Particle phenomenology on noncommutative spacetime

TL;DR

This paper explores the implications of noncommutative spacetime on particle phenomenology, constraining the noncommutativity scale through CPT violation and magnetic moment measurements, and analyzing electromagnetic interactions and form factors.

Contribution

It introduces a framework for particle phenomenology on noncommutative spacetime and derives experimental bounds on the noncommutativity scale from existing measurements.

Findings

Upper bound on noncommutativity length scale from $K^{0}-\bar{K}^{0}$ system: $10^{-32}$ m

Constraint on noncommutativity from muon $g-2$ difference: $10^{-20}$ m

Altered electromagnetic form factors affecting charge and magnetization distributions

Abstract

We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is constrained from the CPT violation measurements in $K^{0}-\bar{K}^{0}$ system and $g-2$ difference of $\mu^+ - \mu^-$. The $K^{0}-\bar{K}^{0}$ system provides an upper bound on the length scale of spacetime noncommutativity of the order of $10^{-32} \textrm{m}$, corresponding to a lower energy bound $E$ of the order of $E \gtrsim 10^{16}\textrm{GeV}$. The $g-2$ difference of $\mu^+ - \mu^-$ constrains the noncommutativity length scale to be of the order of $10^{-20} \textrm{m}$, corresponding to a lower energy bound $E$ of the order of $E \gtrsim 10^{3}\textrm{GeV}$. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level in the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.