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

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 $1Hz\ll 3kHz$ in the Lamb shift of Hydrogen atom leads to an NC correction about $10MHz$ in the Lorentz violating noncommutative QED and about $400GHz$ in the Lorentz conserving noncommutative QED.

Comments: 15 pages, to appear in EPJC