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 $\gamma^{(p)}_\pi = -36.4 \pm 1.5$ $(-36.6)$, $\gamma^{(n)}_\pi = 58.6 \pm 4.0$ $(58.3)$, $(\gamma^{(p)}_0= -0.58\pm 0.20)$, $(\gamma^{(n)}_0 = +0.38\pm 0.22)$ 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

Baryons as relativistic three-quark bound states

“…There has been much recent interest in a precision determination of the nucleon's polarisabilities, which is reflected in a number of reviews on the topic [441,[638][639][640][641][642][643]. The electric polarisability α and magnetic polarisability β tell us how the nucleon responds to an external electromagnetic field, with current PDG values α = 11.2(4) × 10 −4 fm 3 and β = 2.5(4) × 10 −4 fm 3 for the proton [9].…”

“…In principle both relations hold for arbitrary η, which defines the generalized polarisabilities α(η) and β(η) and the generalized GDH integral. For extensive discussions of the various sum rules derived from CS we refer to the reviews [642,643].…”

Polarizability of the nucleon

“…

The status of the experimental and theoretical investigations on the polarizabilities of the nucleon is presented. This includes a confirmation of the validitiy of the previously introduced recommended values of the polarizabilities [1,2]. It is shown that the only meaningful approach to a prediction of the polarizabilities is obtained from the nonsubtracted dispersion theory, where the appropriate degrees of freedom taken from other precise experimental data are taken into account.

…”

“…In retrospect this is not a surprise, because constituent quarks generate their mass mainly through interaction with the QCD vacuum via the exchange of a σ meson. This mechanism is predicted by the linear σ model on the quark level (QLLσM) [2] which also predicts the mass of the σ meson to be m σ =666 MeV. The σ meson has the capability of interacting with two photons being in parallel planes of linear polarization.…”

Mass generation via the Higgs boson and the quark condensate of the QCD vacuum

“…Therefore, it is possible to use the polarizabilities as a tool to test the predicted mass and structure of the σ meson. This is summarized in the following equations [14] |σ (41) correspond to the s-channel and have been calculated from high-precision meson photoproduction amplitudes [14].…”