The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off
-shell scattering amplitudes which are light-front analogs of the Berends-Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.
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.
The perturbative QCD formula for minijet production consitutes an important ingredient in models describing the total cross section and multiparticle production in hadron-hadron scattering at high energies. Using arguments based on s-channel unitarit
y we set bounds on the minimum value of p_T for which the leading twist minijet formula can be used. For large impact parameters where correlations between partons appear to be small we find that the minimum value of p_T should be greater than 2.5 GeV for LHC energies and greater than 3.5 GeV for cosmic ray energies of about 50 TeV. We also argue that for collisions with values of impact parameters typical for heavy particle production the values of minimum p_T are likely to be considerably larger. We also analyze and quantify the potential role of saturation effects in the gluon density. We find that although saturation effects alone are not sufficient to restore unitarity, they are likely to play an important role at LHC energies.
We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renorma
lization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.
