Hadron Structure Functions in a Chiral Quark Model: Regularization, Scaling and Sum Rules

TL;DR

This paper develops a consistent regularization method for calculating hadron structure functions in a chiral quark model, ensuring correct scaling, sum rules, and anomaly preservation, with specific focus on the Pauli-Villars scheme.

Contribution

It introduces a regularization procedure that maintains QCD anomalies and scaling behavior, and clarifies the regularization of structure functions beyond static hadron properties.

Findings

Pauli-Villars regularization preserves anomalies and scaling.

Correct pion structure function obtained.

Gottfried sum rule remains unregularized in this model.

Abstract

We provide a consistent regularization procedure for calculating hadron structure functions in a chiral quark model. The structure functions are extracted from the absorptive part of the forward Compton amplitude in the Bjorken limit. Since this amplitude is obtained as a time-ordered correlation function its regularization is consistently determined from the regularization of the bosonized action. We find that the Pauli-Villars regularization scheme is most suitable because it preserves both the anomaly structure of QCD and the leading scaling behavior of hadron structure functions in the Bjorken limit. We show that this procedure yields the correct pion structure function. In order to render the sum rules of the regularized polarized nucleon structure functions consistent with their corresponding axial charges we find it mandatory to further specify the regularization procedure. This specification goes beyond the double subtraction scheme commonly employed when studying static hadron properties in this model. In particular the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. In this regard we conclude somewhat surprisingly that in this model the Gottfried sum rule does not undergo regularization.