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 PARTON DENSITIES WITH THE QUARK LINEAR POTENTIAL IN THE STATISTICAL APPROACH

2013 ◽  
Vol 28 (18) ◽  
pp. 1350089 ◽  
Author(s):  
ABOLFAZL MIRJALILI ◽  
MAJID DEHGHANI ◽  
MOHAMMAD MEHDI YAZDANPANAH
Keyword(s):  
Statistical Approach ◽  
Distribution Functions ◽  
Light Front ◽  
Special Method ◽  
Linear Potential ◽  
Parton Distribution Functions ◽  
Statistical Parameters ◽  
Bjorken X ◽  
Theoretical Results ◽  
Good Agreement

The statistical approach is used to calculate the parton distribution functions (PDFs) of the nucleon. At first it is assumed that the partons are free particles and the light-front kinematic variables are employed to extract the Bjorken x-dependence of the PDFs. These PDFs are used to evaluate the combinations of the sea quarks such as [Formula: see text]. As our first attempt to improve the result, we make the statistical parameters to depend on Q2, using different values of Gottfried sum rule. The related results are indicating better behavior by accessing to the PDFs while they contain the Q2 dependence parameters. As a further task and in order to have more improvement in the calculations, a linear potential is considered to describe the quark interactions. The solution of the related Dirac equation yields the Airy function and is considered as a wave function in spatial space. Using the Fourier transformation the wave functions are obtained in momentum space. Based on the light-front kinematic variables and using a special method which we call it "k-method," these functions can be written in terms of the Bjorken x-variable. Following that the statistical features are accompanied with these functions. Considering an effective approach which is used in this paper, we do not need to resort to any extra effects as were assumed in some papers to get proper results for PDFs. The obtained results for [Formula: see text] and the [Formula: see text] ratio, using our effective approach, are in good agreement with the available experimental data and some theoretical results.

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 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.

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.

H1 INCLUSIVE CROSS-SECTION MEASUREMENTS AND AN EXTRACTION OF PARTON DISTRIBUTION FUNCTIONS

2005 ◽  
Vol 20 (21) ◽  
pp. 1557-1571
Author(s):  
BURKARD REISERT
Keyword(s):  
Cross Section ◽  
Parton Distribution ◽  
Inclusive Cross Section ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Single Experiment ◽  
Parton Distributions ◽  
The Standard Model ◽  
Qcd Analysis

An extraction of the parton distributions of the proton by a next-to-leading order QCD fit in the framework of the Standard Model is presented. The fit implements a novel decomposition of the quark species into up- and down-type quark distributions, which is the key to enable a determination of flavor separated parton distributions from a single experiment. The fit is performed on the inclusive unpolarized neutral and charged current cross-section measurements by the H1 collaboration at HERA. The discussion of uncertainties of parton distribution functions is based upon but extends the QCD analysis published together with the H1 data.

UNCERTAINTY OF POLARIZED PARTON DISTRIBUTIONS

2003 ◽  
Vol 18 (08) ◽  
pp. 1203-1210 ◽  
Author(s):  
◽  
M. HIRAI ◽  
Y. GOTO ◽  
T. HORAGUCHI ◽  
H. KOBAYASHI ◽  
...  
Keyword(s):  
Experimental Data ◽  
Parton Distribution ◽  
Gluon Distribution ◽  
Distribution Functions ◽  
Prompt Photon ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Photon Process ◽  
Hessian Method ◽  
Polarized Gluon

Polarized parton distribution functions are determined by a χ2 analysis of polarized deep inelastic experimental data. In this paper, uncertainty of obtained distribution functions is investigated by a Hessian method. We find that the uncertainty of the polarized gluon distribution is fairly large. Then, we estimate the gluon uncertainty by including the fake data which are generated from prompt photon process at RHIC. We observed that the uncertainty could be reduced with these data.

scholarly journals Spin Structure Functions of the Nucleon and Twist-3 Operators in QCD

1997 ◽  
Vol 50 (1) ◽  
pp. 79 ◽  
Author(s):  
Kazuhiro Tanaka
Keyword(s):  
Spin Structure ◽  
Unique Feature ◽  
Anomalous Dimension ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
View Point ◽  
Loop Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
The One

We investigate the twist-3 spin-dependent parton distribution functions hL(x; Q2) and gT (x; Q2). We discuss the physical relevance of the parton distributions from the view point of the factorization theorem in QCD. A unique feature of the ‘measurable’ higher-twist distributions hL and gT is emphasized. We investigate the Q2 -evolution of hL and gT in the framework of the renormalization group and standard QCD perturbation theory. We calculate the anomalous dimension matrix for the twist-3 operators for hL and gT in the one-loop order. The operator mixing among the relevant twist-3 operators, including the operators proportional to the QCD equations of motion, is treated properly in a consistent scheme. Implications for future experiments are also discussed.

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