The Weak Scale from BBN

TL;DR

This paper explains the measured weak scale and first generation masses through multiverse considerations, showing how small parameter variations lead to universe instabilities and proposing that large weak scales are rare, solving the fine-tuning problem.

Contribution

It introduces a multiverse-based explanation for the weak scale and first generation masses, linking parameter variations to universe stability and anthropic constraints.

Findings

Small parameter variations cause universe instabilities.

Large weak scales lead to helium abundance independent of v.

Rare universes with large v are required to explain observations.

Abstract

The measured values of the weak scale, $v$, and the first generation masses, $m_{u,d,e}$, are simultaneously explained in the multiverse, with all these parameters scanning independently. At the same time, several remarkable coincidences are understood. Small variations in these parameters away from their measured values lead to the instability of hydrogen, the instability of heavy nuclei, and either a hydrogen or a helium dominated universe from Big Bang Nucleosynthesis. In the 4d parameter space of $(m_u,m_d,m_e,v)$, catastrophic boundaries are reached by separately increasing each parameter above its measured value by a factor of $(1.4,1.3,2.5,\sim5)$, respectively. The fine-tuning problem of the weak scale in the Standard Model is solved: as $v$ is increased beyond the observed value, it is impossible to maintain a significant cosmological hydrogen abundance for any values of $m_{u,d,e}$ that yield both hydrogen and heavy nuclei stability. For very large values of $v$ a new regime is entered where weak interactions freeze out before the QCD phase transition. The helium abundance becomes independent of $v$ and is determined by the cosmic baryon and lepton asymmetries. To maintain our explanation of $v$ from the anthropic cost of helium dominance then requires universes with such large $v$ to be rare in the multiverse. Implications of this are explored, including the possibility that new physics below 10 TeV cuts off the fine-tuning in $v$.