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 F2 and FL at the next-to-leading logarithmic level. We discuss how this resummation can be performed in different factorization schemes, including the commonly used MS¯ 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 10−2 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.