We study spin-dependent sum rules for forward virtual Compton scattering (VVCS) off the nucleon in heavy baryon chiral perturbation theory (HBChPT) at order O(p 4 ). We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitude. We study in particular the Burkhardt-Cottingham sum rule in HBChPT and the higher terms in the low energy expansion, which can be related to generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality Q 2 can be accessed, at small and intermediate Q 2 values, from existing and forthcoming data at Jefferson Lab.

We derive the spectrum of the Dirac operator for the linear model with quarks in the large N c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term are recovered. We calculate the coefficient of the next to leading term and investigate the spectrum beyond the low energy regime.

The beam-helicity asymmetry has been measured simultaneously for the reactions → e p → e p γ and → e p → e p π 0 in the ∆(1232) resonance region at Q 2 = 0.35 (GeV/c) 2 . The experiment was performed at MAMI with a longitudinally polarized beam and an out-of-plane detection of the proton. The results are compared with calculations based on Dispersion Relations for virtual Compton scattering and with the MAID model for pion electroproduction. There is an overall good agreement between experiment and theoretical calculations. The remaining discrepancies may be ascribed to an imperfect parametrization of some γ ( * ) N → πN multipoles, mainly contributing to the non-resonant background. The beam-helicity asymmetry in both channels (γ and π 0 ) shows a good sensitivity to these multipoles and should allow future improvement in their parametrization. PACS. 13.40.-f Electromagnetic processes and properties -13.60.Fz Elastic and Compton scattering -13.60.Le Meson production -14.20.Gk Baryon resonances with S=0

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