NJL model on the light cone and pion structure function

TL;DR

This paper formulates the NJL model on the light cone, derives an effective fermionic Lagrangian, and investigates pion properties and structure functions using two regularization schemes, demonstrating formal equivalences with traditional formulations.

Contribution

It introduces a light-cone formulation of the NJL model, compares regularization schemes, and applies the model to study pion structure functions, providing new insights into light-cone dynamics.

Findings

The effective 4-fermion Lagrangian is derived on the light cone.

Two regularization schemes are discussed and compared.

The pion structure function is analyzed in both schemes.

Abstract

The NJL model is formulated on the light cone. Using the 1/N expansion to solve the fermionic constraint, an effective 4-fermi lagrangian is derived. Pionic properties are investigated using this lagrangian, and the formal equivalence to the equal-time formulation is demonstrated. Two regularization schemes in terms of light-cone variables are discussed: An extension of the 'invariant mass cut-off scheme', and a transverse momentum cut-off scheme. It is shown that the first one is equivalent to the covariant 3-momentum cut-off (dispersion cut-off) scheme in the equal-time formulation. As an application the structure function of the pion is studied in both regularization schemes.