# Electromagnetic polarizabilities and the excited states of the nucleon

## TL;DR

This paper analyzes the electromagnetic polarizabilities of the nucleon, decomposing them into resonant, nonresonant, and t-channel contributions, and confirms the role of two-photon couplings to the sigma meson in these properties.

## Contribution

It provides a detailed breakdown of nucleon polarizabilities and links dominant contributions to two-photon couplings with the sigma meson, supporting theoretical predictions.

## Key findings

- Polarizabilities are mainly composed of nonresonant, t-channel, and resonant contributions.
- Deviations from experimental data are due to multiple resonant and nonresonant processes with cancellations.
- Dominant contributions can be modeled via two-photon couplings to the sigma meson with specific mass and width.

## Abstract

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant $\alpha_p(E_{0+})=+3.2$, $\alpha_n(E_{0+})=+4.1$,the $t$-channel $\alpha^t_{p,n}=-\beta^t_{p,n}=+7.6$ and the resonant $\beta_{p,n}(P_{33}(1232))=+8.3$ contributions (in units of $10^{-4}$fm$^3$. The remaining deviations from the experimental data $\Delta\alpha_p=1.2\pm 0.6$, $\Delta\beta_p=1.2\mp 0.6$, \Delta\alpha_n=0.8\pm 1.7$ and $\Delta\beta_n=2.0\mp 1.8$ are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon couplings to the $\sigma$-meson having the predicted mass $m_\sigma=666$ MeV and two-photon width $\Gamma_{\gamma\gamma}=2.6$ keV.