Virtual Compton scattering and nucleon generalized polarizabilities

Abstract

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

Soft-photon radiative corrections to the $e^- p \to e^- p l^- l^+$ process

“…Therefore, although the cross section by itself has a relatively high sensitivity on the low-energy constant b 3,0 , for an experimental extraction of b 3,0 the inclusion of the radiative corrections is imperative. A comparable importance of the radiative corrections was also found in the extraction of the proton generalized polarizabilities from the cross sections of the VCS process e − p → e − pγ [7,37].…”

“…where β M 2 is the magnetic quadrupole polarizability determined from real Compton scattering [47], and β M 1 (0) is the slope at Q 2 = 0 of the generalized magnetic dipole polarizability which is accessed through virtual Compton scattering, see Ref. [7] for a recent review. While the terms of O(k 0 ) and O(k 2 ) in the low-energy structure of the amplitude B1 at ν = 0 are empirically constrained from real or virtual Compton scattering, the low-energy constant b 3,0 is not determined empirically so far because the tensor structure T µν 3 in Eq.…”

“…[1][2][3][4] for reviews. The virtual Compton scattering (VCS) process, γ * p → γp with initial space-like virtual photon, which can be accessed as a subprocess of the e − p → e − pγ reaction, has also been studied extensively over the past three decades to access the generalized nucleon polarizabilities [1,[5][6][7]. These structure quantities allow to obtain, through a Fourier transform, a spatial representation of the deformation of the charge and magnetization distributions of the nucleon under the influence of an external static electromagnetic field [8].…”

Low-energy doubly virtual Compton scattering from dilepton electroproduction on a nucleon

“…where β M2 is the magnetic quadrupole polarizability determined from real Compton scattering [27], and β M1 (0) is the slope at Q 2 = 0 of the generalized magnetic dipole polarizability, which is accessed through virtual Compton scattering, see Ref. [28] for a recent review. The low-energy constant b 3,0 is not determined empirically so far because the tensor structure T μν 3 decouples when either the initial or final photon is real.…”

Nucleon Polarizabilities and Compton Scattering as Playground for Chiral Perturbation Theory

“…A recent theoretical discussion of nucleon polarizabilities in χPT and beyond can be found in [25]. Other commendable reviews include Guichon and Vanderhaeghen [26] or Fonvieille et al [27] (VCS and generalized polarizabilities), Drechsel et al [28] or Pasquini and Vanderhaeghen [29] (dispersion relations for CS), Pascalutsa et al [30] (∆(1232) resonance), Phillips [31] (neutron polarizabilities), Griesshammer et al [32] (χEFT and RCS experiments), Holstein and Scherer [33] (pion, kaon, nucleon polarizabilities), Geng [34] (BχPT), Pascalutsa [9] (dispersion relations), and Deur et al [35] (nucleon spin structure). A textbook introduction to χPT can be found in [36].…”