AI 中文总结
针对多标量理论假真空隧穿率计算缺乏可控解析方法的问题，证明大场区域下一维径向反弹解主导领头阶隧穿率，推导了含有效四次耦合的解析公式，并应用于2HDM+a等模型的真空稳定性研究。
AI 中文摘要
许多超出标准模型的理论都包含多个标量粒子。这类多标量理论原则上可能存在更低能量的真空，因此预言我们的宇宙会因假真空衰变而具有有限寿命。由于甚至标准模型的电弱真空都已被证明是亚稳态的，这种情形无法被先验排除；不过为了理论自洽性，我们仍要求模型预言的寿命不会远小于宇宙年龄。多标量理论中这类隧穿率的领头阶计算通常采用数值方法，或是常缺乏解析控制的近似方法。本文证明，在大场区域下，一维径向反弹解总能给出领头阶隧穿率的精确主导贡献，且修正项呈指数压低。这使得我们能够用有效四次耦合$λ_\text{eff}$写出计算多标量理论隧穿率的简单解析表达式。对于具有双二次标量势的理论，我们还推导了用原理论耦合表示的$λ_\text{eff}$的直接解析表达式。最后，我们给出了结果的示例应用，用于研究2HDM+a模型和3-3-1模型的真空稳定性。
英文摘要
Many theories beyond the standard model exhibit multiple scalar particles. Such multi-scalar theories can in principle host lower-energy vacua, and thus predict that our universe has a finite lifetime due to false vacuum decay. This scenario cannot be ruled out a priori as even the standard model's electroweak vacuum has been shown to be metastable; however, for theoretical consistency, we still require that the model does not predict a lifetime much smaller than the age of the universe. The calculation of these tunneling rates at leading order for multi-scalar theories typically includes numerical approaches, or approximations which are frequently not analytically controlled. In this article we show that, in the large-field regime, a one-dimensional radial bounce always produces the exact dominant contribution to the leading order tunneling rate, with corrections being exponentially suppressed. This allows us to write simple analytical expressions to calculate the tunneling rate in multi-scalar theories, in terms of an effective quartic coupling $λ_\text{eff}$. For theories with biquadratic scalar potentials, we also derive straightforward analytical expressions for $λ_\text{eff}$ in terms of the original theory's couplings. Finally, we provide example applications of our results to study the vacuum stability of the 2HDM+a model and the 3-3-1 model.
Comments15 pages, 5 figures
