具有洛伦兹破缺的 Yang-Mills 理论中的真空极化
Vacuum polarization in Yang-Mills theories with Lorentz violation
AI总结：
本文使用 BFM-gauge 研究了具有洛伦兹破缺的纯 Yang-Mills 理论至二阶洛伦兹破缺系数的单圈结构，推导了各 beta 函数，重点发现 $(k_{AF})_μ$ 系数仅在质量相关重整化方案中对 $β(g)$ 产生规范依赖且红外发散的贡献。
摘要：
具有洛伦兹破缺的纯 Yang-Mills 理论的可重整化扩展，由 CPT-Even $(k_F)_{μνλρ}$ 和 CPT-Odd $(k_{AF})_μ$ 常数洛伦兹系数表征。本文使用 BFM-gauge 研究了该理论在这些洛伦兹破缺系数中至二阶的单圈结构。推导了各 beta 函数的结果，并与文献中关于这些参数一阶的结果进行了对比。特别强调了 beta 函数 $β(g)$，在质量无关和质量相关重整化方案中对其进行了研究。发现在质量无关方案中，$(k_{AF})_μ$ 洛伦兹系数对 $β(g)$ 函数没有贡献，但在质量相关方案中却有贡献，且其贡献依赖于规范并存在红外发散。
英文摘要：
The renormalizable extension of a pure Yang-Mills theory with Lorentz violation is characterized by the CPT-Even $(k_F)_{μνλρ}$ and the CPT-Odd $(k_{AF})_μ$ constant Lorentz coefficients. In this paper, the one-loop structure of the theory up to second order in these Lorentz violating coefficients is studied using the BFM-gauge. Results for the diverse beta functions are derived and contrasted with those given in the literature at first order in these parameters. Special emphasis is putted on the beta function $β(g)$, which is studied in both mass-independent and mass-dependent renormalization schemes. It is found that in a mass-independent scheme the $(k_{AF})_μ$ Lorentz coefficient does not contribute to the $β(g)$ function, but it does in a mass-dependent scheme with contributions that are gauge-dependent and IR divergent.
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