Scalar Kinetic Mixing and the Renormalization Group

TL;DR

This paper clarifies that scalar kinetic mixing in quantum field theories does not require additional parameters in RG analyses, showing how different schemes are related through field redefinitions.

Contribution

It demonstrates that scalar kinetic mixing does not introduce new parameters and provides explicit 1-loop RG equations in various schemes using a toy model.

Findings

Kinetic mixing does not correspond to a physical observable.

Different renormalization schemes are related by scale-dependent field redefinitions.

Explicit 1-loop RG equations are derived in multiple schemes.

Abstract

Quantum field theories containing scalar fields with equal quantum numbers allow for a mixed kinetic term in the Lagrangian. It has been argued that this mixing must be taken into consideration when performing renormalization group (RG) analyses of such a theory. However, from the fact that scalar kinetic mixing does not correspond to a physical observable, we show that no extra parameters need to be introduced. Using a toy model, we explicitly derive the 1-loop RG equations (RGEs) in three different renormalization schemes to demonstrate how this issue can be dealt with. In schemes without kinetic mixing, either the fields mix during renormalization to produce non-diagonal anomalous dimensions or the RGEs explicitly depend on the scalar masses. Finally, we show how the different schemes are related to each other by scale dependent field redefinitions.