QCD Evolutions in the small–x Region

The curvature of DIS structure functions like F p 2 (x,Q ), i.e., its second derivative with respect to the photon’s virtuality Q at fixed values of x, plays a decisive role in probing the range of validity of perturbative QCD evolutions of parton distributions in the small-x region. This has been observed recently [1, 2, 3, 4] and it was demonstrated that NLO(MS) evolutions imply a positive curvature which increases as x decreases. Such rather unique predictions provide a check of the range of validity of perturbative QCD evolutions. However, the curvature is a rather subtle mathematical quantity which a priori may sensitively depend on the theoretical (non)perturbative assumptions made for calculating it. Our main purpose is to study the dependence and stability of the predicted curvature with respect to a different choice of the factorization scheme (DIS versus MS) and to the perturbative order of the evolutions by extending the common NLO (2-loop) evolution [3] to the next-to-next-toleading 3-loop order (NNLO) [4]. The valence qv = uv, dv and sea w = q̄, g distributions underlying F p 2 (x,Q ) are parametrized at an input scale Q0 = 1.5 GeV 2 as follows: