Eur. Phys. J. C (2014) 74: 2852
https://doi.org/10.1140/epjc/s10052-014-2852-0

Regular Article - Theoretical Physics

Chiral perturbation theory of muonic-hydrogen Lamb shift: polarizability contribution

¹ Cluster of Excellence PRISMA Institut für Kernphysik, Johannes Gutenberg-Universität, Mainz, 55099, Germany
² Theoretical Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK
³ Institute for Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya 25, 117218 , Moscow, Russia

^* e-mail: alarcon@kph.uni-mainz.de

Received: 6 December 2013
Accepted: 9 April 2014
Published online: 29 April 2014

Abstract

The proton polarizability effect in the muonic-hydrogen Lamb shift comes out as a prediction of baryon chiral perturbation theory at leading order and our calculation yields ΔE^(pol)(2P-2S) = 8_-1⁺³ µeV. This result is consistent with most of evaluations based on dispersive sum rules, but it is about a factor of 2 smaller than the recent result obtained in heavy-baryon chiral perturbation theory. We also find that the effect of Δ(1232)-resonance excitation on the Lamb shift is suppressed, as is the entire contribution of the magnetic polarizability; the electric polarizability dominates. Our results reaffirm the point of view that the proton structure effects, beyond the charge radius, are too small to resolve the ‘proton radius puzzle’.