Preferred hierarchy scales from the product landscape

TL;DR

This paper proposes using the peak of parameter distributions on logarithmic scales as a benchmark for hierarchy in the product landscape method, highlighting the inefficiency of pure product distributions and the need for additional effects.

Contribution

It introduces a new benchmark for hierarchy scales based on distribution peaks and analyzes the inefficiency of pure product distributions in generating hierarchies.

Findings

Distribution peak indicates preferred hierarchy scales

Pure product distributions are inefficient for hierarchy generation

Additional effects are needed to improve hierarchy generation

Abstract

The product landscape method has been recently proposed to solve hierarchy problems such as the cosmological constant problem. We suggest that the parameter distribution on logarithmic scales should be used as a benchmark for hierarchy, and the preferred hierarchy scales can be obtained from the distribution peak. It is shown that generating hierarchy from purely product distribution is very inefficient. To achieve a reasonably acceptable efficiency, other effects such as accumulation of weak hierarchy in the effective theory should be incorporated.