We calculate the one-loop corrections to a general off-forward deeply virtual Compton process at leading twist for both parton helicity-dependent and independent cases. We show that the infrared divergences can be factorized entirely into off-forward parton distributions, even when one of the two photons is on shell. We argue that this property persists to all orders in perturbation theory. We obtain the next-to-leading order Wilson coefficients for the general leading-twist expansion of the product of two electromagnetic currents in the MS scheme. ͓S0556-2821͑98͒04521-4͔

Following a previous study of the one-loop factorization of the nonsinglet g 2 structure function of the nucleon, we present in this paper the next-to-leading order coefficient functions in the singlet sector. To obtain the result, the partonic processes of virtual Compton scattering off two and three "on-shell" gluons are calculated. A key step in achieving the correct factorization is to separate the correct twist-two contribution. The Burkardt-Cottingham sum rule is nominally satisfied at this order.

The Drell-Hearn-Gerasimov and Bjorken sum rules are special examples of dispersive sum rules for the spin-dependent structure function G1(ν,Q2) at Q2 = 0 and ∞. We generalize these sum rules through studying the virtual-photon Compton amplitudes S1(ν,Q2) and S2(ν,Q2). At small Q2, we calculate the Compton amplitudes at leading order in chiral perturbation theory; the resulting sum rules will be able to be tested against data soon available from the Jefferson Laboratory. For Q2>>ΛQCD2, the standard twist-expansion for the Compton amplitudes leads to the well known deep-inelastic sum rules. Although the situation is still relatively unclear in a small intermediate-Q2 window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the Q2-evolution of the G1(ν,Q2) sum rule from Q2 = 0 to ∞.

We calculate the forward spin-dependent photon-nucleon Compton amplitudes S 1 and S 2 as functions of photon energy ν and mass Q 2 at the nextto-leading (O(p 4 )) order in chiral perturbation theory, from which we extract the contribution to a generalized Drell-Hearn-Gerasimov sum rule at low Q 2 . The result indicates a much rapid Q 2 variation of the sum rule than a simple dimensional analysis would yield.

We calculate the forward spin-dependent photon-nucleon Compton amplitude as a function of photon energy at next-to-leading "O(p 4 )… order in chiral perturbation theory, from which we extract the contribution to the nucleon spin polarizability. The result shows a large correction to the leading order contribution.