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We discuss how momentum conservation is implemented in perturbative computations based on expansions of anomalous dimensions appropriate at small $x$. We show that for any given choice of $F_2$ coefficient functions there always exists a…
To resum large logarithms in multi-scale problems a generalization of $\MS$ is introduced allowing for as many renormalization scales as there are generic scales in the problem. In the new \lq\lq minimal multi-scale subtraction scheme''…
Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage…
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…
We summarize our recent results on the small x resummation of the singlet anomalous dimension. We recall the main features of our approach, and briefly describe some work in progress on the inclusion of subleading corrections to it.
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through…
This talk summarises the current status of the NLL corrections to BFKL physics and discusses the question of small-x factorisation.
The growth-fragmentation equation arises in many different contexts, ranging from cell division, protein polymerization, biopolymers, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a…
As an alternative to directly integrating their defining equations to find the running coupling $a(\mu)$ and the running mass $m(\mu)$, we expand these quantities in powers of $\ln\left(\frac{\mu}{\mu^\prime}\right)$ and their boundary…
We consider the region of small transverse momenta in the production of high-mass systems in hadronic collisions. By using the current knowledge on the infrared behaviour of tree-level and one-loop QCD amplitudes at O(alpha_s^2), we…
The small-$x$ contributions to the Bjorken sum rule within double logarithmic $ln^2x$ approximation for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Analytical solutions of the evolution equations for full and…
We present a general-purpose algorithm to extrapolate a low rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum…
To describe the transverse momentum spectrum of heavy color-singlet production, the joint resummation of threshold and transverse momentum logarithms is investigated. We obtain factorization theorems for various kinematic regimes valid to…
We revisit the basic steps necessary to obtain next-to-leading-logarithmic accurate small-$x$ results for the DGLAP splitting functions, and their implementations within the HELL framework. We derive new analytical all-order results for the…
Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the…
I review recent progress in the determination of PDFs with the inclusion of small-x resummation, and its impact in precision phenomenology, and discuss future prospects.
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…