Chiral symmetry breaking and the polarized photon structure function in QED

The structure function of a polarized photon g1γ(x) satisfies a remarkable sum rule: ∫g1γ(x)dx=0. The zero arises as a cancellation between explicit (mass-induced) and anomalous chiral symmetry breaking. We analyse this cancellation by studying the helicity structure of the cross section γ∗(λ1)+γ(λ2)→l+(λ3)+l−(λ4). The structure function g1 γ(x) is found to consist of two pieces, g1,like and g1,unlike, corresponding to final l+l− states with like and unlike helicities. The function g1,like is constant in x, and integrates to +12, while g1,unlike is x-dependent and integrates to −−12. When the target photon is virtual (|k2| ⪢ m2), the integral ∫g1,likedx drops to zero, while ∫1, unlikedx stays constant at the value −12. We conclude that the “explicit” and “anomalous” parts of g1γ(x) are uniquely associated with final l+l− states with equal or opposite helicities. The survival of the like-helicity component is a “quasi-paradox” analogous to the survival of helicity-flip bremsstrahlung at high energies. Some implications for the QCD process γ∗g→QQ are noted.