Scale-invariant instantons and the complete lifetime of the standard model

• Published in: Physical review. D 2018-03, Vol.97 (5), Article 056006
• Main Authors: Andreassen, Anders, Frost, William, Schwartz, Matthew D.
• Format: Article
• Language: English
• Subjects: Bosons; Fermions; Field theory; Gauge invariance; Instantons; Invariants; Phase diagrams; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum field theory; Quantum theory; Quarks; Scalars; Uncertainty; Universe
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.97.056006

In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing, and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions, and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our Universe: 10139  years. With 95% confidence, we expect our Universe to last more than 1058  years. The uncertainty is part experimental uncertainty on the top quark mass and on αs and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the mt/mh and the mt/αs planes, with uncertainty bands. To rule out absolute stability to 3σ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on αs(mZ) pushed below 0.00025.