Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time

TL;DR

This paper investigates how noncommutative quantum electrodynamics affects hydrogen and muonic hydrogen spectra, revealing different correction ratios depending on Lorentz symmetry violation, with implications for experimental Lamb shift measurements.

Contribution

It compares noncommutative effects on hydrogen spectra in Lorentz violating and conserving frameworks, highlighting distinct correction ratios and potential experimental signatures.

Findings

Lorentz violating NCQED correction ratio is (m_mu/m_e)^3

Lorentz conserving NCQED correction ratio is (m_mu/m_e)^5

Estimated NC corrections are 10 MHz and 400 GHz for different models

Abstract

Comparing electronic Hydrogen with muonic Hydrogen shows that the discrepancy in measurement of the Lamb shift in the both systems are relatively of order of $(\frac{m_\mu}{m_e})^{4-5}$. We explore the spectrum of Hydrogen atom in noncommutative $QED$ to compare the noncommutative effects on the both bound states. We show that in the Lorentz violating noncommutative QED the ratio of NC-corrections is $(\frac{m_\mu}{m_e})^3$ while in the Lorentz conserving NCQED is $(\frac{m_\mu}{m_e})^5$. An uncertainty about $1 \,Hz\ll 3\,kHz$ in the Lamb shift of Hydrogen atom leads to an NC correction about $10 \,MHz$ in the Lorentz violating noncommutative QED and about $400 \,GHz$ in the Lorentz conserving noncommutative QED.