Renormalisation and invariants for two U(1)s

TL;DR

This paper develops a covariant renormalisation framework for models with two U(1) gauge symmetries, enabling the study of kinetic mixing and the construction of gauge-invariant observables like millicharges.

Contribution

It introduces a non-canonical gauge kinetic term formulation that simplifies RG equations and allows for the creation of invariants under gauge reparametrisations.

Findings

Derived simple two-loop MSbar RG equations for two U(1)s.

Provided a method to compute effective millicharges at low energy.

Constructed gauge-invariant parameters related to observable millicharges.

Abstract

We revisit the renormalisation of models with two U(1) gauge symmetries, in a formulation with non-canonical gauge kinetic terms which is covariant under field reparametrisations among the two gauge bosons. This approach is convenient to study the appearance of kinetic mixing in scale evolution, because a coupling matrix is attributed to the gauge kinetic terms. We obtain simple MSbar renormalisation group equations up to two-loop, which can be solved to give effective millicharges at low energy which depend on the running couplings and heavy mass scales of the model. This formulation allows to construct ``invariants'' out of running Lagrangian parameters, which are invariant under generic gauge field reparametrisations, including rescalings, and which can be related directly to observables such as the millicharge.