Light-Front projection of spin-1 electromagnetic current and zero-modes

TL;DR

This paper investigates zero-mode contributions to the light-front projection of the electromagnetic current in spin-1 particles, revealing that only the zero-to-zero helicity matrix element contains such contributions, with implications for phenomenological models.

Contribution

It provides a generalized analytical framework showing zero-mode contributions are confined to a specific matrix element in symmetric spin-1 models, extending previous simplified results.

Findings

Only the 0→0 matrix element has zero-mode contributions.

Zero-modes are absent in other helicity matrix elements.

Results apply to symmetric and smeared vertex models.

Abstract

The issue of the contribution of zero-modes to the light-front projection of the electromagnetic current of phenomenological models of vector particles vertices is addressed in the Drell-Yan frame. Our analytical model of the Bethe-Salpeter amplitude of a spin-1 fermion-antifermion composite state gives a physically motivated light-front wave function symmetric by the exchange of the fermion and antifermion, as in the $\rho$-meson case. We found that among the four independent matrix elements of the plus component in the light-front helicity basis only the $0\to 0$ one carries zero mode contributions. Our derivation generalizes to symmetric models, important for applications, the above conclusion found for a simplified non-symmetrical form of the spin-1 Bethe-Salpeter amplitude with photon-fermion point-like coupling and also for a smeared fermion-photon vertex model.