Unambiguous extraction of the electromagnetic form factors for spin-1 particles on the light-front

Abstract

The electromagnetic form factors of a composite vector particle within the lightfront 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. With some relations between the electromagnetic matrix elements of the electromagnetic current J + ji , as demonstrated analytical here, it was possible to calculate the electromagnetic form factors for spin-1 particles without zero-modes or non-valence contributions.

Elastic electromagnetic form factors of vector mesons

“…It was found herein that G V E always exhibits a zero; and analysed as a function of x = Q 2 /m 2 V , that zero moves toward x = 0 with increasing current-quark mass [Eq. (25)]. These features can also be understood as consequences of DCSB; and they support a qualitative argument that the character of emergent mass in the Standard Model may ensure a zero in G p E .…”

“…Whilst not immediately apparent, the location of the zeros in G K * Eu and G K * Es can also be understood using the arguments developed after Eq. (25). To elucidate, we note that G K * E (x K * = Q 2 /m 2 K * ) does not exhibit a pole at x = −1 because a virtual photon cannot transition to a K * -meson.…”

“…Whilst not immediately apparent, the location of the zeros in G K * Eu and G K * Es can also be understood using the arguments developed after Eq. (25). To elucidate, we…”

“…(18). For comparison: an average of computed ρ-meson results tabulated elsewhere [25] yields rρ = 0.67(12) fm, µρ = 2.17 (21), Qρ = −0.55 (28); and using an interaction similar to that defined by Eqs. (10), (11), Ref.…”

“…The short lifetime of the ρ-meson means that related measurements are generally impractical, although there is an empirically-based estimate of the associated magnetic moment [24]: µ ρ = 2.15 ± 0.5. Notwithstanding the absence of experimental data, there are many theoretical computations of ρ-meson electromagnetic form factors, using a wide variety of tools [25].…”