Sensitivity coefficients to variation of fundamental constants

TL;DR

This paper discusses how atoms and molecules can detect changes in fundamental constants like alpha and mu, clarifying common misconceptions about sensitivity coefficients used in such studies.

Contribution

It clarifies errors and misconceptions related to the use of sensitivity coefficients in probing variations of fundamental constants.

Findings

Identifies common errors in calculating sensitivity coefficients

Clarifies the distinction between fractional and absolute sensitivities

Provides guidance for correct interpretation of sensitivity coefficients

Abstract

Atoms and molecules can serve as sensitive probes of a possible variation of the fine structure constant $\alpha$ and electron-to-proton mass ratio $\mu$. Two types of sensitivity coefficients are often used to quantify and compare the sensitivity of different species to the variation of fundamental constants. The dimensionless coefficients $K$ are related to the fractional sensitivity, while dimensional factors $q$ are related to the absolute sensitivity. Here we discuss several common errors and misconceptions regarding these coefficients that frequently appear in the literature.