Related papers: Mass corrections to the DGLAP equations
A matrix-based approach to numerical integration of the DGLAP evolution equations is presented. The method arises naturally on discretisation of the Bjorken x variable, a necessary procedure for numerical integration. Owing to peculiar…
We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature,…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
We derive relations between polarized transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption…
Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional DGLAP equation. The method relies on the fact that the anomalous dimensions of…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon…
The orbital angular momentum (OAM) spatial degree of freedom of light has been widely explored in many applications, including telecommunications, quantum information and light-based micro-manipulation. The ability to separate and…
uPDFevolv2 is a software package designed for evolving collinear and Transverse Momentum Dependent (TMD) parton densities using the DGLAP evolution equation. A comprehensive description of both the theoretical framework and technical…
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that…
Using recent and updated world data on polarized structure functions $g_1$ and $g_2$ we perform QCD analysis at the next-next-to-leading-order (NNLO) accuracy. We include also target mass correction and higher twist effect to get more…
A range of issues pertaining to the use of Wilson lines in integrated and transverse-momentum dependent (TMD) parton distribution functions (PDF) is discussed. The relation between gauge invariance and the renormalization properties of the…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…
The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide…
This paper introduces a transverse-momentum dependent (TMD) factorization scheme designed to unify both large and small Bjorken-x regimes. We compute the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the gluon TMD…
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing…
Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse…