# Kinetic mixing effect in noncommutative $B-L$ gauge theory

## TL;DR

This paper investigates the kinetic mixing effects in a noncommutative $B-L$ gauge theory, exploring how these mixings influence electroweak precision tests and the model's physical predictions.

## Contribution

It constructs a detailed noncommutative $B-L$ gauge model and analyzes the interplay between kinetic mixing and symmetry breaking effects.

## Key findings

- Kinetic mixing impacts electroweak precision observables.
- The model provides insights into neutrino mass and dark matter.
- Detailed physical implications of kinetic mixing are derived.

## Abstract

It is well established that the $SU(P)_L$ gauge symmetry for $P\geq 3$ can address the question of fermion generation number due to the anomaly cancellation, but it neither commutes nor closes algebraically with electric and baryon-minus-lepton charges. Hence, two $U(1)$ factors that determine such charges are required, yielding a complete gauge symmetry, $SU(P)_L\otimes U(1)_X\otimes U(1)_N$, apart from the color group. The resulting theory manifestly provides neutrino mass, dark matter, inflation, and baryon asymmetry of the universe. Furthermore, this gauge structure may present kinetic mixing effects associated to the $U(1)$ gauge fields, which affect the electroweak precision test such as the $\rho$ parameter and $Z$ couplings as well as the new physics processes. We will construct the model, examine the interplay between the kinetic mixing and those due to the symmetry breaking, and obtain the physical results in detail.