Structure of the $\sigma$-meson and diamagnetism of the nucleon

Abstract

The structure of the $\sigma$ meson and the diamagnetism of the nucleon are shown to be topics which are closely related to each other. Arguments are found that the $\sigma$ meson couples to two photons via its non-strange $q\bar{q}$ structure component. This ansatz leads to a quantitative explanation of the $t$-channel component of the difference of electromagnetic polarizabilities, (\alpha-\beta)^t$,containingthediamagnetismofthenucleon.Thepredictionis$(\alpha-\beta)^t_{p,n}=(5\alpha_e g_{\pi MM})/(6\pi^2 m^2_\sigma f_\pi)=15.3$inunitsof$10^{-4}{\rm fm}^3$tobecomparedwiththeexperimentalvalue$(\alpha-\beta)^t_p=15.1\pm 1.3$fortheprotonand$(\alpha-\beta)^t_n=14.8\pm 2.7$fortheneutron.Theequivalentapproachtoexploitthe$\pi\pi$structurecomponentofthe$\sigma$mesonviatheBEFTsumruleleadsto$(\alpha-\beta)^t_{p,n}=14\pm 2$, what also is in agreement with the experimental results.

Comments: Contribution made by Martin Schumacher to the International Workshop on the Physics of Excited Baryons, 12 - 15 Oct. 2005, Tallahasse, Florida USA