Kinetic mixing, custodial symmetry, $Z$, $Z^{\prime}$ interactions and $Z^{\prime}$ production in hadron colliders

TL;DR

This paper investigates the interactions of Z and Z' bosons arising from kinetic mixing in models beyond the standard model, analyzing their effects on electroweak precision data and collider experiments, especially in dark matter contexts.

Contribution

It provides a detailed analysis of Z and Z' couplings, calculates oblique parameters, and sets collider bounds on Z' mass within a custodial symmetry framework.

Findings

Results align with electroweak precision data for M_{Z'} ≥ M_Z

Lower limit on Z' mass from collider data is approximately 5 TeV

Oblique parameters S and T are consistent with experimental fits

Abstract

In this work we study the interactions of the $Z$ and $Z^{\prime}$ generated by kinetic mixing in a class of theories for physics beyond the standard model motivated by the dark matter problem, containing a spontaneously broken extra $U(1)_{d}$ gauge factor group in a hidden scenario and a Higgs sector respecting custodial symmetry. It is shown that custodial symmetry allows us to write the $Z$ and $Z^{\prime}$ couplings to standard model fermions in terms of the measured values of $\alpha$, $G_{F}$, $M_{Z}$ and $M_{Z^{\prime}}$. Working at the loop level, we calculate the ratio $\rho_{0}=M^{2}_{W}/\hat{c}^{2}_{Z}M^{2}_{Z}\hat{\rho}$ used in the fit to electroweak precision data (EWPD) and use its value to estimate possible effects of kinetic mixing at the electroweak scale. For the $Z$ sector, we calculate the oblique parameters $S$ and $T$, finding that for $M_{Z^{\prime}}\geq M_{Z}$ our results are in agreement with the values of the oblique parameters extracted from the global fit to EWPD at $1\sigma$ level. As to the $Z^{\prime}$ sector, we calculate the $Z^{\prime}$ contributions to charged lepton pair production at the Large Hadron Colliderin the well motivated case of dark matter entering particle physics as the matter fields of the $U(1)_{d}$ gauge symmetry with perturbative couplings at the electroweak scale, finding that data reported by the Compact Muon Selenoid Collaboration impose a lower limit $M_{Z^{\prime}}\gtrsim 5.0 ~TeV$.