Complete Leading-Order, Renormalization-Scheme-Consistent Calculation of Small-xStructure Functions, Including Leading-ln(1/x) Terms

摘要

We present calculations of the structure functions F2(x,Q2) and FL(x,Q2),concentrating on small x. After discussing the standard expansion of the structure functions in powers of alphas(Q2) we consider a leading-order expansion in ln(1/x) and finally an expansion which is leading order in both ln(1/x) and alphas(Q2), and which we argue is the only really correct expansion scheme. Ordering the calculation in a renormalization-scheme-consistent manner, there is no factorization scheme dependence, as there should not be in calculations of physical quantities. The calculational method naturally leads to the 'physical anomalous dimensions' of Catani, but imposes stronger contraints than just the use of these effective anomalous dimensions. In particular, a relationship between the small-x forms of the inputs F2(X,Q20) and FL(x, Q20) is predicted. Analysis of a wide range of data for F2(x,Q2) is performed, and a very good global fit obtained, particularly for data at small x. The fit allows a prediction for FL(x,Q2) to be produced, which is smaller than those produced by the usual NLO-in-as(Q2) fits to F2(x,Q2) and different shape.