Hubble selection of the weak scale from QCD quantum phase transition
  If the strange quark were lighter, QCD phase transition could have been first
order. This implies that QCD may have quantum critical points as the Higgs vev
$v_h$ is varied from its Standard Model value. We show that inflationary
quantum evolution of $v_h$ with the relaxion can drive our universe toward
those critical points, realizing the weak scale close to the observed value
while explaining its closeness to $\Lambda_{\rm QCD}$. We first explore quantum
critical points of $N_f=3$ QCD, parameterized by $v_h$ at $T=0$, and present a
basic model for the weak scale. It results in a sharply localized probability
distribution of the weak scale, which is critical not to the crossover at zero
but to the quantum transition at ${\sim}\Lambda_{\rm QCD}$.
