Small x Resummation with Quarks: Deep-Inelastic Scattering

We extend our previous results on small-x resummation in the pure Yang--Mills theory to full QCD with nf quark flavours, with a resummed two-by-two matrix of resummed quark and gluon splitting functions. We also construct the corresponding deep-inelastic coefficient functions, and show how these can be combined with parton densities to give fully resummed deep-inelastic structure functions F_2 and F_L at the next-to-leading logarithmic level. We discuss how this resummation can be performed in different factorization schemes, including the commonly used MSbar scheme. We study the importance of the resummation effects by comparison with fixed-order perturbative results, and we discuss the corresponding renormalization and factorization scale variation uncertainties. We find that for x below 0.01 the resummation effects are comparable in size to the fixed order NNLO corrections, but differ in shape. We finally discuss the phenomenological impact of the small-x resummation, specifically in the extraction of parton distribution from present day experiments and their extrapolation to the kinematics relevant for future colliders such as the LHC