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\$.
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