# Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space

## TL;DR

This paper uses recent charge-to-mass ratio measurements of protons and anti-protons to set strong constraints on the momentum noncommutativity parameters in noncommutative phase space, highlighting the potential for future experiments to improve these bounds.

## Contribution

It provides the first stringent experimental bounds on momentum noncommutativity using charge-to-mass ratio data.

## Key findings

- Weak constraints on coordinate noncommutativity.
- Strong constraints on momentum noncommutativity, $\sqrt{\xi} \lesssim ext{1 μeV}$.
- Future experiments could further tighten these bounds.

## Abstract

Based on recent measurements on the charge-to-mass ratios of proton and anti-proton, we study constraints on the parameters of noncommutative phase space. We find that while the limit on the parameter of coordinate noncommutativity is weak, it is very strong on the parameter of momentum noncommutativity, $\sqrt{\xi} \lesssim {\rm 1\mu eV}$. Therefore, the charge-to-mass ratio experiment has a strong sensitivity on the momentum noncommutativity, and enhancement of future experimental achievement can further pin down the momentum noncommutativity.