论文标题
经典规模不变电位的最小值
Minima of Classically Scale-Invariant Potentials
论文作者
论文摘要
我们提出了一种新的形式主义，以分析规模不变有效潜力的极值结构。该问题以紧凑的矩阵形式说明，用于得出固定点方程的一般表达式和多场RG改良有效势的质量矩阵。我们的方法改善了（但不限于）Gildener-Weinberg近似，并鉴定了一组信号的条件，以表明存在辐射最小值的情况。当在不同的尺度或场空间的不同子空间满足条件时，有效电势具有多个辐射最小值。我们通过简单的例子说明了该方法，并详细研究了一个标准模型样的场景，其中潜力允许两个辐射最小值。尽管我们主要集中于双宫电位，但我们的结果通过使用张量代数来延续到一般情况下。
We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix of a multi-field RG-improved effective potential. Our method improves on (but is not limited to) the Gildener-Weinberg approximation and identifies a set of conditions that signal the presence of a radiative minimum. When the conditions are satisfied at different scales, or in different subspaces of the field space, the effective potential has more than one radiative minimum. We illustrate the method through simple examples and study in detail a Standard-Model-like scenario where the potential admits two radiative minima. Whereas we mostly concentrate on biquadratic potentials, our results carry over to the general case by using tensor algebra.
