# TTP01-23 The next-to-next-to-leading Order QCD Corrections to the Photon Structure Functions

TTP01-23 The next-to-next-to-leading Order QCD Corrections to the Photon Structure Functions

TTP01-23 The next-to-next-to-leading Order QCD Corrections to the Photon Structure Functions

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 F_1^gamma and F_2^gamma. We present the full photonic coefficient functions at order alpha alpha_s and calculate the first six even-integer moments of the corresponding O(alpha alpha_s^2) photon-quark and photon-gluon splitting functions together with the moments of the alpha alpha_s^2 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_bar to the DIS_gamma factorization scheme and write down the solution of the evolution equations. The numerical impact of the NNLO corrections is discussed in both schemes.

 S. Moch, J.A.M. Vermaseren and A. Vogt Nucl.Phys. B621 (2002) 413 PDF PostScript arXiv