The Das-Mathur-Okubo sum rule for the charged pion polarizability in a chiral model

TL;DR

This paper evaluates the Das-Mathur-Okubo sum rule for charged pion polarizability within the Nambu-Jona-Lasinio model, comparing it with various theoretical and lattice approaches, highlighting the delicate cancellations affecting the sign of the polarizability.

Contribution

It applies the DMO sum rule to the NJL model and compares results with chiral perturbation theory, QCD sum rules, lattice calculations, and spectral density methods, providing insights into pion polarizability.

Findings

The DMO sum rule results depend on intrinsic and recoil contributions.

There is a delicate cancellation affecting the sign of the polarizability.

Comparison reveals differences and similarities among various theoretical approaches.

Abstract

The Das-Mathur-Okubo (DMO) sum rule for the polarizability of charged pions is evaluated for the Nambu-Jona-Lasinio model Lagrangian in both its minimal and extended forms. A comparison is made with the results obtained using the same sum rule from chiral perturbation theory (CHPT), approximate QCD sum rule calculations, explicit calculations on the lattice by Wilcox, and using the semi-empirical Kapusta-Shuryak spectral densities. The $\chi$PT results from Compton scattering are also given. We point to a delicate cancellation between the intrinsic and recoil contributions to $\alpha_{\pi^\pm}$ in the DMO sum rule approach that can lead to calculated polarizabilities of either sign.