On the Chiral Quark Soliton Model with Pauli-Villars Regularization

TL;DR

This paper discusses the limitations of the single-subtraction Pauli-Villars regularization in the chiral quark soliton model and proposes an extended multi-subtraction scheme, comparing it with the proper-time method and analyzing their impact on nucleon observables.

Contribution

It introduces a multi-subtraction Pauli-Villars regularization scheme for the chiral quark soliton model and compares its effects with the proper-time regularization on nucleon properties.

Findings

Single-subtraction Pauli-Villars scheme does not fully eliminate divergences.

Multi-subtraction scheme improves regularization accuracy.

Isovector observables are sensitive to the regularization method.

Abstract

The Pauli-Villars regularization scheme is often used for evaluating parton distributions within the framework of the chiral quark soliton model with inclusion of the vacuum polarization effects. Its simplest version with a single subtraction term should however be taken with some caution, since it does not fully get rid of divergences contained in scalar and psuedoscalar quark densities appearing in the soliton equation of motion. To remedy this shortcoming, we propose here its natural extention, i.e. the Pauli-Villars regularization scheme with multi-subtraction terms. We also carry out a comparative analysis of the Pauli-Villars regularization scheme and more popular proper-time one. It turns out that some isovector observables like the isovector magnetic moment of the nucleon is rather sensitive to the choice of the regularization scheme. In the process of tracing the origin of this sensitivity, a noticeable difference of the two regularization scheme is revealed.