Deformed dispersion relation constraint with hydrogen atom 1S-2S transition *

Abstract

Abstract We use the latest results of the ultra-high accuracy 1S-2S transition experiments in the hydrogen atom to constrain the forms of the deformed dispersion relation in the non-relativistic limit. For the leading correction of the non-relativistic limit, the experiment sets a limit at an order of magnitude for the desired Planck-scale level, thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments. For the next-to-leading term, the bound is two orders of magnitude away from the Planck scale, however it still amounts to the best limit, in contrast to the previously obtained bound in the non-relativistic limit from the cold-atom-recoil experiments.