Abstract
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: 10^139 years. With 95% confidence, we expect our universe to last more than 10^58 years. The uncertainty is part experimental uncertainty on the top quark mass and on ${\alpha}s$ and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the $mt/mh$ and the $mt/{\alpha}s$ planes, with uncertainty bands. To rule out absolute stability to $3{\sigma}$ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on ${\alpha}s(mZ)$ pushed below 0.00025.
Highlights
Tunneling through a barrier is a quintessentially quantum phenomenon
[11,19,61,62]: cut off the divergence in the Jacobian by the Higgs mass and assume the integral over R is dominated by the bubble size Rm with the maximal rate
We show that the entire series of leading contributions can be summed in closed form
Summary
Tunneling through a barrier is a quintessentially quantum phenomenon. In quantum mechanics (QM), tunneling has been studied analytically, numerically, and experimentally, leading to a consistent and comprehensive picture of when and how fast tunneling occurs. Even if we ignore gauge dependence and trust the decay rate formulas, we encounter a new roadblock in trying to evaluate tunneling rates in QFTs like the Standard Model, due to classical scale invariance. For the decay rate in the Standard Model, people always just invoke dimensional analysis [11,19,61,62]: cut off the divergence in the Jacobian by the Higgs mass and assume the integral over R is dominated by the bubble size Rm with the maximal rate. We show that the entire series of leading contributions can be summed in closed form With these scale invariance problems solved, we proceed to compute the functional determinants around the bounce over real scalar, complex scalar, vector boson, and fermionic fluctuations.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
