The $Z\to e^{+}{e}^{-}$ decay is studied based on the noncommutative standard model with the hybrid gauge transformation. It is shown that if the latter is not included, the noncommutative correction to the amplitude of the $Z\to e^{+}{e}^{-}$ 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.

• Received 10 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.025031