# Signal for space-time noncommutativity: the Z -> gamma gamma decay in the renormalizable gauge sector of the theta-expanded NCSM

## TL;DR

This paper investigates the forbidden Z -> gamma gamma decay as a potential signal of space-time noncommutativity, calculating its rate within a renormalizable noncommutative standard model framework and setting experimental bounds around 1 TeV.

## Contribution

It introduces a calculation of the Z -> gamma gamma decay in a renormalizable noncommutative standard model, proposing it as a probe for space-time noncommutativity and Lorentz invariance violation.

## Key findings

- Z -> gamma gamma decay width computed in noncommutative model
- Decay is finite and divergence-free, indicating possible new symmetries
- Experimental bound on noncommutativity scale set around 1 TeV

## Abstract

We propose the Z -> gamma gamma decay, a process strictly forbidden in the standard model, as a signal suitable for the search of noncommutativity of coordinates at very short distances. We compute the Z -> gamma gamma partial widthin the framework of the recently proposed renormalizable gauge sector of the noncommutative standard model. The one-loop renormalizability is obtained for the model containing the usual six representations of matter fields of the first generation. Even more, the noncommutative part is finite or free of divergences, showing that perhaps new interaction symmetry exists in the noncommutative gauge sector of the model. Discovery of such symmetry would be of tremendous importance in further search for the violation of the Lorentz invariance at very high energies. Experimental possibilities of Z -> gamma gamma decay are analyzed and a firm bound to the scale of the noncommutativity parameter is set around 1 TeV.