A Criterion of Naturalness in Renormalization

Abstract

The sensitivity criterion is widely used in measuring the level of fine-tuning, although many examples show it doesn't work under certain circumstances. We discuss the mathematics behind the fine-tuning problems, explain the mathematical meanings of the sensitivity criterion, point out three implicit assumptions behind this criterion. Because of these assumptions, the sensitivity criterion can't reflect the fine-tuning level correctly. By analyzing two well known examples that the sensitivity criterion failed, we point out the dimensional effect is the main reason why we have these problems. To solve these problems, we proposed a new criterion to replace the sensitivity criterion.