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We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $epto epgamma$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon.
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We perform an expansion of the virtual Compton scattering amplitude for low energies and low momenta and show that this expansion covers the transition from the regime to be investigated in the scheduled photon electroproduction experiments to the real Compton scattering regime. We discuss the relation of the generalized polarizabilities of virtual Compton scattering to the polarizabilities of real Compton scattering.
The Virtual Compton scattering (VCS) process at low energies explores the electromagnetic structure of the proton in terms of generalized polarizabilities (GPs). In the one-photon exchange approximation, VCS can be accessed with exclusive photon production reactions with electron or positron beams. The extraction of the GPs from VCS with electron beam has seen substantial progress over the past two decades. Nonetheless, a consistent picture of the GPs from low to higher scales demands further investigations. Complementary measurements with positron beams offer an unique possibility, and we present an impact study of such experimental program.
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinbergs power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible.
We derive two relations involving spin polarizabilities of a spin-1/2 particle and consider their empirical implications for the proton. Using the empirical values of the proton anomalous magnetic moment, electric and magnetic charge radii, moments of the spin structure functions $g_1$, $g_2$, and of two spin polarizabilities, the present relations constrain the low-momentum behavior of generalized polarizabilities appearing in virtual Compton scattering. In the case of the proton, the dispersive model evaluations of the spin and generalized polarizabilities appear to be consistent with these relations. The ongoing measurements of different electromagnetic observables at the MAMI, Jefferson Lab, and HI$gamma$S facilities may be able to put these relations to a test, or use them to unravel the low-energy spin structure of the nucleon.
A factorized Regge-pole model for deeply virtual Compton scattering is suggested. The use of an effective logarithmic Regge-Pomeron trajectory provides for the description of both ``soft (small $|t|$) and ``hard (large $|t|$) dynamics. The model contains explicitly the photoproduction and the DIS limits and fits the existing HERA data on deeply virtual Compton scattering.
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