Increase with energy of parton transverse momenta in the fragmentation region in DIS and related phenomena

Abstract

The dipole and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) approximations are combined with the ${k}_{t}$ factorization theorem to demonstrate the fundamental property of perturbative QCD: the smaller the size of the colorless quark-gluon configurations in the fragmentation region, the more rapid is the increase of its interaction with the target as a function of energy. First, we consider two closely related properties of the wave function of the projectile: (i) the transverse momenta of the quark(antiquark) within the $q\overline{q}$ pair, produced in the fragmentation region by the strongly virtual photon, increase with the decrease of $x$ for fixed ${Q}^{2}$, (ii) the relative contribution of perturbative QCD to the structure functions increases as compared to the soft QCD contribution at central impact parameters due to a rapid increase with energy of the cross section of interaction of small dipoles. Practical consequences of these effects are presented for the cases of the cross sections of deep inelastic scattering (DIS) and double virtual compton scattering (DVCS). We predict that the ratio of DVCS to DIS amplitudes should very slowly approach one from above at very large collision energies. Second, we study a closely related phenomenon of the increase of the transverse momenta with the energy of the characteristic transverse momenta of the gluon/quark configurations responsible for the transition to the black disk regime. We discuss the impact of this phenomenona on the slowing of the dependence on the initial energy of the coherence length. We demonstrate that a rapid projectile has the biconcave shape, which is different from the expectations of the pre-QCD parton model where a fast hadron has a pancake shape. We show that the increase of the transverse momenta leads to a new expression for the total cross section of a DIS at very large energies, relevant to LHeC and LHC. We discuss the impact of the discovered phenomena on the hard processes in $pp$ collisions, and on the dominance of different phases of chiral and conformal symmetries in the central and peripheral $pp$, $pA$, and $AA$ collisions.