AI 中文总结
本文研究含规范不变洛伦兹破缺算子的阿贝尔质量矢量场的传播与共振，发现U(1)对称破缺后矢量极化分两支，其双共振结构无法用有限微扰插入解释，分支贡献依赖动量几何与背景类型。
AI 中文摘要
我们研究了在由单个优选四矢量构造的规范不变、CPT偶、四维洛伦兹破缺动力学算子存在时，阿贝尔质量矢量场的传播与共振行为。在无质量理论中，传播子包含一个额外的代数极点，该极点与守恒流解耦，仅留下两个物理自由度。在内部U(1)对称性自发破缺后，所有三个矢量极化态均变为物理态，但会分离为两个正交的色散分支，分别携带两个和一个物理极化态。我们表明，对于横向物质真空极化，该分解在戴森重求和下得以保留，并计算了相应的衰变率和费米子湮灭振幅。这种分裂极点结构及相关的双共振行为无法通过有限数量的微扰洛伦兹破缺插入来理解。物理过程中第二分支的贡献强烈依赖于初始动量几何：在类时背景下，无质量对头费米子的该贡献消失；而被加速至近乎平行的构型可产生能量增强的修正。类空与类光背景还会导致共振信号的方向变化及潜在的恒星时变化。
英文摘要
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.
Comments14 pages
