Models with classical scale symmetry, which feature radiative symmetry breaking, generically lead to a supercooled first-order phase transition in the early Universe resulting in a strong gravitational-wave signal, potentially observable by LISA. This is thanks to the absence of mass terms in the potential and the resulting logarithmic structure of the zero-temperature effective potential. It is known that imposing a symmetry at classical level does not prohibit breaking it by quantum corrections. In the case of scale symmetry, a mass term can in principle appear through renormalisation. This is not the case in the commonly used MS‾ or Coleman–Weinberg schemes. In this work, we renormalise a scale-invariant model in the on-shell scheme to check whether parameterising it with the physical masses will introduce mass terms to the potential. We find that indeed mass terms appear for an arbitrary choice of the physical masses. However, we formulate an on-shell condition for radiative symmetry breaking, sufficient and necessary for the cancellation of mass terms in the renormalised potential, yielding a logarithmic potential needed for supercooled phase transitions.

中文翻译：

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壳上视角的辐射对称性打破


具有经典尺度对称性的模型，其特点是辐射对称性被打破，通常会导致早期宇宙中的过冷一阶相变，从而产生强烈的引力波信号，可能被 LISA 观察到。这要归功于电势中没有质量项以及由此产生的零温度有效电势的对数结构。众所周知，在经典水平上施加对称性并不禁止通过量子校正来打破它。在尺度对称的情况下，质量项原则上可以通过重整出现。在常用的 MS ̅ 或 Coleman-Weinberg 方案中，情况并非如此。在这项工作中，我们在 on-shell 方案中重新归一化了尺度不变模型，以检查用物理质量参数化它是否会为势能引入质量项。我们发现质量项确实出现在物理质量的任意选择中。然而，我们制定了一个辐射对称性打破的壳上条件，该条件对于消除重整化势中的质量项来说是充分和必要的，从而产生过冷相变所需的对数势。