Overlapping resonance branches of a gauge-invariant Lorentz-violating massive vector

Abstract

We investigate the propagation and resonance behavior of an Abelian massive vector field in the presence of a gauge-invariant, CPT-even, dimension-four Lorentz-violating kinetic operator constructed from a single preferred four-vector. In the massless theory, the propagator contains an additional algebraic pole that decouples from conserved currents, leaving two physical degrees of freedom. After spontaneous breaking of the internal U(1) symmetry, all three vector polarizations become physical but separate into two orthogonal dispersion branches carrying two and one physical polarization states, respectively. We show that this decomposition is preserved under Dyson resummation for a transverse matter vacuum polarization and calculate the corresponding decay rates and fermion-annihilation amplitude. The split-pole structure and associated double resonance behavior cannot be understood through a finite number of perturbative Lorentz-violating insertions. The contribution of the second branch in physical processes is strongly dependent on the initial momentum geometry: it vanishes for massless head-on fermions in a timelike background, whereas boosted nearly parallel configurations can generate an energy-enhanced correction. Spacelike and lightlike backgrounds additionally lead to directional and potentially sidereal variations of the resonance signal.