Generalized dipole polarizabilities and the spatial structure of hadrons

Abstract

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.

41 pages, 5 figures, RevTex file

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• Dispersion Theory in Electromagnetic Interactions
• A new measurement of the structure functions $P_{LL}-P_{TT}/epsilon$ and $P_{LT}$ in virtual Compton scattering at $Q^2=$ 0.33 (GeV/c)${}^2$
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• Dispersion Effects in Nucleon Polarisabilities
• Virtual Compton Scattering and the Generalized Polarizabilities of the Proton at Q^2=0.92 and 1.76 GeV^2
• New Predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
• Towards charged hadron polarizabilities from four-point functions in lattice QCD
• Real and Virtual Compton Scattering: the nucleon polarisabilities
• Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering $\pi e\to \pi e\gamma$
• Pion-delta sigma-term
• Compton Scattering off Pions and Electromagnetic Polarizabilities
• Chiral perturbation theory - Success and challenge
• Charged pion electric polarizability from four-point functions in lattice QCD
• Two-current transition amplitudes with two-body final states
• Hyperon scalar form factors
• New approach to low energy Virtual Compton Scattering and generalized polarizabilities of the nucleon
• Polarization in low energy kaon-hyperon interaction
• Low energy kaon-hyperon interaction
• Nucleon Polarizabilities: Theory
• First Measurement of pi e -> pi e gamma Pion Virtual Compton Scattering
• Chiral effective field theories of the strong interactions
• Dipole polarizabilities of light pseudoscalar mesons within the Domain Model of QCD vacuum
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• Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory
• Aligning a Majorana fermion's anapole moment with an external current through photon emission mediated by the fermion's generalized polarizabilities
• Augmenting the Gauge-Gravity Correspondence to include Hadron Polarizabilities