Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen

Abstract

While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic structure of protons that could be extracted from the experimental values of the ground state hyperfine splitting in hydrogen and muonic hydrogen.Using recent theoretical results on the proton polarizability effects and the experimental hydrogen hyperfine splitting we obtain for the Zemach radius of the proton the value 1.040(16) fm. We compare it to the various theoretical estimates the uncertainty of which is shown to be larger that 0.016 fm. This point of view gives quite convincing arguments in support of projects to measure the hyperfine splitting of muonic hydrogen.

Nucleon deformation and atomic spectroscopy

“…Compared to other corrections in the hydrogen hyperfine structure [20] this seems to be a big effect. We emphasize that this deformation contribution is already included in the experimental proton charge radius [21].…”

Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

“…The results are in reasonable agreement between each other and with the extractions from atomic spectroscopy of Refs. [2,25,[58][59][60] as well as previous evaluations of Eqs. (4,10) [39,61,62].…”

“…The new highly precise insights on the proton electromagnetic structure will be obtained by the forthcoming measurements of 1S hyperfine splitting (HFS) in muonic hydrogen with an unprecedented ppm precision by the CREMA [24] and FAMU [25,26] Collaborations as well as at J-PARC [27]. In these experiments, the expected accuracy level is two orders of magnitude smaller than the theoretical knowledge of the TPE correction with 213 ppm uncertainty in the dispersive estimate [28] and 109 ppm in the effective field theory approach [29].…”

Non-spherical proton shape and hydrogen hyperfine splittingThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

“…The most important corrections to the pointlike dipole-dipole interaction energy in Eq. (1) are due to (i) QED, (ii) nucleon recoil, (iii) finite proton size, and (iv) proton polarization effects [28]. First, there is the anomalous magnetic moment of the electron, which is mainly caused by the QED vertex correction.…”