Comments on the Hydrogen Atom Spectrum in the Noncommutative Space

TL;DR

This paper clarifies the debate on whether noncommutative space induces corrections to the hydrogen atom spectrum, demonstrating that proton structure leads to such effects and confirming previous bounds on noncommutativity.

Contribution

It provides a general argument linking proton structure to spectrum corrections and validates earlier bounds on noncommutativity parameters using a simple quark model.

Findings

Proton structure causes noncommutative corrections to hydrogen spectrum.

The bound on noncommutativity parameter remains valid.

Results agree with previous electron-in-electric-field calculations.

Abstract

There has been disagreement in the literature on whether the hydrogen atom spectrum receives any tree-level correction due to noncommutativity. Here we shall clarify the issue and show that indeed a general argument on the structure of proton as a nonelementary particle leads to the appearance of such corrections. As a showcase, we evaluate the corrections in a simple nonrelativistic quark model with a result in agreement with the previous one we had obtained by considering the electron moving in the external electric field of proton. Thus the previously obtained bound on the noncommutativity parameter, $\theta < (10^4 GeV)^{-2}$, using the Lamb shift data, remains valid.