Looking for quark saturation in proton and nuclei

The quark saturation behavior at low [Formula: see text] is shown in a numeric solution of the DGLAP equation with parton recombination corrections, which resembles the widely discussed JIMWLK saturation of gluons. Our calculation suggests that the partonic saturation can be interpreted as a dynamical balance between the splitting and the fusion processes of partons, without any other condensation mechanisms added. The nuclear shadowing saturation at small [Formula: see text] resulted from the proposed quark saturation is also discussed.

Fragmentation in the ϕ3 theory and the LPHD hypothesis

We present analytic solution of the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation at leading order (LO) in the [Formula: see text] theory in 6 space-time dimensions. If the [Formula: see text] model was the theory of strong interactions, the obtained solution would describe the distribution of partons in a jet. We point out that the local parton-hadron duality (LPHD) conjecture does not work in this hypothetical situation. That is, treatment of hadronisation of shower partons is essential for the description of hadron distributions in jets stemming from proton-proton (pp) collisions at [Formula: see text] TeV and from electron-positron ([Formula: see text]) annihilations at various collision energies. We use a statistical model for the description of hadronisation.

Comparison of Analytical Solution of DGLAP Equations forF2NS(x,t)at Smallxby Two Methods

The DGLAP equation for the nonsinglet structure functionF2NS(x,t)at LO is solved analytically at lowxby converting it into a partial differential equation in two variables: Bjorkenxandt (t=ln(Q2/Λ2)and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. The two solutions are then compared with the available data on the structure function. The relative merits of the two solutions are discussed calculating the chi-square with the used data set.

THE KINETIC INTERPRETATION OF THE DGLAP EQUATION, ITS KRAMERS–MOYAL EXPANSION AND POSITIVITY OF HELICITY DISTRIBUTIONS

According to a rederivation — due to Collins and Qiu — the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound |Δ f(x, Q)| < f(x, Q) between polarized and unpolarized distributions, or positivity of the helicity distributions, for any Q. We reanalyze this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in αs, which we illustrate. We also elaborate on some of the formal properties of the Collins–Qiu form and comment on the underlying regularization, introduce a Kramers–Moyal expansion of the equation and briefly analyze its Fokker–Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution qV and for the transverse spin distribution h1.