3 will open an opportunity of probing the correlations pre- dicted by the QCD evolution directly . For this purpose, the double parton cross sections of the equal sign W pair production (with a high resolution scale) in pp collisions at 1 TeV ≤ √$_{s}$ ≤ 14 TeV are considered in Ref. [24]. As a main result, the contribution of the term with corre- lations in the equal sign W pairs production might con- tribute almost 40% to the cross section at √$_{s}$ = 1 TeV and about 20% at 14 TeV. Here we would like to bring attention to the D0 mea- surement of the process-independent parameter of double parton scattering, σ exp eff , done as a function of the second (ordered in the transverse momentum p$_{T}$ ) jet p$_{T}$ , p jet2 T , that can serve as a resolution scale. It is shown in Fig. 1 (see also Fig. 11 from Ref. [5]) and can be considered as a first inderect manifestation of the evolution effect since σ exp eff shows a tendency to be dependent on the resolution scale. At first glance the dimensional parameter σ$_{eff}$ en- tering into Eq. (1) contains the information related with the non-perturbative structure of the proton and corre- sponds to the overlap of the matter distributions in the colliding hadrons and therefore it is independent of the hard process scale a priori . However the experimental effective cross section σ exp eff is not measured directly but is calculated (extracted) using the normalization to the product of two single cross sections: (GeV) jet2 T p 15 20 25 30 (mb) eff 0 5 10 15 20 25 -1  = 1.0 fb int D0, L FIG. 1: Effective cross section σ exp eff measured in the three p jet2 T bins at the D0 experiment [5]. The solid ( k = 0 . 5) and dashed ( k = 0 . 1) lines are the results from Eq. (11) at p jet2 T 0 = 22 . 5 GeV and σ 0 eff = 16 . 3 mb. D i $_{p}$( x$_{i}$, 0) D j $_{p}$( x$_{j}$, 0)(1 − x$_{i}$ − x$_{j}$ ) which is supposed to be factorized at the reference scale t = 0 ( Q 2 = µ $^{2}$) and D i $_{p}$( x$_{i}$, t ) D j $_{p}$( x$_{j}$, t $^{)(1}$− x$_{i}$ − x$_{j}$ ) R ij 2 ( x$_{i}$, x$_{j}$, t ) (9) σ γ +3 j DP S σ $^{γj}$σjj = [ σ exp eff ] − 1 (6) [ σ exp eff ] − 1 ≃ [ σ$_{eff}$ ] − $^{1}$[1 + Δ( t )] , (10) D ij p ( x$_{i}$, x$_{j}$, t ) = D i $_{p}$( x$_{i}$, t ) D j $_{p}$( x$_{j}$, t )(1 − x$_{i}$ − x$_{j}$ )[1 + R ij 1 ( x$_{i}$, x$_{j}$, t ) + R ij 2 ( x$_{i}$, x$_{j}$, t )] , (7) D i $_{p}$( x$_{i}$, t ) D j $_{p}$( x$_{j}$, t )(1 − x$_{i}$ − x$_{j}$ )[1 + R ij 1 ( x$_{i}$, x$_{j}$, t )] (8) in both the CDF and D0 experiments. Here σ γj and σ jj are the inclusive γ + jet and dijets cross sections, σ γ +3 j DP S is the inclusive cross section of the γ + 3 jets events pro- duced in the double parton process. The factor 2 before σ exp eff is not needed in this case of distinguishable scat- terings unlike the four-jet process. It is worth noticing that the CDF and D0 Collaborations extract σ exp eff with- out any theoretical predictions on the γ + jet and dijets cross sections, by comparing the number of observed dou- ble parton γ + 3 jets events in one hard p ¯ p collision to the number of γ + 3 jets events with hard interactions occurring in two separate p ¯ p collisions. At such a normalization (6) and the presence of corre- lations in the two-parton distributions the experimentally extracted dimensional factor σ exp eff will be different from one σ$_{eff}$ incoming in Eq. (1). Indeed, in accordance with QCD evolution instead of the factorization ansatz (2) we can write [14, 24]: where is the solution of the homogeneous generalized GLAPD evolution equation with the given initial condition where Δ( t ) is a some positive contribution induced by the correlation term R ij 2 ( x$_{i}$, x$_{j}$, t ). This contribution in- creases [14, 24] with a growth of the resolution scale t ( Q $^{2}$) and can be right up 40% at Q = M$_{W}$ = 80 . 4 GeV fol- lowing Ref. [24]. Taking into account that namely σ$_{eff}$ is the true process-independent dimensional parameter we conclude: the experimentally extracted effective cross section σ exp eff must decrease with the growth of the reso- lution scale. The experimental data in Fig. 1 show just such a tendency in spite of large experimental uncertain- ties which do not allow the D0 Collaboration to make this conclusion. is a particular solution of the complete equation with zero initial condition R ij 2 ( x$_{i}$, x$_{j}$, 0) = 0. At t > 0 this solution is always positive as it is the integral convolu- tion of positive single distributions with the kernels of nonhomogeneous part of the evolution equation. These kernels (probabilities) are defined without negative δ - function regularization and therefore are always positive unlike the kernels of homogeneous part which have neg- ative contributions. In the kinematical range of interest for the actual case (we never exceed x = 0 . 1 practically) the contribution of the term R ij 1 ( x$_{i}$, x$_{j}$, t ) to Eq. (7) is negligible [24]. Substituting Eq. (7) in Eq. (1), and ne- glecting the factor (1 − x$_{i}$ − x$_{j}$ ) as it is usually done at relatively small x$_{i}$, x$_{j}$ , and using Eq. (6) we derive