Sum rules for light-by-light scattering

Abstract

We derive a set of sum rules for the light-by-light scattering and fusion: $\gamma \gamma \to all$, and verify them in lowest order QED calculations. A prominent implication of these sum rules is the superconvergence of the helicity-difference total cross-section for photon fusion, which in the hadron sector reveals an intricate cancellation between the pseudoscalar and tensor mesons. An experimental verification of superconvergence of the polarized photon fusion into hadrons is called for, but will only be possible at $e^{+}{e}^{-}$ and $\gamma \gamma$ colliders with both beams polarized. We also show how the sum rules can be used to measure various contributions to the low-energy light-by-light scattering.

4 pages, 3 figures; minor corrections, published version

References in corpus (9)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• High-statistics measurement of neutral-pion pair production in two-photon collisions
• High-statistics study of ${\boldmath ηπ^0}$ production in two-photon collisions
• High statistics measurement of the cross sections of gamma gamma -> pi^+ pi^- production
• Amplitude Analysis of High Statistics Results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and the Two Photon Width of Isoscalar States
• Measurement of K^+K^- production in two-photon collisions in the resonant-mass region
• The Spin Structure of a Polarized Photon
• CLASSICAL PHOTOABSORPTION SUM RULES

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