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We argue that parton distributions in coordinate space provide a more natural object for nonperturbative methods compared to the usual momentum distributions in which the physics of different longitudinal distances is being mixed. To…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We investigate the angular distribution of the lepton pair in the process $p \bar{p} \rightarrow \gamma^{\ast} + X \rightarrow \ell^+\ell^- + X$, where the virtual photon is produced at high transverse momentum. The angular distribution of…
We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of non-standard…
Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist…
We calculate the Wigner functions for a quark target dressed with a gluon. These give a combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs) and…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…
We review the analysis of polarized structure function data using perturbative QCD at next-to-leading order. We use the most recent experimental data to obtain updated results for polarized parton distributions, first moments and the strong…
The most striking feature of quark distribution functions transformed to the longitudinal distance representation is the recognizable separation of small and large longitudinal distances. While the former are responsible for the average…
There has recently been surprising progress in understanding the spin and flavor dependence of deep inelastic structure functions in terms of the same physics needed in the simple quark models used for hadronic spectroscopy. However, the…
We explore further applications of the twist-two quark interference fragmentation functions introduced earlier. We show that semi-inclusive production of two pions in the current fragmentation region in deep inelastic scattering of a…
We describe a new method to extract parton distribution functions both in the unpolarized and the polarized case, based on a type of neural networks, the Self-Organizing Maps. Initial quantitative results of our Next to Leading Order…
The generalized parton distributions, introduced nearly a decade ago, have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and…
We present the results of our QCD analysis for polarized quark distribution and structure function $xg_1 (x,Q^2)$. We use very recently experimental data to parameterize our model. New parameterizations are derived for the quark and gluon…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
In the framework of the chiral quark-soliton model of the nucleon we investigate the properties of the polarized quark distribution. In particular we analyse the so called anomalous difference between the representations of the quark…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
We suggest a method of constructing gauge invariant quark and gluon distributions that describe an abstract QCD observable and apply this method to analyze angular momentum of a hadron. In addition to the known quark and gluon polarized…
The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…