Related papers: On the analytical approximation to the GLAP evolut…
We propose a systematic approximation scheme for solving GLAP evolution equations at small Bjorken-$x$. The approximate solutions interpolate smoothly between hard (singular as $x^{-(1+\lambda)}$, $\lambda> 0$) and soft (singular at most as…
We examine critically the evidence for deviations from next-to-leading order perturbative DGLAP evolution in HERA data. We briefly review the status of perturbative small-x resummation and of global determinations of parton distributions.…
The very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascertained. We present a study of the…
We search for deviations from next-to-leading order QCD evolution in HERA structure function data. We compare to data predictions for structure functions in the small x region, obtained by evolving backwards to low Q^2 the results of a…
An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…
Nonsinglet contributions to the $g_1(x,Q^2)$ structure function are calculated in the double-logarithmic approximation of perturbative QCD in the region $x \ll 1$. Double logarithmic contributions of the type $(\alpha_s \ln ^2 (1/x))^k$…
We construct an anomalous dimension for small x evolution which goes beyond standard fixed order perturbative evolution by including resummed small x logarithms deduced from the leading order BFKL equation with running coupling.…
The QCD evolution of both unpolarized and polarized generalized parton distributions (GPDs) to next-to-leading order (NLO) accuracy is presented, in both the DGLAP and ERBL regions, for two appropriately symmetrized input distributions…
An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…
The standard analytic solution to the DGLAP equation in Mellin space is improved by resumming the large x divergences. Explicit results are given to next-to-leading order and next-to-leading logarithmic accuracy. Numerically, the…
The small x behaviour of the non-singlet structure function is studied within the double logarithmic approximation (DLA) of perturbative QCD. Since there is neither $k_T$ nor $\theta$ ordering in the ladder Feynman graphs, the predicted…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
In this paper we compare the experimental HERA data with the next-to-leading order approach (NLO) of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029). This approach includes the re-summed NLO…
Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the…
We present a small x resummation for the GLAP anomalous dimension and its corresponding dual BFKL kernel, which includes all the available perturbative information and nonperturbative constraints. Specifically, it includes all the…
We study the impact of the QCD DGLAP evolution on the geometric scaling of the gluon distributions which is expected to hold at small x within the saturation models. To this aim we solve the DGLAP evolution equations with the initial…
In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized…
We present a method for the analytic solution of small $x$ structure functions. The essential small $x$ logarithms are summed to all orders in the anomalous dimensions and coefficient functions. Although we work at leading logarithmic…