Neutron-Proton Mass Difference by Dispersion Theory

Abstract

versal by about 16°C, in contrast to the Te-Se alloy mentioned above, for which the reversal temperature was apparently lowered about 5°C. The impurity concentration of the two samples of Fig. 1, as determined from the Hall coefficient R at 77 °K and the approximate formula R = l/pe (/> = carrier density, e=1.6xl0~1 9 coulomb), is 7.2 xlO 14 carriers/cm 3 for sample 1 and 2.2xlO 15 carriers/cm 3 for sample 2. In addition, the upper reversal temperature for a third sample with p = 7.2 xlO 18 was found to occur at 498°K and this demonstrates the shift of the upper reversal temperature with impurity concentration. Long 13 has computed that the hydrostatic pressure used in this experiment causes the energy gap to decrease by 0.032 ev, and this in turn is responsible both for the decrease in the lower reversal temperature which he reported and for the decrease in Hall coefficient with pressure in the region below the "crossover" point at about 217°C on both pairs of curves in the present experiment. However, the cause of the upper reversal shift still remains unknown.An attempt to explain the neutron-proton mass difference by introducing in the divergent inte-grals of the second-order electromagnetic selfmass a fundamental length has been made by Feynman and Speisman. 1 They show that the proton can in fact turn out lighter than the neutron, in spite of its electrostatic energy, if the anomalous moments of the nucleons are introduced in the interaction and the integrals are cut off at sufficiently high energy. Since then it has been realized that the electromagnetic selfmasses of the nucleons might be finite even in a microscopic causal theory if the electromagnetic form factors vanish sufficiently rapidly at high momenta, as indicated by certain consistency requirements. 2 With this assumption Wick and Sorensen 3 have attempted a calculation of the nucleon mass difference on the basis of a formalism developed by Low. 4 Their calculation yields a negative result, giving a proton heavier than the neutron. No direct comparison can, however, be made between the two calculations. In FS the relativistic Born approximation to the self-energy is used, while WS are essentially led to a Born approximation formula with form factors, in which only positive-energy states are kept.For this reason we have re-examined the problem by using as a basis the expression of the Compton scattering amplitude derived with a dispersion relation approach. The single-nucleon contribution is in our case simply the FS expression with their arbitrary cutoffs replaced by the electromagnetic form factors of the nucleons. We find that the mass difference that one obtains by extrapolating at high momenta the experimental form factors is wrong in sign and in magnitude. The reason is that the radii of the experimental distributions correspond to cutoffs considerably lower than those used in FS. We also find that the correct mass difference can be obtained, from the single-nucleon contribution and without contradicting the Stanford data, with a rather pat...

Massive Photons: An Infrared Regularization Scheme for LatticeQCD+QED

“…One impressive calculation includes both sources of isospin breaking simultaneously and yields, among other quantities, a postdiction for the nucleon isospin splitting with ∼ 5σ statistical significance [8]. There exists an alternate means for determining the electromagnetic self-energy of the nucleon, from the Cottingham formula [17][18][19][20], which makes use of experimental cross sections as input to dispersion integrals. However, the uncertainty attained with this method [21][22][23] is not yet competitive with the LQCD calculations.…”

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

“…Performing a Wick rotation of the integration contour to imaginary photon energy, the nucleon self-energy can be related to the structure functions arising from the scattering of space-like photons through dispersion theory, giving rise to what is known as Cottingham's formula (the Cottingham sum rule) [29,31]. In principle, this allows the integral in Eq.…”

Mass Difference between the Sigma Hyperons

“…* Case 1. Same structure for ~+, ~and ~o The structure will be described by the form factors (8) and (9) with the same )0 for all the three~. Therefore the charge distributions of ~and ~+ are perfectly symmetrical.…”

“…The corresponding form factor could be taken as (8) and (9) Another possibility would be to suppose that 1,'0 has not the same radius and external distribution than I+ and I-. Taking an exponential form factor, as an example, we obtain the following Table: Table II Our problem now is to discuss the influence of the terms like H s, H4 and Ha which appear in the interaction (2) upon the hyperon mass differences iJ.M_+ and aM_o• These terms mean the consideration of electromagnetic self-energy correc- where iJM" is the mass difference between ~and ~o.…”

“…Recently Hiida-Sawamura 7 ) and Cini et al 8 ) tried to explain the mass difference between neutron and proton by the use of exponential form factors, for the nucleons, obtained from Stanford experiments, and they got a negative result. Nevertheless, by making a critical analysis of the results of Stanford experiments, Katayama, Taketani and co-workers9) (this paper is hereafter denoted by [AJ) have shown that it is possible to obtain a correct neutron-proton mass difference, by a convenient modification of the form factors in the region of high energies, where experimental data are not yet available.…”