Dispersion theory of nucleon Compton scattering and polarizabilities

Abstract

A status report on the topic Compton scattering and polarizabilities is presented with emphasis on the scalar t-channel as entering into dispersion theory. Precise values for the polarizabilities are obtained leading to ${\alpha }_p=12.0\pm 0.6$ $(12.0)$, ${\beta }_p=1.9\mp 0.6$ $(1.9)$, ${\alpha }_n=12.5\pm 1.7$ $(13.4)$, ${\beta }_n=2.7\mp 1.8$ $(1.8)$ in units of $10^{-4}$ fm${}^3$ and ${\gamma }_{\pi }^{(p)}=-36.4\pm 1.5$ $(-36.6)$, ${\gamma }_{\pi }^{(n)}=58.6\pm 4.0$ $(58.3)$, $({\gamma }_0^{(p)}=-0.58\pm 0.20)$, $({\gamma }_0^{(n)}=+0.38\pm 0.22)$ in units of $10^{-4}$ fm${}^4$, for the proton (p) and neutron (n), respectively. The data given with an error are {\it recommended} experimental values with updates compared to [1] where necessary, the data in parentheses are predicted values. These predicted values are not contained in [1], but are the result of a newly developed analysis which is the main topic of the present paper. The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the $\sigma$ meson as part of the constituent-quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the $\sigma$ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the $\sigma$ meson of $m_{\sigma }=600\pm 70$ MeV. From the experimental ${\alpha }_p$ and predicted differences $({\alpha }_n-{\alpha }_p)$ neutron polarizabilities in the range ${\alpha }_n=12.0-13.4$ are predicted, where the uncertainties are related to the $f_0(980)$ and $a_0(980)$ scalar mesons.

References in corpus (5)

• Unitary Isobar Model - MAID2007
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Higher order forward spin polarizability
• Constituent Quark Masses and the Electroweak Standard Model
• Comment on "Two-photon decay of the sigma meson"

Cited by in corpus (10)

• Baryons as relativistic three-quark bound states
• Hadron Polarizabilities
• The Quark-Level Linear σ Model
• Virtual Compton Scattering measurements in the nucleon resonance region
• Nambu's Nobel Prize, the $\sigma$ meson and the mass of visible matter
• Mass generation via the Higgs boson and the quark condensate of the QCD vacuum
• Towards a microscopic understanding of nucleon polarizabilities
• Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory
• Mass and structure of the nucleon: Gluon trace anomaly versus spontaneous symmetry breaking
• A Tale Of Two Amplitudes In High Energy Physics