Relaxing the Higgs mass and its vacuum energy by living at the top of the potential

Understand

We consider an ultra-light scalar coupled to the Higgs in the presence of heavier new physics.

• In the electroweak broken phase the Higgs gives a tree-level contribution to the light-scalar potential, while new physics contributes at loop level.
• Thereby, the theory has a cosmologically meta-stable phase where the light scalar is around the top of its potential, and the Higgs is a loop factor lighter than new physics.
• Such regions with precarious naturalness are anthropically and environmentally selected, as regions with heavier Higgs crunch quickly.