Nonlinear corrections to the DGLAP equations in view of the HERA data Original Research Article

The effects of the first nonlinear corrections to the DGLAP evolution equations are studied by using the recent HERA data for the structure function F2(x,Q2) of the free proton and the parton distributions from CTEQ5L and CTEQ6L as a baseline. By requiring a good fit to the H1 data, we determine initial parton distributions at Q02=1.4 GeV2 for the nonlinear scale evolution. We show that the nonlinear corrections improve the agreement with the F2(x,Q2) data in the region of x∼3×10−5 and Q2∼1.5 GeV2 without paying the price of obtaining a worse agreement at larger values of x and Q2. For the gluon distribution the nonlinear effects are found to play an increasingly important role at x≲10−3 and Q2≲10 GeV2, but rapidly vanish at larger values of x and Q2. Consequently, contrary to CTEQ6L, the obtained gluon distribution at Q2=1.4 GeV2 shows a power-like growth at small x. Relative to the CTEQ6L gluons, an enhancement up to a factor ∼6 at x=10−5, Q02=1.4 GeV2 reduces to a negligible difference at Q2≳10 GeV2.