Parameterization of General Z-gamma-Z' Mixings in an Electroweak Chiral Theory

TL;DR

This paper introduces a comprehensive eight-parameter framework for describing Z-gamma-Z' mixings in an electroweak chiral theory, linking phenomenological parameters to theoretical coefficients and experimental measurability.

Contribution

It proposes a new general parameterization with eight mixing parameters for Z, gamma, and Z' bosons within an electroweak chiral Lagrangian, extending previous models.

Findings

Eight phenomenological parameters fully determine Z-Z' mixing and mass ratio.

The parameters are fixed by eight theoretical coefficients in the EWCL.

Experimental measurability depends on the Z-Z' mass ratio, not extended neutral current.

Abstract

A new general parameterization with eight mixing parameters among Z, gamma and an extra neutral gauge boson Z' is proposed and subjected to phenomenological analysis. We show that in addition to the conventional Weinberg angle theta_W, there are seven other phenomenological parameters G', xi, eta, theta_l, theta_r, r, l for the most general Z-gamma-Z' mixings, in which parameter G' arises due to the presence of an extra Stueckelberg-type mass coupling. Combined with the conventional Z-Z' mass mixing angle theta', the remaining six parameters xi, eta, theta_l-theta', theta_r-theta', r, l are caused by general kinetic mixings. In all the eight phenomenological parameters theta_W, G', xi, eta, theta_l, theta_r, r, l, we can determine the Z-Z' mass mixing angle theta' and the mass ratio M_Z/M_Z'. The Z-gamma-Z' mixings we discuss are based on the model-independent description of the extended electroweak chiral Lagrangian (EWCL) previous proposed by us. In addition, we show that there are eight corresponding independent theoretical coefficients in our EWCL which are fully fixed by our eight phenomenological mixing parameters. We further find that the experimental measurability of these eight parameters does not rely on the extended neutral current for Z', but depends on the Z-Z' mass ratio.