Learning from Dispersive Effects in the Nucleon Polarisabilities

Static nucleon polarisabilities gauge the stiffness of the nucleon against an external electro-magnetic field, parameterising the part of the real Compton amplitude at zero energy which is not explained by the pole terms, i.e. by the successive interactions of two photons with a point-like nucleon of anomalous magnetic moment κ. Dynamical nucleon polarisabilities are the energy dependent generalisation to real Compton scattering and thus provide more information about the low energy effective degrees of freedom inside the nucleon. Here, I sketch their definition and interpretation in terms of the low energy degrees of freedom, referring to 1,2 for particulars and references. Investigating in more detail the nucleon polarisabilities at non-zero photon energy, one first subtracts the “nucleon pole” effects from the real Compton amplitude T , writing T̄ (ω, z) = Ā1(ω, z) (~ǫ ′∗ ·~ǫ)+ Ā2(ω, z) (