Electromagnetic Self-Energy Contribution to ${M}_{p}\ensuremath{-}{M}_{n}$ and the Isovector Nucleon Magnetic Polarizability

Electromagnetic Self-Energy Contribution to $M_{p} - M_{n}$ and the Isovector Nucleon Magnetic Polarizability

André Walker-Loud, Carl E. Carlson, and Gerald A. Miller

Phys. Rev. Lett. 108, 232301 – Published 7 June 2012

Abstract

We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham’s formula is corrected, and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find $δ M_{p − n}^{γ} = 1.30 (03) (47) MeV$ . The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with additional input from lattice QCD to constrain this polarizability as: $β_{p - n} = - 0.87 (85) \times 10^{- 4} {fm}^{3}$ .

Received 7 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.232301

Authors & Affiliations

André Walker-Loud^1,2, Carl E. Carlson³, and Gerald A. Miller^1,4

¹Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
²Department of Physics, University of California, Berkeley, California 94720, USA
³Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA
⁴Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA