This review gives an update on virtual Compton scattering (VCS) off the nucleon, γ * N → N γ, in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model predictions for these observables. We present the GP extraction methods that are used in the experiments: the approach based on the low-energy theorem for VCS and the formalism of Dispersion Relations. We then review the experimental results, with a focus on the progress brought by recent experimental data on proton GPs, and we conclude by some perspectives in the field of VCS at low energy.
Theoretical frameworkThis section reviews the formalism related to the nucleon GPs. We first outline some basic properties of polarizabilities and their generalization to finite Q 2 (Sect. 3.1). Then the main ingredients of the low-energy theorem in VCS are summarized in Sect. 3.2. A synthetic overview of model predictions for GPs is given in Sect. 3.3, and the DR formalism is presented in more details in Sect. 3.4. We then move closer to experimental aspects with Sects. 3.5 to 3.7.
From real to virtual Compton scatteringThe polarizabilities of a composite object are fundamental characteristics of the system, just as its mass or shape. Among all the known properties of the nucleon, polarizabilities have the unique status of characterizing the nucleon dynamical response to an external electromagnetic (EM) field, describing how easy the charge and magnetization distributions inside the nucleon are distorted by the EM field. Real Compton scattering (RCS) experiments, performed since more than 50 years, have accumulated an 1 Note that this is up to a rotation of the leptonic plane by the azimuthal angle ϕ ′ e lab of the scattered electron. If specified, ϕ ′ e lab is then a sixth independent variable. 2 Other sets of variables are sometimes used, such as (k lab , k ′ lab , θ ′ e lab ) or (Q 2 , √ s, ǫ) for the leptonic vertex, and t instead of cos θ cm . 3 We also findQ = Q2 , andq 0cm defined in the Appendix. 4 This is for instance the case for all experimental values of Q 2 in Sect. 4. 2 qcm √ Q 2 q 0