# Proton Decay and the Quantum Structure of Spacetime

## TL;DR

This paper explores how noncommutative spacetime and virtual black holes influence proton decay, suggesting proton lifetime measurements could reveal spacetime's microscopic structure.

## Contribution

It introduces a model of virtual black holes in noncommutative spacetime and analyzes their impact on proton decay across different dimensions.

## Key findings

- Proton lifetime depends on the noncommutativity parameter and spacetime dimensions.
- Proton decay rates could serve as probes for the quantum structure of spacetime.
- The model generalizes to D-dimensional spacetime, affecting phenomenological predictions.

## Abstract

Virtual black holes in noncommutative spacetime are investigated using coordinate coherent state formalism such that the event horizon of black hole is manipulated by smearing it with a Gaussian of width $ \sqrt \theta $, where $ \theta$ is the noncommutativity parameter. Proton lifetime, the main associated phenomenology of the noncommutative virtual black holes, has been studied: first in $4$ dimensional spacetime and then generalized to $D$ dimensions. The lifetime depends on $ \theta$ and the number of spacetime dimensions such that it emphasizes on the measurement of proton lifetime as a potential probe for the micro-structure of spacetime.