Next-to-next-to-leading order QCD corrections to the photonʹs parton structure Original Research Article

The next-to-next-to-leading order (NNLO) corrections in massless perturbative QCD are derived for the parton distributions of the photon and the deep-inelastic structure functions F1γ and F2γ. We present the full photonic coefficient functions at order ααs and calculate the first six even-integer moments of the corresponding O(ααs2) photon–quark and photon–gluon splitting functions together with the moments of the ααs2 coefficient functions which enter only beyond NNLO. These results are employed to construct parametrizations of the splitting functions which prove to be sufficiently accurate at least for momentum fractions x≳0.05. We also present explicit expressions for the transformation from the MS to the DISγ factorization scheme and write down the solution of the evolution equations. The numerical impact of the NNLO corrections is discussed in both schemes.