Theoretical Aspects of the Polarizability of the Nucleon

Abstract

Two aspects of the nucleon electromagnetic polarizabilities, αN and βN, are discussed. The first one is the interrelation between static and Compton polarizabilities. Relativistically consistent treatment of the polarization effects based on effective Lagrangians results in the conclusion that the Compton polarizabilities, rather than the static ones, drive the energy shift of the nucleon in external fields. The cluster substructure of the static polarizabilities is shown to be crucial for consistent calculations of the polarizabilities. The second aspect concerns the dominant role of pion degrees of freedom in αN as seen through dispersion relations, chiral perturbation theory, and constituent models. The reported calculations of αN within soliton models are shown to be inconsistent with gauge invariance. The difficulties in explaining the observed large diamagnetic component of βN are emphasized.

Quantum corrections to baryon properties in chiral soliton models

“…A first hint that not all is well with the statement voiced in [75] [76] may be derived from the fact that the tree expression for the electric polarizability (3.70) evaluated in the chiral limit (where an analytical treatment akin to the case of the σ-term is possible) agrees with the result obtained in HBChP T [55] [56]:…”

“…Thus, in contrast to the common belief, neither nonminimal couplings nor the explicit inclusion of vector mesons is able to cure the problem with the much too large electric polarizabilities obtained in tree approximation from soliton models. Such a conclusion is of course valid only if the way to calculate polarizabilities as sketched above is correct, which has recently been doubted [75] [76]. The explicit statement was that the terms quadratic in the external electric or magnetic fields (seagull terms) do not contribute at all.…”

Electric polarizability of hadrons

“…In this data, there are four experimental results, [4,5,6,7]; but [7] incorporates [4]. L'vov [8] corrected the earlier values by adding 0.6 × 10 −4 fm 3 to their results. The experiments measure α − β and the results are found using a sum rule that gives α + β.…”

Virtual Compton Scattering—Generalized Polarizabilities of Nucleons and Pions

“…The Taylor series coefficients are expressed in terms of the charge, mass, and magnetic moment of the target. Terms of second order in the frequency, which are not determined by this LET, can be parametrized in terms of two new structure constants, the electric and magnetic polarizabilities α and β (see, e.g., [3,4]). …”