Cottingham formula and nucleon polarisabilities

Abstract

The difference between the electromagnetic selfenergies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections -provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment.

Two-photon exchange correction to muon–proton elastic scattering at low momentum transfer

“…Following the idea of Refs. [17,18], the subtraction function can be obtained from an unsubtracted dispersion relation for the amplitude…”

Nucleon spin-averaged forward virtual Compton tensor at large Q2

“…These contributions dominate the uncertainty of the proton charge radius measured in muonic hydrogen [1] and have been the subject of recent intense scrutiny and controversy [2,3,4,5]. The difference between spin-averaged proton and neutron forward Compton amplitudes determines the electromagnetic contribution to the protonneutron mass splitting, also the subject of recent controversy [6,7,8,9,10]. The tensor representation of the spin-averaged Compton amplitude (cf.…”

Nucleon in a periodic magnetic field

“…[4]). The elastic part is singular at q 2 → 0, whereas the inelastic part is regular and is related to the nucleon magnetic polarizability at q 2 = 0.…”

“…[3,4]. If the forward scattering amplitude does not contain any so-called fixed pole (this issue is related to the so-called Reggeon dominance hypothesis), then S 1 (q 2 ) for all q 2 < 0 is uniquely 1 Note that, recently, a substantial progress has been achieved in the direct evaluation of this difference on the lattice [1,2].…”