Constraints on the virtual Compton scattering on the nucleon in a new dispersive formalism

Abstract

The dispersive representation of the virtual Compton forward scattering amplitude has been recently reexamined in connection with the evaluation of the Cottingham formula for the proton-neutron electromagnetic mass difference. The most difficult part of the analysis is related to one of the invariant amplitudes, denoted as $T_1(\nu ,Q^2)$, which requires a subtraction in the standard dispersion relation with respect to the energy $\nu$ at fixed photon momentum squared $q^2=-Q^2$. We propose an alternative dispersive framework, which implements analyticity and unitarity by combining the Cauchy integral relation at low and moderate energies with the modulus representation of the amplitude at high energies. Using techniques of functional analysis, we derive a necessary and sufficient condition for the consistency with analyticity of the subtraction function $S_1(Q^2)=T_1(0,Q^2)$, the electron-proton cross sections measured at low and moderate energies and the Regge model assumed to be valid at high energies. From this condition we obtain model-independent constraints on the subtraction function, confronting them with the available information on nucleon magnetic polarizabilities and results reported recently in the literature. The formalism can be used also for testing the existence of a fixed pole at $J=0$ in the angular momentum plane, but more accurate data are necessary for a definite answer.

13 pages, 5 figures. Minor changes, additional references, title slightly changed, matches the version published in PRD

References in corpus (11)

• Unitary Isobar Model - MAID2007
• The Proton Radius Puzzle
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Two-photon exchange correction to muon-proton elastic scattering at low momentum transfer
• Dispersive estimate of the electromagnetic charge symmetry violation in the octet baryon masses
• Electromagnetic Contribution to the Proton-Neutron Mass Splitting
• Functional-analysis based tool for testing quark-hadron duality

Cited by in corpus (10)

• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• The proton radius (puzzle?) and its relatives
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Sum rule for the Compton amplitude and implications for the proton-neutron mass difference
• Hyperfine splitting in ordinary and muonic hydrogen
• Two-photon exchange on neutron and the hyperfine splitting
• Lattice QCD calculation of the Compton amplitude subtraction function
• Analyticity and Regge asymptotics in virtual Compton scattering on the nucleon