Angular momentum decomposition of chiral multiplets in front form

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.