Unambiguous Extraction of the Electromagnetic Form Factors for Spin-1 Particles on the Light-Front

TL;DR

This paper investigates methods to accurately extract electromagnetic form factors of spin-1 particles using light-front formalism, highlighting issues with zero-mode contamination and identifying a prescription immune to such effects.

Contribution

It demonstrates that the Inna Grach prescription reliably extracts form factors without zero-mode contamination, ensuring consistency with instant form quantum field theory.

Findings

Different prescriptions yield varying results due to zero-mode contamination.

The Inna Grach prescription is immune to zero-modes and consistent with instant form results.

Light-front matrix elements are affected by zero-modes, impacting form factor extraction.

Abstract

The electromagnetic form factors of a composite vector particle within the light-front formulation of the Mandelstam formula is investigated. In order to extract the form factors from the matrix elements of the plus component of the current in the Drell-Yan frame, where the momentum transfer is chosen such that $q^+=q^0+q^3=0$, one has in principle the freedom to choose between different linear combinations of matrix elements of the current operator. The different prescriptions to calculate the electromagnetic form factors, $G_0,G_1$ and $G_2$, i.e., charge form factor, magnetic and quadrupole respectively. If the covariance is respected, all prescriptions give the same results, misfortune, is not the situation, the light-front approach produce different results, which depend of the prescriptions as utilized to extract the electromagnetic form factors in the case of the spin-1 particles. The main differences of the prescriptions appear because of the light-front matrix elements of the electromagnetic current are contaminated by the zero-modes contributions to the same with the plus component of the matrix elements of the electromagnetic current. However, the Inna Grach prescription is immune to the zero-modes contributions to the electromagnetic current, then the electromagnetic form factors extracted with that prescriptions do not have zero-modes contribution and give the same result compared with the instant form quantum field theory. Another's prescriptions with the light-front approach are contaminated by the zero-modes contributions to the matrix elements of the electromagnetic current with the plus component of the current.