Bound on Noncommutative Standard Model with Hybrid Gauge Transformation via Lepton Flavor Conserving $Z$ Decay

TL;DR

This paper investigates how hybrid gauge transformations in the noncommutative standard model affect the $Z\rightarrow e^{+}e^{-}$ decay, providing bounds on noncommutative parameters based on experimental data.

Contribution

It introduces the impact of hybrid gauge transformations on the noncommutative correction to $Z$ decay, which was previously considered only as a phase factor.

Findings

Hybrid gauge transformation induces observable effects in $Z$ decay.

Bounds on noncommutative parameters are derived from experimental data.

Without hybrid transformation, no physical effect on decay width.

Abstract

The $Z\rightarrow e^{+}e^{-}$ decay is studied basing on the noncommutative standard model (NCSM) with the hybrid gauge transformation. It is shown that if the latter is not included, the noncommutative correction to the amplitude of the $Z\rightarrow e^{+}e^{-}$ appears only as a phase factor, so that there is no new physical effect on the decay width. However, when the hybrid gauge transformation is included, the noncommutative effect appears in the two-body decay process. The discrepancy between the experimental branch ratio and the standard model prediction allows us to set the bound on the noncommutative parameters.