The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure

Higher moments of nucleon spin structure functions in heavy baryon chiral perturbation theory and in a resonance model

The third moment $d_2$ of the twist-3 part of the nucleon spin structure function $g_2$ is generalized to arbitrary momentum transfer $Q^2$ and is evaluated in heavy baryon chiral perturbation theory (HBChPT) up to order ${\mathcal{O}}(p^4)$ and in a unitary isobar model (MAID). We show how to link $d_2$ as well as higher moments of the nucleon spin structure functions $g_1$ and $g_2$ to nucleon spin polarizabilities. We compare our results with the most recent experimental data, and find a good description of these available data within the unitary isobar model. We proceed to extract the twist-4 matrix element $f_2$ which appears in the $1/Q^2$ suppressed term in the twist expansion of the spin structure function $g_1$ for proton and neutron.Comment: 30 pages, 7 figure

Measurement of the LT-asymmetry in \pi^0 electroproduction at the energy of the \Delta (1232) resonance

The reaction p(e,e'p)pi^0 has been studied at Q^2=0.2 (GeV/c)^2 in the region of W=1232 MeV. From measurements left and right of q, cross section asymmetries \rho_LT have been obtained in forward kinematics \rho_LT(\theta_\pi^0=20deg) = (-11.68 +/- 2.36_stat +/- 2.36_sys)$ and backward kinematics \rho_LT(\theta_\pi^0=160deg) =(12.18 +/- 0.27_stat +/- 0.82_sys). Multipole ratios \Re(S_1+^* M_1+)/|M_1+|^2 and \Re(S_0+^* M_1+)/|M_1+|^2 were determined in the framework of the MAID2003 model. The results are in agreement with older data. The unusally strong negative \Re(S_0+^* M_1+)/|M_1+|^2 required to bring also the result of Kalleicher et al. in accordance with the rest of the data is almost excluded.Comment: 7 pages, 7 figures, 4 tables. Changed content. Accepted for publication in EPJ

The Generalized Gerasimov-Drell-Hearn Integral and the Spin Structure of the Nucleon

The spin structure functions g1 and g2 have been calculated in the resonance region and for small and intermediate momentum transfer. The calculation is based on a gauge-invariant and unitary model for one-pion photo- and electroproduction. The predictions of the model agree with the asymmetries and the spin sturcture functions recently measured at SLAC, and the first moments of the calculated spin structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5-10 %.Comment: 22 pages LATEX including 5 postscript figures, replaced with 2 new figure

Measurement of the recoil polarization in the p (\vec e, e' \vec p) pi^0 reaction at the \Delta(1232) resonance

The recoil proton polarization has been measured in the p (\vec e,e'\vec p) pi^0 reaction in parallel kinematics around W = 1232 MeV, Q^2 = 0.121 (GeV/c)^2 and epsilon = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components P_x/P_e = (-11.4 \pm 1.3 \pm 1.4) %, P_y = (-43.1 \pm 1.3 \pm 2.2) %, and P_z/P_e = (56.2 \pm 1.5 \pm 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (-6.4\pm 0.7_{stat}\pm 0.8_{syst}) % was determined from P_x in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.Comment: 5 pages LaTeX, 1 table, 2 eps figure

Electroproduction of nucleon resonances

The unitary isobar model MAID has been extended and used for a partial wave analysis of pion photo- and electroproduction in the resonance region W < 2 GeV. Older data from the world data base and more recent experimental results from Mainz, Bates, Bonn and JLab for Q^2 up to 4.0 (GeV/c)^2 have been analyzed and the Q^2 dependence of the helicity amplitudes have been extracted for a series of four star resonances. We compare single-Q^2 analyses with a superglobal fit in a new parametrization of Maid2003 together with predictions of the hypercentral constituent quark model. As a result we find that the helicity amplitudes and transition form factors of constituent quark models should be compared with the analysis of bare resonances, where the pion cloud contributions have been subtracted.Comment: 6 pages Latex including 5 figures, Invited talk at ICTP 4th International Conference on Perspectives in Hadronic Physics, Trieste, Italy, 12-16 May 200

Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory

We study spin-dependent sum rules for forward virtual Compton scattering(VVCS) off the nucleon in heavy baryon chiral perturbation theory 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 amplitudes. We study in particular the Burkhardt -Cottingham sum rule in HBChPT and higher terms in the low energy expansion, which can be related to the 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.Comment: 16 pages,4 fig

A measurement of the axial form factor of the nucleon by the p(e,e'pi+)n reaction at W=1125 MeV

The reaction p(e,e'pi+)n was measured at the Mainz Microtron MAMI at an invariant mass of W=1125 MeV and four-momentum transfers of Q^2=0.117, 0.195 and 0.273 (GeV/c)^2. For each value of Q^2, a Rosenbluth separation of the transverse and longitudinal cross sections was performed. An effective Lagrangian model was used to extract the `axial mass' from experimental data. We find a value of M_A=(1.077+-0.039) GeV which is (0.051+-0.044) GeV larger than the axial mass known from neutrino scattering experiments. This is consistent with recent calculations in chiral perturbation theory.Comment: 14 pages, 5 figures, uses elsart.cl

Pseudovector vs. pseudoscalar coupling in one-boson exchange NN potentials

We examine the effects of pseudoscalar and pseudovector coupling of the pi and eta mesons in one-boson exchange models of the NN interaction using two approaches: time-ordered perturbation theory unitarized with the relativistic Lippmann-Schwinger equation, and a reduced Bethe-Salpeter equation approach using the Thompson equation. Contact terms in the one-boson exchange amplitudes in time-ordered perturbation theory lead naturally to the introduction of s-channel nucleonic cutoffs for the interaction, which strongly suppresses the far off-shell behavior of the amplitudes in both approaches. Differences between the resulting NN predictions of the various models are found to be small, and particularly so when coupling constants of the other mesons are readjusted within reasonable limits.Comment: 24 pages, 4 figure

Chiral effective field theories of the strong interactions

Effective field theories of the strong interactions based on the approximate chiral symmetry of QCD provide a model-independent approach to low-energy hadron physics. We give a brief introduction to mesonic and baryonic chiral perturbation theory and discuss a number of applications. We also consider the effective field theory including vector and axial-vector mesons.Comment: 22 pages, 9 figures, proceedings of "Many-Body Structure of Strongly Interacting Systems", Mainz, Germany, Feb. 23-25 201