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  • Letter
  • Open Access

Hubble selection of the weak scale from QCD quantum critical point

Sunghoon Jung1,2,* and TaeHun Kim1,†

  • 1Center for Theoretical Physics, Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
  • 2Astronomy Research Center, Seoul National University, Seoul 08826, Korea

  • *sunghoonj@snu.ac.kr
  • †gimthcha@snu.ac.kr
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Phys. Rev. Research 4, L022048 – Published 31 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022048

Abstract

There is growing evidence that the small weak scale may be related to self-organized criticality. In this regard, we note that if the strange quark were lighter, the QCD phase transition could have been first order, possibly exhibiting quantum critical points at zero temperature as a function of the Higgs vacuum expectation value vh smaller than (but near) the weak scale. We show that these quantum critical points allow a dynamical selection of the observed weak scale, via quantum-dominated stochastic evolutions of the value of vh during eternal inflation. Although the values of vh in different Hubble patches are described by a probability distribution in the multiverse, inflationary quantum dynamics ensures that the peak of the distribution evolves toward critical points (self-organized criticality), driven mainly by the largest Hubble expansion rate there—the Hubble selection of the universe. To this end, we first explore the quantum critical points of the three-flavor QCD linear sigma model, parametrized by vh at zero temperature, and we present a relaxion model for the weak scale. Among the patches that have reached reheating, it results in a sharp probability distribution of vh near the observed weak scale, which is critical not to the crossover at vh=0 but to the sharp transition at ∼ΛQCD.

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Phys. Rev. Research 4, L022048– Published 31 May, 2022
  • Received 1 August 2021
  • Accepted 9 May 2022
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