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

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

Nucleon generalized polarizabilities within a relativistic Constituent Quark Model

Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $\beta_{para}(q)$, as a function of the virtual-photon three-momentum transfer $q,$ is explicitly evaluated within a relativistic constituent quark model by adopting transition form factors obtained in the light-front formalism. The discussion is focussed on the role played by the effects due to the relativistic approach and to the transition form factors, derived within different models.Comment: 14 pages and three figures (included), to appear in Phys. Rev. C (May 1998

Structure analysis of the virtual Compton scattering amplitude at low energies

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $ep\to e'p'\gamma$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon.Comment: 19 pages, LaTeX2e/RevTeX, no figures, original sections IV.-VI. removed, to be discussed in a separate publication, none of the conclusions change

Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions and NN-potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green's functions in order to ensure gauge invariance and the correct Thomson limit. With this Green's-function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use Chiral Effective Field Theory with explicit \Delta(1232) degrees of freedom within the Small Scale Expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $\gamma d$ data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find \alpha_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and \beta_M^s = (3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are essentially the same.Comment: 47 pages LaTeX2e with 20 figures in 59 .eps files, using graphicx. Minor modifications; extended discussion of theoretical uncertainties of polarisabilities extraction. Version accepted for publication in EPJ

Baryon magnetic moments and sigma terms in lattice-regularized chiral perturbation theory

An SU(3) chiral Lagrangian for the lightest decuplet of baryons is constructed on a discrete lattice of spacetime points, and is added to an existing lattice Lagrangian for the lightest octets of mesons and baryons. A nonzero lattice spacing renders all loop integrations finite, and the continuum limit of any physical observable is identical to the result obtained from dimensional regularization. Chiral symmetry and gauge invariance are preserved even at nonzero lattice spacing. Specific calculations discussed here include the non-renormalization of a conserved vector current, the magnetic moments of octet baryons, and the pi N and KN sigma terms that relate to the nucleon's strangeness content. The quantitative difference between physics at a nonzero lattice spacing and physics in the continuum limit is easily computed, and it represents an expectation for the size of discretization errors in corresponding lattice QCD simulations.Comment: 19 pages, 5 figures, one paragraph added to introduction, to appear in Phys Rev

πΔΔ\pi \Delta\Delta coupling constant

We calculate the $\pi \Delta\Delta$ coupling $g_{\pi^0\Delta^{++}\Delta^{++}}$ using light cone QCD sum rule. Our result is $g_{\pi^0\Delta^{++}\Delta^{++}}=(11.8\pm 2.0)$.Comment: RevTex, 5 pages + 1 PS figur

Generalized dipole polarizabilities and the spatial structure of hadrons

We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process gamma* h -> gamma h. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. We then motivate a gauge-invariant separation into a generalized Born term containing ground-state properties only, and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of Lorentz-invariant residual amplitudes. Particular emphasis is laid on a physical interpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is argued that three dipole polarizabilities, namely the longitudinal electric alpha_L(q^2), the transverse electric alpha_T(q^2), and the magnetic beta(q^2) ones are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, alpha_T(q^2), describes an effect of higher order in the soft final-photon momentum q'. We argue that the associated spatial distributions obtained via the Fourier transforms in the Breit frame are meaningful even for such a light particle as the pion. The spatial distributions are determined at large distances r ~ 1/m_pi for pions, kaons, and octet baryons by use of ChPT.Comment: 41 pages, 5 figures, RevTex fil

Parity Violation in gamma proton Compton Scattering

A measurement of parity-violating spin-dependent gamma proton Compton scattering will provide a theoretically clean determination of the parity-violating pion-nucleon coupling constant $h_{\pi NN}^{(1)}$. We calculate the leading parity-violating amplitude arising from one-loop pion graphs in chiral perturbation theory. An asymmetry of ~5 10^{-8} is estimated for Compton scattering of 100 MeV photons.Comment: 6 pages, 1 figure, latex. Reference adde