Large Hierarchies from Attractor Vacua

TL;DR

The paper proposes a mechanism within multi-vacua theories like String Theory that naturally explains the small Higgs mass hierarchy through an attractor landscape, avoiding the need for low-energy UV physics.

Contribution

It introduces a novel landscape-based approach where a discrete symmetry and heavy branes dynamically set the Higgs mass, providing a new solution to the Hierarchy Problem.

Findings

Vacua with small Higgs mass form an attractor in the landscape.

Heavy branes convert the Higgs mass into a dynamical variable.

The model predicts a small Higgs mass controlled by QCD scale and constrains quark Yukawa matrices.

Abstract

We discuss a mechanism through which the multi-vacua theories, such as String Theory, could solve the Hierarchy Problem, without any UV-regulating physics at low energies. Because of symmetry the number density of vacua with a certain hierarchically-small Higgs mass diverges, and is an attractor on the vacuum landscape.The hierarchy problem is solved in two steps. It is first promoted into a problem of the super-selection rule among the infinite number of vacua (analogous to theta-vacua in QCD), that are finely scanned by the Higgs mass. This rule is lifted by heavy branes, which effectively convert the Higgs mass into a dynamical variable. The key point is that a discrete "brane-charge-conjugation" symmetry guarantees that the fineness of the vacuum-scanning is set by the Higgs mass itself. On a resulting landscape in all, but a measure-zero set of vacua the Higgs mass has a common hierarchically-small value. In minimal models this value is controlled by the QCD scale and is of the right magnitude. Although in each particular vacuum there is no visible UV-regulating low energy physics, the realistic models are predictive. For example, we show that in the minimal case the "charge conjugation" symmetry is automatically a family symmetry, and imposes severe restrictions on quark Yukawa matrices.