CLASSICAL PHOTOABSORPTION SUM RULES

Abstract

We use a quantum loop expansion to derive sum rule constraints on polarized photoabsorption cross sections in the Standard Model, generalizing earlier results obtained by Altarelli, Cabibbo, and Maiani. We show that the logarithmic integral of the spin-dependent photoabsorption cross section $\int^\infty_{ν_{th}} {dν\over ν} Δσ_{\rm Born}(ν) $ vanishes for any $2 \to 2$ Standard Model or supersymmetric process $γa \to b c$ in the classical, tree-graph approximation. Here $ν= {p \cdot q}/M$ and $Δσ(ν) = σ_P(ν)- σ_A(ν)$ is the difference between the photoabsorption cross section for parallel and antiparallel photon and target helicities. Tests of the sum rule for the reactions $γe \to W ν$ and $γγ\to W^+ W^-$ can provide new tests of the canonical magnetic and quadrupole couplings of the Standard Model. We also extend the sum rule to certain virtual photon processes.