通过梯度流正则化的规范不变希格斯机制
Gauge-invariant Higgs mechanism via gradient-flow regularization
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中文总结 AI 辅助
本文提出用梯度流正则化实现标准模型中希格斯机制的规范不变描述，将相变视为平滑交叉，并在单圈级别验证了与MS方案的一致匹配，为电弱精密物理奠定基础。
中文摘要 AI 辅助
我们提供了标准模型中希格斯机制的显式规范不变描述，将其不是视为局部对称性的破缺，而是视为从高温对称相到低温希格斯相的平滑解析交叉。取规范不变局域标量算符的真空期望值，并从拉格朗日量的原始场构造复合准粒子态，通常会引入接触项发散。先前通过双局域算符规避此问题的尝试仍不令人满意。在此，我们证明流动时间为$t$的梯度流提供了一种干净、结构健全且洛伦兹协变的正则化，允许在尺度$\mu \sim 1/\sqrt{2t}\gg m_t$下与标准$\overline{\text{MS}}$方案进行一致且无重整化子匹配。除了其理论吸引力外，此构造澄清了许多概念性和实践性问题。我们在单圈级别展示了此框架的实用性，从而为未来在此方法中进行电弱精密物理奠定了基础。
英文摘要
We provide a manifestly gauge-invariant description of the Higgs mechanism in the Standard Model, casting it not as the breaking of a local symmetry, but as a smooth, analytic crossover from a high-temperature symmetric phase to a low-temperature Higgs phase. Taking the vacuum expectation value of a gauge-invariant local scalar operator and constructing composite quasi-particle states from the original fields of the Lagrangian usually introduces contact-term divergences. Previous attempts to circumvent this issue via bilocal operators remain unsatisfactory. Here we demonstrate that the gradient flow at a flow time $t$ provides a clean, structurally sound, and Lorentz-covariant regularization that permits a consistent, renormalon-free matching onto the standard $\overline{\text{MS}}$ scheme at a scale $μ\sim 1/\sqrt{2t}\gg m_t$. Beyond its theoretical appeal, this construction clarifies a number of conceptional and practical questions. We demonstrate the utility of this framework at the one-loop level, thereby establishing the foundation for future electroweak precision physics in this approach.
发表机构
- Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）
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