arXiv subjects
Publications and source records attributed to Thomas R. Hemmert.
I discuss recent results regarding the influence of pion-nucleon and and nucleon-resonance physics on the (spin-) polarizabilities of the nucleon as measured in (polarized) Compton scattering.
We are studying the electron scattering process e p to e' p' gamma in order to obtain information on the genuine virtual Compton scattering (VCS) process gamma^* N to gamma N. In addition to the two kinematical variables of real Compton scattering, e.g. the scattering angle theta and the energy omega' of the outgoing photon, the invariant amplitude for VCS depends on a third kinematical variable, which we choose as the absolute value of the three-momentum transfer to the nucleon. The structure-dependent coefficients in the VCS amplitude therefore acquire a momentum dependence and are termed ``generalized polarizabilities'' of the nucleon in analogy to real Compton scattering. Utilizing the heavy baryon formalism of chiral perturbation theory we present predictions for the momentum dependence of the ``generalized polarizabilities'' and discuss the VCS response functions to be measured in the scheduled electron scattering experiments.
Previous calculations of the polarizabilities of the nucleon within the framework of heavy baryon chiral perturbation theory have included the contribution of the $Δ$(1232) only its effect on various contact terms or have been performed in chiral SU(3) where systematic errors are difficult to control. Herein we perfrom a corresponding calculation in chiral SU(2) wherein $Δ$(1232) is treated as an explicit degree of freedom and the expansion is taken to third order in soft momenta, the pion mass and the quantity $M_Δ-M_N$, collectively denoted by $ε$. We present the results of a systematic $O(ε^3)$ calculation of forward Compton scattering off the nucleon, extract the electric polarizability $\barα_E$, the magnetic polarizability $\barβ_M$ and the spin polarizability $γ$ and compare with available information from experiments and from previous calculations. Concluding with a critical discussion of our results, we point out the necessity of a future $O(ε^4)$ calculation.
Starting from a relativistic formulation of the pion-nucleon-delta system, the most general structure of 1/M corrections for a heavy baryon chiral lagrangian including spin 3/2 resonances is given. The heavy components of relativistic nucleons and delta fields are integrated out and their contributions to the next-to-leaing order lagrangians are constructed explicitly. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $m_π$ and the delta-nucleon mass difference $Δ$. As an application, we consider neutral pion photoproduction at threshold to third order in this small scale expansion.
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg's power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible.
We examine mass-corrected SU(6) symmetry predictions in the quark model relating vector, axial-vector and strong NN and NΔcouplings, and demonstrate that the experimental NΔvalue is significantly higher than predicted in each case. Nevertheless the Goldberger-Treiman relation is satisfied in both sectors. Possible origins of the discrepancy of the quark model predictions with experiment are discussed.