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

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 ${\ensuremath{\omega}}^{\ensuremath{\mu}}.$ The LFWFs with definite total angular momentum are eigenstates of a kinematic angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents ${M}_{0}^{2}=(\ensuremath{\sum}{k}^{\ensuremath{\mu}}{)}^{2}$ and the light-cone momentum fractions ${x}_{i}{=k}_{i}\ensuremath{\cdot}\ensuremath{\omega}/p\ensuremath{\cdot}\ensuremath{\omega}$ multiplied by invariants constructed from the spin matrices, polarization vectors, and ${\ensuremath{\omega}}^{\ensuremath{\mu}}.$ 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 an anomalous dependence of form factors on Q rather than ${Q}^{2}.$ In contrast, the dependence of LFWFs on ${M}_{0}^{2}$ 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.