Necessity of mixed kinetic term in the description of general system with identical fields

TL;DR

This paper discusses how mixed kinetic terms naturally arise in systems with identical scalar fields, affecting renormalization and tree-level analysis, and provides conditions to prevent their running in certain cases.

Contribution

It highlights the importance of mixed kinetic terms in the analysis of systems with identical fields and derives conditions to avoid their running.

Findings

Mixed kinetic terms naturally appear in systems with identical scalar fields.

Accounting for these terms modifies renormalization group equations and tree-level analysis.

Conditions are derived to prevent the running of kinetic mixing in specific cases.

Abstract

Most general renormalizable interaction in the system with a set of scalar fields having identical quantum numbers generates naturally mixed kinetic terms in the Lagrangian. Taking into account these terms leads to modification both the renormalization group equations and the tree level analysis as compare with many published results. We obtain conditions for non-appearance of such a running mixing in some important cases.