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Register a new userGeneralized Polarizabilities and the Chiral Structure of the Nucleon
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Thomas R. Hemmert
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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.
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The spin-independent part of the virtual Compton scattering (VCS) amplitude from the nucleon is calculated within the framework of heavy baryon chiral perturbation theory (HBChPT). The calculation is performed to third order in external momenta according to chiral power counting. The relation of the tree-level amplitudes to what is expected from the low-energy theorem is discussed. We relate the one-loop results to the structure coefficients of a low-energy expansion for the model-dependent part of the VCS amplitude recently defined by Fearing and Scherer. Finally we discuss the connection of our results with the generalized polarizabilities of the nucleon defined by Guichon, Liu and Thomas.
This review gives an update on virtual Compton scattering (VCS) off the nucleon, $gamma^* N to N gamma$, in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model predictions for these observables. We present the GP extraction methods that are used in the experiments: the approach based on the low-energy theorem for VCS and the formalism of Dispersion Relations. We then review the experimental results, with a focus on the progress brought by recent experimental data on proton generalized polarizabilities, and we conclude by some perspectives in the field of VCS at low energy.
Background: Generalized polarizabilities (GPs) are important observables to describe the nucleon structure, and measurements of these observables are still scarce. Purpose: This paper presents details of a virtual Compton scattering (VCS) experiment, performed at the A1 setup at the Mainz Microtron by studying the $e p to e p gamma$ reaction. The article focuses on selected aspects of the analysis. Method: The experiment extracted the $P_{LL} -P_{TT} / epsilon$ and $P_{LT}$ structure functions, as well as the electric and magnetic GPs of the proton, at three new values of the four-momentum transfer squared $Q^2$: 0.10, 0.20 and 0.45 GeV$^2$. Results: We emphasize the importance of the calibration of experimental parameters. The behavior of the measured $e p to e p gamma$ cross section is presented and compared to the theory. A detailed investigation of the polarizability fits reveals part of their complexity, in connection with the higher-order terms of the low-energy expansion. Conclusions: The presented aspects are elements which contribute to minimize the systematic uncertainties and improve the precision of the physics results.
The measurement of nuclear Generalized Parton Distributions (GPDs) represents a valuable tool to understand the structure of bound nucleons and the phenomenology of hard scattering off nuclei. By using a realistic, non-relativistic microscopic approach for the evaluation of GPDs of 3He, it will be shown that conventional nuclear effects, such as isospin and binding ones, or the uncertainty related to the use of a given nucleon-nucleon potential, are bigger than in the forward case so that, if great attention is not paid, conventional nuclear effects can be easily mistaken for exotic ones. It is stressed that 3He, for which the best realistic calculations are possible, represents a unique target to discriminate between conventional and exotic effects. The complementary information which could be obtained by using a 3H target, the possible extraction of the neutron information, as well as the relevance of a relativistic treatment, will be also addressed.
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 Weinbergs 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.
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