Running parameters and Higgs effective potential at four loops in the Standard Model

2012年，欧洲核子研究中心的大型强子对撞机发现了希格斯玻色子，并证实了其预测性质，极大地巩固了基本粒子及其相互作用的标准模型。通过分析我们所处的希格斯有效势的真空状态的稳定性，我们可以得出关于宇宙命运的结论，这也具有基本的宇宙学意义。事实上，人们预计在接近普朗克质量的场值时，会出现第二种这样的状态，在这种状态下，引力足以产生粒子和反粒子对。如果第二个最小值被证明更低，那么我们的真空最终会衰减，这将抹去宇宙中生命的基础。除了稳定和不稳定之外，我们的真空的寿命也有可能超过宇宙的寿命（亚稳态），这实际上不是不可能的。为了加深我们对这一重要问题的理解，我们将把运行参数（质量和耦合）和希格斯有效势的重整化群分析推进到标准模型中的四个量子环，比目前的成就高出一个环阶。具体来说，将评估β函数，它控制参数在重整化尺度上的依赖关系，在四个循环和阈值修正，将它们与物理粒子质量和耦合常数相匹配，在各自测量的能量尺度上，在三个循环。这些运行参数，特别是希格斯质量和四次自耦合，进入希格斯有效势，我们也将在四个循环中计算。我们将使用先进的多环微积分技术来实现这一点。紫外线的有限性，测量独立性，以及与各种对象相关的特定一致性检查将使我们能够确保结果的正确性。核心研究团队多年来积累的电弱微扰理论和多环计算经验将使我们能够成功地实现我们的目标。我们将利用我们在beta函数和阈值校正方面的先进知识来升级我们发布的c++程序库rm，它允许人们匹配并运行标准模型的参数。这将为粒子物理学和宇宙学社区提供未来分析的关键输入。我们关于宇宙命运的最新和尖锐的结论可能会影响公众的世界观。

The discovery of the Higgs boson in 2012 at the CERN Large Hadron Collider and the confirmation of its predicted properties has greatly consolidated the Standard Model of elementary particles and their interactions. This has also fundamental cosmological consequences by allowing conclusions regarding the fate of the universe via the analysis of the stability of the vacuum state of the Higgs effective potential in which we live. In fact, one expects a second such state at field values close to the Planck mass, where gravity is strong enough to create pairs of particles and antiparticles. If this second minimum turns out to be lower, then our vacuum will eventually decay, which would erase the basis for life in the universe. Besides stability and instability, there also exists the possibility that the lifetime of our vacuum exceeds that of the universe (metastability), which is actually not unlikely. To deepen our understanding of this vital issue, we will push the renormalization group analysis of the running parameters (masses and couplings) and the Higgs effective potential to four quantum loops in the Standard Model, one loop order beyond present achievements. Specifically, will evaluate the beta functions, which control the dependencies of the parameters on the renormalization scale, at four loops and the threshold corrections, which match them to physical particle masses and coupling constants at the energy scales of the respective measurements, at three loops. These running parameters, especially the Higgs mass and quartic self coupling, enter the Higgs effective potential, which we will also calculate at four loops. We will do this using advanced technology of multi-loop calculus. Ultraviolet finiteness, gauge independence, and specific consistency checks relating the various objects will allow us to enure the correctness of our results. Experience in electroweak perturbation theory and multi-loop calculations collected by the core research team over many years will enable us to successfully accomplish our goals. We will exploit our advanced knowledge of beta functions and threshold corrections to upgrade our published C++ program library rm, which allows one to match and run the parameters of the Standard Model. This will serve the particle physics and cosmology communities as crucial input for future analyses. Our updated and sharpened conclusions regarding the fate of the universe may affect the worldview of the general public.