Dispersion relations in two-photon hadronic processes
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
The general principles of quantum field theory, such as unitarity of the S-matrix, crossing symmetry and causality (dispersion relations), allow for construction of the full forward Compton scattering (CS) amplitude off protons based on experimental hadronic photoproduction cross sections. This amplitude is an essential test for the low-energy effective field theories, and its low-energy behaviour provides model-independent constraints on the extraction of the electro- magnetic polarizabilities of the proton via sum rules. A numerical evaluation of the forward CS amplitude off the proton together with the corresponding observables and sum rules is provided.
Furthermore, the direct assessment of the forward CS amplitude is examined by utilizing the di-lepton photoproduction off protons. It is described how the real part of the unpolarized forward CS amplitude can be accessed at a regime with sufficiently low momentum transfer and outgoing photon virtuality, through the measurement of the forward-backward asymmetry of the outgoing lepton pair interchange in the di-lepton photoproduction process. Estimates of this asymmetry for various kinematics setups at Jefferson Lab and at a planned Electron-Ion Collider are provided. Such measurements may help discriminate between the existing state-of-the-art fits of the total photoabsorption data, ultimately improving our understanding of the high-energy behavior of the hadronic total cross sections, required for the planning of future high-energy colliders, as well as for interpreting cosmic ray experiments.
A similar approach to access the J/ψ – proton and Υ – proton forward scattering amplitudes is applied. An analysis of these amplitudes is performed, by relating their imaginary parts to the corresponding photoproduction cross section data. By calculating the s-wave scattering length for these quarkonia from the real parts of the amplitudes, the possibility of bound states in nuclear systems is investigated. It is shown for the J/ψ case that the forward-backward asymmetry of the di-lepton photoproduction at Jefferson Lab can be a very sensitive observable for a refined extraction of the scattering length. For the Υ state, the experimental feasibility at a planned Electron-Ion Collider is examined and a clear potential to extract the scattering length from precision photoproduction measurements is concluded.
The application of dispersion relations is extended also to the case of hadronic light-by-light scattering, which is currently one of the two dominant uncertainties in the interpretation of the 3 – 4 σ discrepancy between experiment and the Standard Model prediction of the muon’s anomalous magnetic moment. A model-independent treatment of the forward light-by-light amplitudes is considered by comparing a direct calculation of the real part of this amplitude through lattice quantum chromodynamics with a sum rule evaluation based on the phenomenological input of the γ∗γ∗-fusion cross sections.