The Complete Lifetime of the Standard Model

March 22, 2018

Figure 1*. [Reprinted under the terms of the Creative Commons Attribution 4.0 International license]

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, graduate student Anders Andreassen, 2017 Harvard PhD William Frost, and Prof. Matthew Schwartz uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. They also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing, and finite mass effects. In addition, they 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, the physicists produce the first complete calculation of the lifetime of our Universe: 10139 years . With 95% confidence, they estimate our Universe to last more than 1058 years . The uncertainty is part experimental uncertainty on the top quark mass and on α s and part theory uncertainty from electroweak threshold corrections.

*See Anders Andreassen, William Frost, and Matthew D. Schwartz, "Scale-invariant instantons and the complete lifetime of the standard model," Phys. Rev. D 97 (12 March 2018) DOI: