Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution

Abstract

We quantify a limitation in the usual accounting of the finite-size effects, where the leading [(Zα) 4 ] and subleading [(Zα) 5 ] contributions to the Lamb shift are given by the mean-square radius and the third Zemach moment of the charge distribution. In the presence of any non-smooth behaviour of the nuclear form factor at scales comparable to the inverse Bohr radius, the expansion of the Lamb shift in the moments breaks down. This is relevant for some of the explanations of the "proton size puzzle". We find, for instance, that the de Rújula toy model of the proton form factor does not resolve the puzzle as claimed, despite the large value of the third Zemach moment. Without relying on the radii expansion, we show how tiny, milli-percent (pcm) changes in the proton electric form factor at a MeV scale would be able to explain the puzzle. It shows that one needs to know all the soft contributions to proton electric form factor to pcm accuracy for a precision extraction of the proton charge radius from atomic Lamb shifts.

Triton charge radius to next-to-next-to-leading order in pionless effective field theory

“…Both experimental [50][51][52] and theoretical [53] efforts are being carried out to reexamine the electronic hydrogen spectroscopy results. Other possible theoretical explanations include using new muonic forces [54][55][56] and new proton structures [57][58][59][60][61][62]. Using the value for the proton charge radius from muonic hydrogen gives a triton point charge radius of 1.6178 ± 0.040 fm.…”

Nucleon polarizabilities: From Compton scattering to hydrogen atom

“…2, in order to make a maximal impact on the puzzle, the fluctuation G E must be located at the extremi of w(Q) in Eq. (19a) 1 around either the eH or µH inverse Bohr radius. Here we shall only consider the latter case and set one of the position parameters to the MeV scale:…”

“…The dashed red curve shows the modified FF from Ref. [1]. The dotted blue curve is the modified FF of this work.…”

“…The formalism developed in Ref. [1] was illustrated by a modification of the proton electric form factor (FF), G E , which could reconcile the discrepancy in the various proton radius extractions. As is correctly pointed out in the Comment [2], this modification is inconsistent with the analyticity constraints.…”

Chiral perturbation theory of hyperfine splitting in muonic hydrogen

“…We investigate both the finite-size and the polarizability effects on the HFS. In a recent paper [7], we study the applicability of the expansion of finite-size corrections to the Lamb shift in moments of the charge distribution. We now present an extension of this work to the HFS.…”