On the shape of a rapid hadron in QCD

We visualize the fundamental property of pQCD: the smaller is the size of the colorless quark-gluon configuration, more rapid is the increase of its interaction with energy. Within the frame of the dipole model we use the k_t factorization theorem to generalize the DGLAP approximation and/or leading ln (x₀ / x) approximation and evaluate the interaction of the quark dipole with a target. In the limit of fixed Q² and x → 0 we find the increase with energy of transverse momenta of quark (antiquark) within the q over(q, ̄) pair produced by the strongly virtual photon. The average p_t² is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass² of the q over(q, ̄) pair increases with the energy as 0.7 Q² (10^{- 2} / x)^{0.4 αs Nc / π}, for transverse photons, and ∼ 0.7 Q² exp 0.36 [(α_s N_c / π) log (10^{- 2} / x)]^{1 / 2} for longitudinal photons. We found similar pattern of the energy dependence of M² in the LO DGLAP approximation generalized to account for the k_t factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the collision energy and demonstrate that in the regime of complete absorption effective shape of the sufficiently energetic hadron (nucleus) has the biconcave form instead of the pancake. We explain that the different representations of chiral symmetry for the central and peripheral collisions would be characteristic property of hadron (nucleus) nucleus collisions at large energies. Some implications of the found phenomena for pp collisions are discussed.