相变引力波谱的精确拟合公式
A Precise Fitting Formula for Gravitational Wave Spectra from Phase Transitions
AI总结：
针对声壳模型计算昂贵、单一拐折幂律忽略声壳厚度的问题，本文提出含两个特征频率拐折的双拐折幂律拟合，并在$α$-$v_w$平面标定参数，以更低成本精确生成相变引力波谱。
摘要：
获得相变所预言引力波（GW）谱的精确形式，是一个与超越标准模型（BSM）物理学家高度相关的课题。目前，用于估算该谱主要贡献的最精密半解析框架是声壳模型；然而，在该框架内进行完整计算可能具有很高的计算成本，尤其是在大规模参数扫描中。因此，学界通常使用引力波谱的拟合函数，其中应用最广泛的是单一拐折幂律。我们基于声壳模型提供了一种更精确的拟合函数：该拟合函数采用双拐折幂律，具有两个频率拐折，分别对应问题的两个特征长度尺度——气泡间距和声壳厚度，而第二个尺度在单一拐折幂律拟合中被忽略。与此前提出的拟合相比，我们证明，在支配相变的热力学参数空间的大部分区域内，我们的拟合函数能够更忠实地捕捉由声壳模型完整计算得到的引力波谱。我们在底层声壳模型中研究了拟合参数的物理来源及其对热力学参数的依赖：特别是，我们在相变强度（$α$）与气泡壁速度（$v_w$）构成的平面上，对这些量进行了一系列详细扫描。在可能的情况下，我们还对这些扫描的物理解释作出了评述。对于相关的BSM情景，只要给定初始输入$α$、$v_w$、$β/H$（成核率参数）和$T_n$（成核温度），我们的研究结果即可用于通过该拟合函数生成准确的引力波谱。
英文摘要：
Obtaining a precise form for the predicted gravitational wave (GW) spectrum from a phase transition is a topic of great relevance for beyond Standard Model (BSM) physicists. Currently, the most sophisticated semi-analytic framework for estimating the dominant contribution to the spectrum is the sound shell model; however, full calculations within this framework can be computationally expensive, especially for large-scale scans. The community therefore generally manages with fit functions to the GW spectrum, the most widely used of which is a single broken power law. We provide a more precise fit function based on the sound shell model: our fit function features a double broken power law with two frequency breaks corresponding to the two characteristic length scales of the problem -- inter-bubble spacing and thickness of sound shells, the second of which is neglected in the single broken power law fit. Compared to previously proposed fits, we demonstrate that our fit function more faithfully captures the GW spectrum coming from a full calculation of the sound shell model, over most of the space of the thermodynamic parameters governing the phase transition. The physical origins of the fit parameters and their dependence on the thermodynamic parameters are studied in the underlying sound shell model: in particular, we perform a series of detailed scans for these quantities over the plane of the strength of the phase transition ($α$) and the bubble wall velocity ($v_w$). Wherever possible, we comment on the physical interpretations of these scans. The result of our study can be used to generate accurate GW spectra with our fit function, given initial inputs of $α$, $v_w$, $β/H$ (nucleation rate parameter) and $T_n$ (nucleation temperature) for the relevant BSM scenario.
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