Is Coleman-Weinberg symmetry breaking in the standard model ruled out?

Abstract

In the standard model with Coleman-Weinberg symmetry breaking a symmetric vacuum (〈 φ〉 = 0) always exists at any non-zero temperature; the transition to the symmetry-breaking vacuum can only occur after much supercooling. Witten has shown that this transition occurs when the strong interactions break chiral symmetry; the transition temperature is O(200) MeV and a large (but not fatal) amount of entropy is produced. It is noted here that since the strong coupling grows as the universe cools in the metastable symmetric vacuum, the Yukawa coupling to the top quark will also grow. This causes top quark loops to dominate the effective potential at small scales, drastically altering the nature of the transition. We show that if m t ⪆ 65 GeV , a metastable vacuum at 〈 φ〉 ≈ 0(1) GeV forms which persists to T = 0; the resulting transition would generate far too much entropy to be compatible with the current baryon to entropy ratio, ruling out the CW mechanism. If m t ⪅ 65 GeV, we argue that a metastable vacuum might also exist, but a breakdown of perturbation theory precludes a definitive statement.