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

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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.