We study the $W^+W^-$ and $Z^0Z^0$ electroweak boson production in double parton scattering using QCD evolution equations for double parton distributions. In particular, we analyze the impact of splitting terms in the evolution equations on the doubl
e parton scattering cross sections. Unlike the standard terms, the splitting terms are not suppressed for large values of the relative momentum of two partons in the double parton scattering. Thus, they play an important role which we discuss in detail for the single splitting contribution to the cross sections under the study.
Double parton distribution functions (DPDFs) are used in the QCD description of double parton scattering. The DPDFs evolve with hard scales through relatively new QCD evolution equations which obey nontrivial momentum and valence quark number sum rul
es. Based on the constructed numerical program, we present results on the QCD evolution of the DPDFs. In particular, we discuss the problem how to specify initial conditions for the evolution equations which exactly fulfill the sum rules.
We analyze the Drell-Yan lepton pair production at forward rapidity at the Large Hadron Collider. Using the dipole framework for the computation of the cross section we find a significant suppression in comparison to the collinear factorization formu
la due to saturation effects in the dipole cross section. We develop a twist expansion in powers of Q_s^2/M^2 where Q_s is the saturation scale and M the invariant mass of the produced lepton pair. For the nominal LHC energy the leading twist description is sufficient down to masses of 6 GeV. Below that value the higher twist terms give a significant contribution.
