scholarly journals Theory and applications of parton pseudodistributions

2020 ◽  
Vol 35 (05) ◽  
pp. 2030002 ◽  
Author(s):  
A. V. Radyushkin
Keyword(s):  
Time Distribution ◽  
Valence Quark ◽  
Basic Feature ◽  
Distribution Functions ◽  
Ultraviolet Divergence ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Gauge Link ◽  
Generalized Parton Distributions ◽  
Lorentz Invariants

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

scholarly journals Generalized Parton Distributions and the Structure of the Hadrons

2018 ◽  
Vol 47 ◽  
pp. 1860099
Author(s):  
O. V. Selyugin
Keyword(s):  
Form Factors ◽  
Distribution Functions ◽  
Electromagnetic Form Factors ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Hadron Interaction ◽  
High Energies ◽  
Generalized Parton Distributions ◽  
Momentum Transfer Dependence ◽  
The Impact

The dependence of the hadron interaction on its structure is examined in the framework of the generalized parton distributions (GPDs). The [Formula: see text] dependence of the GPDs is determined by the parton distribution functions (PDFs), which were obtained from the deep inelastic scattering. The analysis of the whole sets of experimental data on the electromagnetic form factors of the proton and neutron with taking into account many forms of PDFs, obtained by the different Collaborations, make it possible to obtain the special momentum transfer dependence of the GPDs. This permits us to obtain the electromagnetic and gravitomagnetic form factors of the nucleons. The impact parameter dependence of the proton and neutron charge and matter densities is examined. The elastic hadron scattering at high energies was analyzed in the framework of the model that takes into account both these form factors (electromagnetic and gravitomagnetic).

Q2-DEPENDENCE OF THE STATISTICAL PARTON DISTRIBUTIONS IN THE VALON APPROACH

2012 ◽  
Vol 27 (16) ◽  
pp. 1250083 ◽  
Author(s):  
S. SOHAILY ◽  
M. M. YAZDANPANAH ◽  
A. MIRJALILI
Keyword(s):  
Statistical Approach ◽  
Chemical Potential ◽  
Sum Rules ◽  
Valence Quark ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Statistical Parameters ◽  
Parton Distributions ◽  
Accessible Volume ◽  
Analytic Expressions

We employ the statistical approach to obtain the nucleon parton distributions. Statistical distributions are considered as well for partons in the valon model in which a nucleon is assumed to be a state of three valence quark clusters (valon). Analytic expressions of the x-dependent of parton distribution functions (PDFs) in the valon model are obtained statistically in the whole x region [0, 1] in terms of the statistical parameters such as temperature, chemical potential and accessible volume. Since PDFs are obtained by taking the required sum rules including Gottfried sum rule at different energy scales, the Q2-dependence of these parameters can be obtained. Therefore the parton distributions as a function of Q2will be resulted. To make the calculations more precise, we extend our results to contain three flavors rather than two light u and d quarks.

scholarly journals DIFFRACTIVE PHENOMENA

2002 ◽  
Vol 17 (23) ◽  
pp. 3204-3219
Author(s):  
GIUSEPPE IACOBUCCI
Keyword(s):  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Hadronic Interactions ◽  
Theoretical Approaches ◽  
Generalized Parton Distributions ◽  
Diffractive Scattering ◽  
Target Frame ◽  
Dipole Picture ◽  
Shed Light

The most recent theoretical and experimental results in the field of diffractive scattering are reviewed. A parallel between the two current theoretical approaches to diffraction, the DIS picture in the Breit frame and the dipole picture in the target frame, is given, accompanied by a description of the models to which the data are compared. A recent calculation of the rescattering corrections, which hints at the universality of the diffractive parton distribution functions, is presented. The concept of generalized parton distributions is discussed together with the first measurement of the processes which might give access to them. Particular emphasis is given to the HERA data, to motivate why hard diffraction in deep inelastic scattering is viewed as an unrivalled instrument to shed light on the still obscure aspects of hadronic interactions.

scholarly journals EXTRACTION OF PARTON DISTRIBUTIONS FROM LATTICE QCD

2003 ◽  
Vol 18 (38) ◽  
pp. 2681-2697 ◽  
Author(s):  
W. DETMOLD ◽  
W. MELNITCHOUK ◽  
A. W. THOMAS
Keyword(s):  
Finite Number ◽  
Lattice Qcd ◽  
Parton Distribution ◽  
Valence Quark ◽  
Physical Region ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Parton Distributions

We review the calculation of moments of both the polarized and unpolarized parton distribution functions of the nucleon in lattice QCD, and in particular their extrapolation to the physical region. We also discuss the reconstruction of the x dependence of the valence quark distributions in the nucleon from a finite number of lattice moments.

PARTON DISTRIBUTION FUNCTIONS AND THE QCD-IMPROVED PARTON MODEL — AN OVERVIEW

1987 ◽  
Vol 02 (04) ◽  
pp. 1369-1387 ◽  
Author(s):  
Wu-Ki Tung
Keyword(s):  
Parton Distribution ◽  
Particle Production ◽  
Heavy Particle ◽  
Parton Model ◽  
Distribution Functions ◽  
Collider Physics ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
First Order ◽  
Small X

Some non-trivial features of the QCD-improved parton model relevant to applications on heavy particle production and semi-hard (small-x) processes of interest to collider physics are reviewed. The underlying ideas are illustrated by a simple example. Limitations of the naive parton formula as well as first order corrections and subtractions to it are dis-cussed in a quantitative way. The behavior of parton distribution functions at small x and for heavy quarks are discussed. Recent work on possible impact of unconventional small-x behavior of the parton distributions on small-x physics at SSC and Tevatron are summarized. The Drell-Yan process is found to be particularly sensitive to the small x dependence of parton distributions. Measurements of this process at the Tevatron can provide powerful constraints on the expected rates of semi-hard processes at the SSC.

scholarly journals ON THE $\bar{d}/\bar{u}$ ASYMMETRY AND PARTON DISTRIBUTIONS

2002 ◽  
Vol 17 (02) ◽  
pp. 269-278
Author(s):  
ALEJANDRO DALEO ◽  
CARLOS A. GARCIA CANAL ◽  
GABRIELA A. NAVARRO ◽  
RODOLFO SASSOT
Keyword(s):  
Parton Distribution ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
The Impact

We discuss the impact of different measurements of the [Formula: see text] asymmetry in the extraction of parametrizations of parton distribution functions.

Color Entanglement in Hadronic Processes for Transverse Momentum Dependent Parton Distribution Functions

2015 ◽  
Vol 37 ◽  
pp. 1560022
Author(s):  
M. G. A. Buffing ◽  
P. J. Mulders
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Initial State ◽  
Color Flow ◽  
Transverse Momentum Dependent ◽  
Gauge Link ◽  
Azimuthal Asymmetries ◽  
Different Parts

In the description of protons, we go beyond the ordinary collinear parton distribution functions (PDFs), by including transverse momentum dependent PDFs (TMDs). As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when looking at azimuthal asymmetries. Hadronic processes require the inclusion of gluon contributions forming the gauge links, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state, such as Drell-Yan (DY), the gauge links from different parts of the process get entangled. We show that in color disentangling this gauge link structure, one becomes sensitive to this color flow. After disentanglement, particular combinations of TMDs will require a different numerical color factor than one naively might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as DY.

scholarly journals Wigner Distributions of Quark

2016 ◽  
Vol 40 ◽  
pp. 1660055
Author(s):  
Asmita Mukherjee ◽  
Sreeraj Nair ◽  
Vikash Kumar Ojha
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Phase Space Distribution ◽  
Generalized Parton Distributions ◽  
Wigner Distributions ◽  
Classical Phase Space

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

scholarly journals Computation of parton distributions from the quasi-PDF approach at the physical point

2018 ◽  
Vol 175 ◽  
pp. 14008 ◽  
Author(s):  
Constantia Alexandrou ◽  
Simone Bacchio ◽  
Krzysztof Cichy ◽  
Martha Constantinou ◽  
Kyriakos Hadjiyiannakou ◽  
...  
Keyword(s):  
Pion Mass ◽  
Distribution Functions ◽  
Matrix Elements ◽  
Parton Distribution Functions ◽  
Physical Point ◽  
Parton Distributions ◽  
The Matrix ◽  
First Results ◽  
Perturbative Renormalization ◽  
Vector Combination

We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with Nf = 2 twisted mass cloverimproved fermions and a proton boosted with momentum [see formula in PDF] = 0.83 GeV. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI’ scheme, following the non-perturbative renormalization prescription recently developed by our group.

scholarly journals A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

2019 ◽  
Vol 2019 ◽  
pp. 1-68 ◽  
Author(s):  
Krzysztof Cichy ◽  
Martha Constantinou
Keyword(s):  
Lattice Qcd ◽  
Cross Sections ◽  
Light Cone ◽  
Distribution Functions ◽  
Strong Interactions ◽  
Parton Distribution Functions ◽  
Hadronic Tensor ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
The Rich

Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal nonperturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transverse momentum dependent parton distributions (TMDs), and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice. In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasidistributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasidistribution approach, such as renormalization, matching to light-cone distributions, and lattice techniques. In addition to a thorough discussion of quasidistributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudodistributions, OPE without OPE, and good lattice cross-sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.

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