Evolution kernels of twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering

The non-singlet and singlet evolution kernels of the twist-2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in ¢O(αs) for the general case of virtualities q2, q′2 ≠ 0. Special cases as the kernels for the general single-variable evolution equation and the Altarelli-Parisi and Brodsky-Lepage limits are derived from these results.