The covariant structure of light-front wave functions and the behavior of hadronic form factors

Abstract

We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector $ω^μ.$ The LFWFs with definite total angular momentum are eigenstates of a {\it kinematic} angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents $M^2_0= (\sum k^μ)^2$ and the light-cone momentum fractions $x_i= {k_i\cd ω/ p \cd ω}$ multiplied by invariants constructed from the spin matrices, polarization vectors, and $ω^μ.$ These properties are illustrated using known nonperturbative eigensolutions of the Wick--Cutkosky model. We analyze the LFWFs introduced by Chung and Coester to describe static and low momentum properties of the nucleons. They correspond to the spin-locking of a quark with the spin of its parent nucleon, together with a positive-energy projection constraint. These extra constraints lead to anomalous dependence of form factors on $Q$ rather than $Q^2.$ In contrast, the dependence of LFWFs on $M^2_0$ implies that hadron form factors are analytic functions of $Q^2$ in agreement with dispersion theory and perturbative QCD. We show that a model incorporating the leading-twist perturbative QCD prediction is consistent with recent data for the ratio of proton Pauli and Dirac form factors.