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

2012年在欧洲核子研究中心大型强子对撞机上发现希格斯玻色子，并证实了其预测的性质，极大地巩固了基本粒子及其相互作用的标准模型。这也有基本的宇宙学后果，通过分析我们生活的希格斯有效势真空态的稳定性，可以得出关于宇宙命运的结论。事实上，我们可以预期在接近普朗克质量的场值下会有第二个这样的状态，那里的引力足够强，可以产生成对的粒子和反粒子。如果第二个极小值变得更低，那么我们的真空最终会衰减，这将消除宇宙中生命的基础。除了稳定性和不稳定性之外，还存在真空寿命超过宇宙寿命的可能性（亚稳定性），这实际上并非不可能。 为了加深我们对这个重要问题的理解，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到标准模型中的四个量子环，比目前的成就高一个环阶。具体而言，将评估β函数，它控制参数对重整化尺度的依赖性，在四个循环和阈值校正，这将它们与物理粒子质量和耦合常数在各自测量的能量尺度匹配，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。我们将使用多循环演算的先进技术来做到这一点。紫外线有限性，规范独立性，和具体的一致性检查有关的各种对象将允许我们确保我们的结果的正确性。核心研究团队多年来在电弱微扰理论和多回路计算方面积累的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，它允许匹配和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服务，作为未来分析的关键输入。我们对宇宙命运的更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.