Implications of Generalized Z-Z' Mixing

TL;DR

The paper analyzes generalized $Z$-$Z'$ mixing in the SM extended by an extra abelian factor $U(1)'$, including gauge kinetic mixing parameter $\chi$ and mass mixing, using the most general renormalizable Lagrangian for the $SU(2)\times U(1)\times U(1)'$ sector. By diagonalizing the kinetic and mass terms, the authors obtain the physical states $A_\mu$, $Z_1$, and $Z_2$, and show how $Z-Z'$ mixing modifies SM couplings via shifts proportional to the hypercharge and new charges, introducing a new weak angle $s_*^2$. They connect these modifications to precision observables, deriving low-energy neutral-current interactions and $Z$-pole shifts in terms of oblique parameters $S$ and $T$, the mixing angle $\xi$, the kinetic mixing $\chi$, and the $Z'$ couplings $\tilde f_V^i$, $\tilde f_A^i$. The work provides explicit formulas for low-energy constraints (APV, parity-violating scattering, neutrino-hadron processes) and a linearized $Z$-pole analysis with coefficients $A_O^S$, $A_O^T$, and $B_O^{(i)}$, showing that even without a large mass hierarchy one can constrain the $Z'$ sector. As a general, model-independent framework, the results enable extraction of the $Z'$ couplings and kinetic mixing from data and are applicable to a broad class of $U(1)'$ extensions beyond canonical $E_6$-motivated models.

Abstract

We discuss experimental implications of extending the gauge structure of the Standard Model to include an additional U(1) interaction broken at or near the weak scale. We work with the most general, renormalizable Lagrangian for the SU(2)\times U(1)\times U(1) sector, with emphasis on the phenomenon of gauge kinetic mixing between the two U(1) gauge fields, and do not restrict ourselves to any of the "canonical" Z' models often discussed in the literature. Low-energy processes and Z-pole precision measurements are specifically addressed.