Quark mass dependence of the nucleon axial-vector coupling constant

We study the quark mass expansion of the axial-vector coupling constant g_A of the nucleon. The aim is to explore the feasibility of chiral effective field theory methods for extrapolation of lattice QCD results - so far determined at relatively large quark masses corresponding to pion masses larger than 0.6 GeV - down to the physical value of the pion mass. We compare two versions of non-relativistic chiral effective field theory: One scheme restricted to pion and nucleon degrees of freedom only, and an alternative approach which incorporates explicit Delta(1230) resonance degrees of freedom. It turns out that, in order to approach the physical value of g_A in a leading-one-loop calculation, the inclusion of the explicit Delta(1230) degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of inelastic pion production processes, a chiral extrapolation function for g_A is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of our extrapolation function near the physical pion mass is found to arise from an interplay between long- and short- distance physics.Comment: 21 pages, LaTeX, 7 figure

Radiative pion capture by a nucleon

The differential cross sections for $\pi^- p \to \gamma n$ and $\pi^+ n \to \gamma p$ are computed up to $O(p^3)$ in heavy baryon chiral perturbation theory (HBChPT). The expressions at $O(p)$ and $O(p^2)$ have no free parameters. There are three unknown parameters at $O(p^3)$, low energy constants of the HBChPT Lagrangian, which are determined by fitting to experimental data. Two acceptable fits are obtained, which can be separated by comparing with earlier dispersion relation calculations of the inverse process. Expressions for the multipoles, with emphasis on the p-wave multipoles, are obtained and evaluated at threshold. Generally the results obtained from the best of the two fits are in good agreement with the dispersion relation predictions.Comment: 24 pages, Latex, using RevTe

Generalized Polarizabilities of the Nucleon in Chiral Effective Theories

Using the techniques of chiral effective field theories we evaluate the so called generalized polarizabilities of the nucleon, which characterize the structure dependent components in virtual Compton scattering (VCS) as probed in the electron scattering reaction e N \to e' N gamma. Results are given for both spin-dependent and spin-independent structure effects to O(p^3) in SU(2) Heavy Baryon Chiral Perturbation Theory and to O(epsilon^3) in the SU(2) Small Scale Expansion. Finally we compare our calculations with results from the pioneering VCS experiment on the proton from Mainz.Comment: 39 pages, 12 figures, revte

Nucleon mass, sigma term and lattice QCD

We investigate the quark mass dependence of the nucleon mass M_N. An interpolation of this observable, between a selected set of fully dynamical two-flavor lattice QCD data and its physical value, is studied using relativistic baryon chiral perturbation theory up to order p^4. In order to minimize uncertainties due to lattice discretization and finite volume effects our numerical analysis takes into account only simulations performed with lattice spacings a5. We have also restricted ourselves to data with m_pi<600 MeV and m_sea=m_val. A good interpolation function is found already at one-loop level and chiral order p^3. We show that the next-to-leading one-loop corrections are small. From the p^4 numerical analysis we deduce the nucleon mass in the chiral limit, M_0 approx 0.88 GeV, and the pion-nucleon sigma term sigma_N= (49 +/- 3) MeV at the physical value of the pion mass.Comment: 12 pages, 4 figures, revised journal versio

Complete one-loop analysis of the nucleon's spin polarizabilities

We present a complete one-loop analysis of the four nucleon spin polarizabilities in the framework of heavy baryon chiral perturbation theory. The first non-vanishing contributions to the isovector and first corrections to the isoscalar spin polarizabilities are calculated. No unknown parameters enter these predictions. We compare our results to various dispersive analyses. We also discuss the convergence of the chiral expansion and the role of the delta isobar.Comment: 4 pp, REVTE

Strange chiral nucleon form factors

We investigate the strange electric and magnetic form factors of the nucleon in the framework of heavy baryon chiral perturbation theory to third order in the chiral expansion. All counterterms can be fixed from data. In particular, the two unknown singlet couplings can be deduced from the parity-violating electron scattering experiments performed by the SAMPLE and the HAPPEX collaborations. Within the given uncertainties, our analysis leads to a small and positive electric strangeness radius, $= (0.05 \pm 0.09) fm^2$. We also deduce the consequences for the upcoming MAMI A4 experiment.Comment: 7 pp, REVTeX, uses epsf, minor correction

Generalized polarizabilities of the nucleon studied in the linear sigma model (II)

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one-loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin-dependent amplitude of virtual Compton scattering. The results fulfill 3 model-independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three-momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the $\pi^{0}$ exchange in the $t$ channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin-polarizabilities appearing in real Compton scattering.Comment: 17 pages, 4 figures, latex2e (Revtex), submitted to Z. Phys.

The Nucleon Spin Polarizability at Order O(p4{\cal O}(p^4) in Chiral Perturbation Theory

We calculate the forward spin-dependent photon-nucleon Compton amplitude as a function of photon energy at the next-to-leading (${\cal O}(p^4)$) order in chiral perturbation theory, from which we extract the contribution to nucleon spin polarizability. The result shows a large correction to the leading order contribution.Comment: 7 pages, latex, 2 figures included as .eps file