EFFECTS OF NONCOMMUTATIVITY ON LIGHT HYDROGEN-LIKE ATOMS AND PROTON RADIUS

Abstract

We study the corrections induced by the theory of noncommutativity, 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 noncommutativity. We apply our study to the muon hydrogen with the aim to solve the puzzle of proton radius [R. Pohl et al., Nature466, 213 (2010) and A. Antognini et al., Science339, 417 (2013)]. The shifts in the spectrum are found more noticeable in muon H(μH) than in electron H(eH) because the corrections depend on the mass to the third power. This explains the discrepancy between μH and eH results. In space–space noncommutativity, the parameter required to resolve the puzzle θ ss ≈(0.35 GeV )-2, exceeds the limit obtained for this parameter from various studies on eH Lamb shift. For space–time noncommutativity, the value θ st ≈(14.3 GeV )-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 μD and improves the agreement between theoretical and experimental values in the case of hydrogen–deuterium isotope shift.