Angular momentum decomposition of chiral multiplets in front form

TL;DR

This paper derives a unitary transformation linking chiral and angular momentum bases for quark-antiquark pairs in a front-form framework, revealing a simple relation in the chiral limit consistent with instant form results.

Contribution

It provides the first derivation of the angular momentum decomposition of chiral multiplets in front form, connecting chiral and non-chiral bases through a unitary transformation.

Findings

The transformation simplifies in the chiral limit, resembling SU(2) Clebsch-Gordan coefficients.

The derived transformation matches the one obtained for canonical spin in instant form.

The work clarifies the relation between chiral and angular momentum bases in front form dynamics.

Abstract

In this article we derive the unitary transformation that relates the $q\bar q$ chiral basis $\{R; I J^{PC} \}$ to the $\{I; ^{2S+1}L_J\}$-basis in a front-form framework. From the most general expression for the Clebsch-Gordan coefficients of the Poincar\'e group one can see that the chiral limit brings the angular momentum coupling into a simple form that permits the relation in terms of SU(2) Clebsch-Gordan coefficients. We demonstrate that such a transformation is identical to the one was obtained for canonical spin in the instant form.