Vector unparticle contributions to lepton g-2

TL;DR

This paper examines how modifications to the unparticle propagator, due to conformal symmetry breaking and vacuum polarization, influence calculations of the lepton g-2, finding minimal deviation within certain parameter ranges.

Contribution

It introduces an integral approximation for the unparticle propagator considering symmetry breaking and polarization effects, analyzing their impact on lepton g-2 calculations.

Findings

Modifications to the propagator cause minimal g-2 deviation for $d\,\lesssim\,1.5$.

The impact of width-like terms is negligible within the studied parameter space.

Constraints on unparticle mass scale depend on the conformal breaking scale and unparticle dimension.

Abstract

The generic unparticle propagator may be modified in two ways. Breaking the conformal symmetry effectively adds a mass term to the propagator, while considering vacuum polarization corrections adds a width-like term. Both of these modifications result naturally from the coupling of the unparticle to standard model (SM) fields. We explore how these modifications to the propagator affect the calculation of the lepton anomalous magnetic moment using an integral approximation of the propagator that is accurate for $d\lesssim1.5$, where $d$ is the unparticle dimension. We find that for this range of $d$ and various values of the conformal breaking scale $\mu$, the value of $g-2$ calculated when allowing various SM fermions to run in the unparticle self-energy loops does not significantly deviate from the value of $g-2$ when the width term is ignored. We also investigate the limits on a characteristic mass scale for the unparticle sector as a function of $\mu$ and $d$.