Sensitivity Parameter and Time Variations of Fundamental Constants

TL;DR

This paper critiques the use of the sensitivity parameter in quantifying fine tuning, highlighting its limitations and proposing ways to improve its reliability, especially in contexts involving time variations of fundamental constants.

Contribution

It identifies the shortcomings of the sensitivity parameter in certain scenarios and discusses how to enhance its reliability when analyzing time-varying fundamental constants.

Findings

Sensitivity parameter can fail under certain conditions.

High sensitivity of energy scale b3 to coupling constants impacts results.

Proper use can improve the reliability of the sensitivity parameter.

Abstract

The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that the problems of the sensitivity parameter are almost identical to the consequences we have to solved if the time-varying fine structure constant is proved to be true. The high sensitivity of the energy scale parameter (\Lambda) to the dimensionless coupling constant plays an important role in these problems. It affects the reliability of the sensitivity parameter via mechanisms such as dynamical symmetry breaking, chiral symmetry breaking etc. The reliability of the sensitivity parameter can be improved if it is used properly.