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 investigate the Λ(1520, 3/2 − ) ≡ Λ * photoproduction off the proton target beyond the resonance region within a model including the Regge contributions, the tree-level diagrams with the nucleon and the certain resonance intermediate states and one contact term. The Reggeized propagators for the K and K * exchanges in the t channel are employed in a gauge-invariant manner. We compute the angular and energy dependences of the cross section and some polarization observables, such as the photon-beam asymmetry and the polarization-transfer coefficients. Our results qualitatively agree with the current experimental data. We find that the Regge contributions are necessary to explain the high-energy data beyond Eγ ≈ 4 GeV, especially for the angular dependences in the forward region. On the contrary, the polarization observables are insensitive to the Regge contributions due to the contact-term dominance which is a consequence of gauge invariance. We also calculate the K − -angle distribution function in the Gottfried-Jackson frame, using the polarization-transfer coefficients in the z direction. We find that it owns a complicated angle and energy dependences in the forward K + scattering region.

In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and particle-hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (k F a) → ∞ and (k F r) → 0, where k F is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space-time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.

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 investigate in detail the effect of making the range of the "contact" interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the 1 S0 channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the sum of a one-pion exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.1 fm, regardless of its particular form.

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.

Polarized beam ␥ ជ p Compton scattering provides a theoretically clean way to extract the isovector parity violating pion-nucleon coupling constant h NN (1) . This channel is more tractable experimentally than the recently proposed extraction of h NN (1) from the Bedaque-Savage process-polarized target ␥p ជ Compton scattering. The leading parity violating effect is calculated using heavy baryon chiral perturbation theory. The size of the asymmetry is estimated to be ϳ4ϫ10 Ϫ8 for 120 MeV photon energy.

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