Effects of Non-Commutativity on Light-Hydrogen-Like Atoms and Proton Radius

Abstract

We study the corrections induced by the theory of non-commutativity, in both space-space and space-time versions, on the spectrum of hydrogen-like atoms. For this, we use the relativistic theory of two-particle systems to take into account the effects of the reduced mass, and we use perturbation methods to study the effects of non-commutativity.We apply our study to the muon hydrogen with the aim to solve the puzzle of proton radius [R. Pohl et al., Nature 466, 213 (2010) and A. Antognini et al., Science 339, 417 (2013)]. The shifts in the spectrum are found more noticeable in muon H (muH) than in electron H (eH) because the corrections depend on the mass to the third power; This explains the discrepancy between muH and eH results. In space-space non-commutativity, the parameter required to resolve the puzzle Theta(ss) (0.35GeV)-2, exceeds the limit obtained for this parameter from various studies on eH Lamb shift. For space-time non-commutativity, the value Theta(st) (14.3GeV)-2 has been obtained and it is in agreement with the limit determined by Lamb shift spectroscopy in eH. We have also found that this value fills the gap between theory and experiment in the case of muD and improves the agreement between theoretical and experimental values in the case of hydrogen-deuterium isotope shift.

17 Pages, No Figures. To appear in International Journal of Modern Physics A

References in corpus (15)

• The Spin Structure of the Nucleon
• Muonic hydrogen and the proton radius puzzle
• Model independent extraction of the proton charge radius from electron scattering
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Proton size anomaly
• Model independent extraction of the proton magnetic radius from electron scattering
• Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering
• On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Third Zemach Moment of the Proton
• Particle-like solutions to classical noncommutative gauge theory
• Why three-body physics do not solve the proton radius puzzle
• The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
• The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
• Noncommutative Corrections to the Robertson-Walker metric

Cited by in corpus (4)

• Model independent extraction of the proton magnetic radius from electron scattering
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• $\mathcal{O}(\theta )$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model
• Ground state hyperfine structure in muonic lithium ions