Dark photon effects with the kinetic and mass mixing in Z boson decay processes

TL;DR

This paper investigates how a new dark photon with kinetic and mass mixing affects Z boson decay processes, using tau polarization data to constrain model parameters and exploring implications for all fermions.

Contribution

It introduces a combined kinetic and mass mixing dark photon model and provides the first global fit to experimental data, constraining the dark photon parameters.

Findings

Dark photon mass is preferred to be larger than Z boson mass.

Fitted kinetic mixing parameter is approximately 0.074.

Mixing ratio parameter is around -1.37, affecting Z boson properties.

Abstract

Motivated by the most recent measurement of tau polarization in $Z\to \tau^+\tau^-$ by CMS, we have introduced a new $U(1)_X$ gauge boson field X, which can have renormalizable kinetic mixing with the standard model $U(1)_Y$ gauge boson field Y. In addition to the kinetic mixing of the dark photon, denoted as $\sigma$, there may also be mass mixing introduced by the additional Higgs doublet with a vacuum expectation value (vev) participating in $U(1)_X$ and electroweak symmetry breaking simultaneously. The interaction of the Z boson with the SM leptons is modified by the introduction of the mixing ratio parameter $\epsilon$, which quantifies the magnitude of both the mass and kinetic mixing of the dark photon. Initially, we use the tau lepton as an example to explore the Z boson phenomenology of the dark photon model with both kinetic and mass mixing. The goal is to determine the allowed parameter regions by taking into account constraints from the vector and axial-vector couplings $g_{V,A}^\tau$, the decay branching ratio $Br(Z\to \tau^- \tau^+)$ and tau lepton polarization in $Z\to \tau^-\tau^+$. We found that the mixing ratio plays important role in the Z boson features by choosing different $\epsilon$ values. Furthermore, we aim to generalize our analysis from the tau-lepton case to include all fermions by conducting global fits. This allows us to identify viable regions by incorporating relevant fermion constraints and the W/Z mass ratio. Correspondingly, we obtain the fit results with the kinetic mixing parameter $\sigma=0.074\pm0.021$, mixing ratio $\epsilon=-1.37\pm0.46$, and dark photon mass $m_X=275\pm39$ GeV. Our global analysis indicates a preference for a dark photon mass larger than $m_Z$.