Electromagnetic Self-Energy Contribution toMp−Mnand the Isovector Nucleon Magnetic Polarizability

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 δM γ p−n = 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: βp−n = −0.87(85) × 10 −4 fm 3 .PACS numbers: 13.40. Dk, 13.40.Ks, 13.60.Fz, 14.20.Dh Given only electrostatic forces, one would predict that the proton is more massive than the neutron but the opposite actually occurs [1-3]:Before we knew of quarks and gluons there were many attempts to explain this contradiction, see Ref.[4] for a review. We now know there are two sources of isospin breaking in the standard model, the masses of the up and down quarks as well as the electromagnetic interactions between quarks governed by the charge operator. The effects of the mass difference between down and up quarks are larger and of the opposite sign than those of electromagnetic effects, see the reviews [5][6][7]. The net result of the quark mass difference and electromagnetic effects is well known, Eq. (1), but our ability to disentangle the contributions from these two sources remains poorly constrained. In contrast, lattice QCD calculations have matured significantly. There are now calculations performed with the light quark masses at or near their physical values [8][9][10][11][12], reproducing the ground state hadron spectrum within a few percent. These advances have allowed for calculations to begin including explicit isospin breaking effects from both the quark masses [13][14][15][16][17] and electromagnetism [15,[18][19][20][21]. While the lattice calculations of m d − m u effects are robust, the contributions from electromagnetism are less mature and suffer from larger systematics, due in large part to the disparity between the photon mass and a typical hadronic scale. Improved knowledge of m d − m u and its effects in nucleons will enhance the ability to use effective field theory to compute a variety of isospin-violating (charge asymmetric) effects in nuclear reactions [7,[22][23][24][25][26][27]].An application [28] of the Cottingham sum rule [29], which relates the electromagnetic self-energy of the nucleon to measured elastic and inelastic cross sections, gives the result δM γ p−n = 0.76 ± 0.30 MeV. Given the high present interest in the precise value of δM γ p−n and its many possible implications, it is worthwhile to revisit this result. Many high quality electron scattering experiments have been performed since 1975 and there have also been theoretical advances. The central aim of this work is to provide a modern, robust evaluation of δM γ p−n . We wil...

Isospin Breaking in the Nucleon Mass and the Sensitivity ofβDecays to New Physics

“…On one hand, the phenomenological determination of the QED contributions to δM N ¼ M n − M p using the Cottingham's sum rule [37,38] has been recently updated finding δM QED N ¼ −1.30ð3Þð47Þ MeV [17], which combined with the experimental value [30] implies the δM QCD N value shown in Table I. Moreover, the error is expected to be reduced in the future through measurements of the isovector magnetic polarizability of the nucleon [17,39,40].…”

“…The estimate of systematic errors is a very complicated issue and future lattice studies of isospin breaking effects are needed to confirm these first calculations. Similar caveats apply to the recent numerical evaluation of the Cottingham formula [17]. Nonetheless, the average reflects the good agreement between current determinations and we will take it as a reference number whose robustness should improve in the future.…”

“…Moreover, the error is expected to be reduced in the future through measurements of the isovector magnetic polarizability of the nucleon [17,39,40].…”

“…Actually, the isospin corrections to the hadron masses, and in particular to the nucleon mass, are starting to receive much attention. While phenomenological determinations are being revised [17], different lattice collaborations have embarked on the ab initio computation of these effects in pure QCD [18][19][20] or even including QED [21][22][23][24][25][26][27].…”

High-accuracy analysis of Compton scattering in chiral effective field theory: Status and future

“…Polarisabilities also enter as one of the bigger sources of uncertainties in theoretical determinations of the proton-neutron mass difference (see e.g. most recently [8]), and of the two-photon-exchange contribution to the Lamb shift in muonic hydrogen (see e.g. most recently [9]).…”