Probing the Perturbative NLO Parton Evolution in the Small–x Region

A dedicated test of the perturbative QCD NLO parton evolution in the very small–x region is performed. We find a good agreement with recent precision HERA–data for F p 2 (x,Q), as well as with the present determination of the curvature of F p 2 . Characteristically, perturbative QCD evolutions result in a positive curvature which increases as x decreases. Future precision measurements in the very small x–region, x < 10, could provide a sensitive test of the range of validity of perturbative QCD. Parton distributions f(x,Q), f = q, q̄, g, underlie a Q–evolution dictated by perturbative QCD at Q > ∼ 1 GeV. It was recently stated [1] that the NLO perturbative QCD Q–evolution disagrees with HERA data [2, 3] on F p 2 (x,Q) in the small–x region, x < ∼ 10. In view of the importance of this statement we perform here an independent study of this issue. In contrast to [1] we shall undertake this analysis in the standard framework where one sets up input distributions at some low Q 0 , here taken to be Q 0 = 1.5 GeV, corresponding to the lowest Q considered in [1], and adapting these distributions to the data considered. In the present case the data considered will be restricted to 1.5 GeV ≤ Q ≤ 12 GeV, 3× 10 . x . 3× 10 (1) as in [1] and will be taken from the corresponding measured F p 2 (x,Q) of the H1 collaboration [2]. The choice of these data is motivated by their higher precision as compared to corresponding data of the ZEUS collaboration [3], in particular in the very small–x region. We shall choose two sets of input distributions based on the GRV98 parton distributions [4]. In the first set we shall adopt uv, dv, s = s̄ and ∆ ≡ d̄ − ū from GRV98 and modify ū+ d̄ and the gluon distribution in the small–x region to obtain an optimal fit to the H1 data [2] in the aforementioned kinematical region. We shall refer to this fit as the ‘best fit’. The second choice will be constrained to modify the GRV98 ū+ d̄ and g distributions in the small–x region as little as possible. We shall refer to this fit as GRVmod. It will turn out that both input distributions are compatible with the data to practically the same extent, i.e. yielding comparable χ/dof . In view of these observations we do not agree with the conclusions of ref. [1], i.e. we do not confirm a disagreement between the NLO Q–evolution of f(x,Q) and the measured [2, 3] Q–dependence of F p 2 (x,Q). The remaining flavor–singlet input distributions at Q 0 = 1.5 GeV to be adapted to