A landscape for the cosmological constant and the Higgs mass

TL;DR

This paper explores how the smallness of the cosmological constant and Higgs mass can be explained through a landscape of vacua in quantum field theories, highlighting the role of symmetries and vacuum decay bounds.

Contribution

It demonstrates that both parameters can be scanned in theories with many vacua using approximate symmetries, and discusses implications for vacuum stability and predictivity.

Findings

Vacuum decay bounds are weaker than previously thought.

Special vacua with light scalars can avoid catastrophic decay.

Non-Gaussian probability distributions may reduce landscape unpredictivity.

Abstract

The cosmological constant and the Higgs mass seem unnaturally small and anthropically selected. We show that both can be efficiently scanned in Quantum Field Theories with a large enough number of vacua controllable thanks to approximated $\mathbb{Z}_2$ symmetries (even for Coleman-Weinberg potentials). We find that vacuum decay in a landscape implies weaker bounds than previously estimated. Special vacua where one light scalar is accidentally light avoid catastrophic vacuum decay if its self-cubic is absent. This is what happens for the Higgs doublet, thanks to gauge invariance. Yukawa couplings can be efficiently scanned, as suggested by anthropic boundaries on light quark masses. Finally, we suggest that the lack of predictivity of landscapes can be mitigated if their probability distributions are non-Gaussian (possibly even fractal).