Precision Tunneling Rate Calculations in Quantum Field Theory and the Ultimate Fate of Our Universe

Abstract

One of the most concrete implications of the discovery of the Higgs boson is that, in the absence of physics beyond the Standard Model, the long-term fate of our universe can now be established through precision calculations. Are we in a metastable minimum of the Higgs potential or the true minimum? If we are in a metastable vacuum, what is its lifetime? To answer these questions, we need to understand tunneling in quantum field theory. We present solutions to several problems in the history of tunneling rate calculations that have persisted for several decades. The first problem is how to extract gauge-invariant information about the true vacuum from the gauge-dependent effective potential, and we show that a new perturbation expansion is needed for a consistent calculation of physical observables. We then derive a new formulation for how to calculate the tunneling rate in quantum field theory, we show that our results match known approximated results, and we clarify a number of opaque details in the standard literature. We then complete the story by resolving several problems in calculating the functional determinants of fluctuations around the bounce solutions, and we present exact closed-form expressions of the functional determinant that have never been done before. Applied to the Standard Model, we then get the first-ever complete calculation of the lifetime of our universe. We also present a new application of jet grooming to the measurement of the top quark mass, the uncertainty of which is the most significant in the determination of the lifetime of the Standard Model. This technique reduces the sensitivity to the Monte Carlo uncertainties from underlying events. Finally, we discuss some new modern applications of machine learning to jet physics using recurrent neural networks.