlet polarized distribution and compare with parametrizations like GRSV.
• Analyzes the role of the axial anomaly and its cancellation in relation to locality and anticommutativity of fermion fields at spacelike separations.

Experimental results

Research questions

• RQ1 Does the anomalous difference between quark and antiquark state representations persist in the polarized isoscalar distribution Δu+Δd after ultraviolet regularization?
• RQ2 Can the Pauli-Villars regularization procedure cancel the quantum anomaly in the isovector polarized distribution Δu−Δd?
• RQ3 Is the equivalence between sums over occupied and non-occupied states preserved in the chiral quark-soliton model for polarized parton distributions?
• RQ4 Does the model predict a non-zero and asymmetric distribution for polarized antiquarks Δu̅(x) and Δd̅(x)?
• RQ5 How does the cancellation of anomalies relate to fundamental QCD properties such as locality and positivity of parton densities?

Key findings

• The isoscalar polarized quark distribution Δu+Δd is ultraviolet finite and free of quantum anomalies, requiring no Pauli-Villars subtraction.
• The anomaly in the isovector distribution Δu−Δd is canceled by the same Pauli-Villars regularization used to control ultraviolet divergences.
• The model's results for Δu+Δd are in reasonable agreement with the GRSV parametrization at a low normalization point.
• The model predicts a significant difference between the polarized antiquark distributions Δu̅(x) and Δd̅(x), contradicting the common assumption of equality.
• The cancellation of anomalies is linked to fundamental QCD properties such as anticommutativity of fermion fields at spacelike separations and charge conjugation invariance.
• The singlet axial charge is computed as gA^(0) = 0.35, consistent with other model calculations and independent of ultraviolet regularization.