Covariant Parton Model Research Articles

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Unpolarized transverse-momentum-dependent sea quark asymmetries of light nuclei in nonperturbative QCD

We investigate the transverse-momentum dependence of sea quark asymmetries in helium and deuteron nuclei. Accordingly, we calculate the nuclear sea quark distributions, in the first step, based on the modified chiral quark exchange formalism at the low Q 2 scale (Q 2 = 0.35 GeV2) in the nonperturbative region of quantum chromodynamics. In this formalism, the sea quark distributions are not symmetric because of chiral symmetry breaking. In the next step, we compute the transverse-momentum dependence of sea quark distributions using the covariant parton model, in which the unpolarized transverse-momentum-dependent (TMD) quark distribution functions are related to corresponding integrated ones. Finally, we obtain TMD quark–antiquark asymmetry of the strange sea for 3 He and deuteron, and also asymmetry for 3 He. To study the European Muon Collaboration (EMC) effect in the 3 He nucleus, we determine the ratio of the TMD strange sea asymmetries of 3 He and deuteron.

Quark-model relations among TMDs in the parton model

The covariant parton model (CPM) is a consequent application of the parton model concept to the nucleon structure. In this model, there is a choice to put quarks either in a pure-spin state or in a mixed-spin state. We show that the mixed-spin version of the CPM does not support the quark-model relations among transverse momentum dependent parton distributions (TMDs) which were shown to hold in a large class of quark models. One can enforce the quark-model relations to be valid in the CPM by imposing a condition which is equivalent to putting the quarks in a pure-spin state. This gives a complementary perspective on the connection of the pure- and mixed-spin state CPM versions, and provides a fresh view on the question whether the quark-model relations could be realized in QCD as "approximate relations" with some useful numerical accuracy.

Nucleon spin structure functions, considering target mass correction, and higher twist effects at the NNLO accuracy and their transverse momentum dependence

Using recent and updated world data on polarized structure functions ${g}_{1}$ and ${g}_{2}$ we perform an analysis based on quantum chromodynamics (QCD) as a theory of strong interactions at next-next-to-leading-order accuracy. We include also target mass corrections and higher twist effects to get more precise results in our fitting procedure. To confirm the validity of our fitting results several sum rules are examined and we do a comparison for them with results from other models. In our analysis we employ the Jacobi polynomials approach to obtain analytical solutions of the Dokshitzer-Gribov-LipatovAltarelli-Parisi evolution equations for parton distribution functions (PDFs). Using the extracted PDFs from our data analysis as input, we also compute the $x$- and ${\mathbf{p}}_{T}$-dependence of some transverse momentum dependence PDFs in polarized case, based on covariant parton model. These functions are naively even time-reversal at twist-two approximation. The results for transverse momentum dependences indicate proper and acceptable behavior with respect to what are presented in other literatures.

Structure of the nucleon at leading and subleading twist in the covariant parton model

The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.

The role of transverse momentum on the nuclear valence and sea quark distribution functions

We investigate the transverse momentum dependence of valence and sea quark distribution functions of light asymmetric nuclei (^{3}He and ^{7}Li). To this end, we first calculate the valence and sea distributions of these nuclei applying a parametrization method in which the parton distribution functions (PDFs) of nucleus are related to those of free nucleon via a weight function that contains the nuclear modifications. Then we obtain the unpolarized transverse momentum dependent (TMD) PDFs of the nucleus using the covariant parton model (CPM) approach. We also compute the valence and sea quark distributions ratios of ^{3}He and ^{7}Li to those of deuteron and present the results with respect to x (Bjorken variable) at fixed values of transverse momentum. It is found that these ratios shift to the larger values of x by increasing the transverse momentum value as expected and they are not transverse momentum dependent in large x region.

Sivers effect in single spin asymmetry based on the covariant parton model

Sivers effect is describing the correlation between the transverse polarization of nucleon and the transverse momentum, [Formula: see text], of its unpolarized constituent partons. This effect is an outstanding subject and in this regard, a great deal in recent years has been considered from experimental and phenomenological points of view. It also plays an essential role to extend our understanding from nucleon structure. Semi-inclusive DIS (SIDIS) process provides us an opportunity to access to Sivers function which is dependent on transverse momentum of partons. In this paper, for the first time the covariant parton model is used to deliver us the [Formula: see text] and [Formula: see text] dependence part of Sivers function. Based on this model, this combinatory dependence is arising out from the HERAPDF parametrization group. In this paper the other required parametrized functions in Sivers function is also changed with respect to Ref. 1. The unknown parameters which exist in Sivers function can be extracted, doing a global fit over the recent available experimental data, including HERMES, COMPASS and JLAB collaborations for the single spin asymmetry (SSA) in [Formula: see text] and [Formula: see text] meson production as well as kaon production to constrain the evolved strange quark. This is done, considering advanced mathematical manipulations to overcome the difficulties which exist to compute the required multiple integrals and finally employing the CERN MINIUTE program to do a global fit. Our results for SSA are in good agreement with the available experimental data. For more confirmation a comparison between our results and the ones from Ref. 2 is also done.

Mass and energy dependence of the transverse momentum densities in covariant parton model

The parton densities which are dependent on transverse momentum, open a way to understand better the structure of quarks and gluons in a more complete way. We are investigating a method based on the covariant quark model which enables us to extract the transverse momentum dependent (TMD) densities from the usual parton densities which are just dependent on the longitudinal momentum. In continuation, we obtain the dependence of the TMDs on binding energy and the mass of quarks. We do some calculations to obtain the TMDs in the unpolarized case while the mass and binding energy of partons are varying. Considering these effects, the results for TMDs are in good agreement with the results of the recent related models.

The polarized TMDs in the covariant parton model approach

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 of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDF g1q(x) as input we predict the x- and pT-dependence of all polarized twist-2 naively time-reversal even (T-even) TMDs.

Relation between transverse momentum dependent distribution functions and parton distribution functions in the covariant parton model approach

We derive relations between 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 of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDFs f_1(x) and g_1(x) as input we predict the x- and pT-dependence of all twist-2 T-even TMDs.

Generalized Cahn effect and parton 3D motion in a covariant approach

The Cahn effect and the unintegrated unpolarized parton distribution function $f_{1}^{q}(x,\mathbf{p}_{T})$ are studied in a covariant approach. The Cahn effect is compared with some other effects due to the parton intrinsic motion. The comparison suggests that the present understanding of parton transverse momenta and intrinsic motion in general is still rather incomplete. The new relation for $f_{1}^{q}(x,\mathbf{p}_{T})$ is obtained in the framework of the covariant parton model from which a prediction for this distribution function follows.

Transverse momentum dependent distribution functions in a covariant parton model approach with quark orbital motion

Transverse parton momentum dependent distribution functions (TMDs) of the nucleon are studied in a covariant model, which describes the intrinsic motion of partons in terms of a covariant momentum distribution. The consistency of the approach is demonstrated, and model relations among TMDs are studied. As a by-product it is shown how the approach allows to formulate the nonrelativistic limit.

Twist-2 contributions to polarized structure functions and new sum rules

The twist-2 contributions to the polarized structure functions in deep inelastic lepton-hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A new relation between two structure functions leading to a sequence of new sum rules is found. The light quark mass corrections to the structure functions are derived in lowest order QCD.

A Covariant Parton Model for Heavy Quark Fragmentation

The effect of the quark mass on the fragmentation of heavy quarks is examined on the basis of a covariant parton model. The distributions of D*, B and other hadrons containing c or b quark are described by the model with reasonable values of mass parameters. The model is also applied to the t quark fragmentation which is sensitive to the deceleration by gluon and photon radiations before the heavy hadron emission. The fragmentation properties of heavy quarks may contain very important clues to understand quark-gluon hadronization dynamics, because the heavy flavor is created almost only in the hard interaction and it can be traced in a heavy hadron after the hadronization. Experimental importance of the heavy quark fragmentation is also without saying for the detection of new quarks and studies of heavy hadrons. As the data on e+ e- annihilation and neutrino induced reactions have recently accumulated very rapidly/) it is now the time to start detailed studies from theoretical side. 2 )-6) In this paper, we study the fragmentation distributions of charm mesons, B and other heavy hadrons in the framework of the covariant parton model,7)-9) which naturally embodies the mass effect of heavy quarks in the fragmentation. The simplest version of our model is able to describe the distribution of D* and other hadrons with reasonable values of mass parameters. Although the model is somewhat similar to the popular one parameter model of Peterson et a1. 4 ) based on the naive parton model with sharp transver­ se momentum cutoff, there exists a clear difference in the formula and its construction. The difference between the two can be easily seen by considering the case when only the light quarks and hadrons are concerned. The formulation is given in the next section, and the comparison with the data is given in § 3. Discussion on the basis of the formula and related approaches are given in § 4.

The influence of α-clusters on deep inelastic lepton-nucleus scattering

The important difference between deep inelastic muon scattering off iron and that off deuterium, is explained, within the framework of our covariant parton model, by a reduced Fermi motion of the quarks bound in iron. It is attributed to a fraction g cℓ of the bound nucleons forming α-clusters. If the twelve valence quarks can move freely through clusters of the size of a free α-particle, the EMC data are well reproduced with g cℓ = (20 ± 5)%.

On a covariant quark parton model with confinement

We examine the standard-parton-model unitarity relations in the context of a covariant quark parton model which incorporates confinement in a very naive way. We also make a deeper analysis than was made in recent papers by the same authors about the sensitivity of the baryonic structure functions to the confinement mechanism. This new analysis shows that, contrarily to what was stated in those papers, one can expect, because of the confinement, changes in the behaviour of the baryonic structure functions similar to those already found for the meson structure functions. However, because of the different quark content of mesons and baryons, we have not found any connection between the size of these changes for mesons and baryons.

Is thex→1Behavior of the Deep-Inelastic Structure Functions in the Bjorken Limit Sensitive to the Confinement Mechanism?

This Letter incorporates confinement to the covariant parton model and investigates its consequences on the qualitative behavior of the deep-inelastic structure functions in the Bjorken limit. It is proved that this incorporation does not change the known behavior of the baryonic structure functions, but it leads, for mesons, to a nonvanishing value of ..nu..W/sub 2/(..omega../sup -1/) and W/sub 1/(..omega../sup -1/) in the ..omega../sup -1/..-->..1 limit and to a violation of the Callan-Gross relation.

Structure of hadron structure functions

We investigate the comparison of the shapes, as functions of $x$, of nonsinglet structure functions of pions and nucleons, ${F}_{\ensuremath{\pi},N}(x, {Q}^{2})$. We argue that we can predict (to leading twist, all orders of quantum-chromodynamic perturbation theory) the shape of a pion structure function in terms of the observed shape of the nucleon structure function at the same ${Q}^{2}$. The uncertainties due to our ignorance of the details of bound-state dynamics are at the 20% level. Our technology is to exploit in detail the relationship between two approaches to the description of structure functions: the operator-product expansion and the covariant parton model.

Meson structure function in the context of the covariant parton model

If in the context of the covariant parton model one takes into account the differences the quark model establishes between baryons and mesons, one can obtain, in turn, essential differences between baryonic and mesonic structure functions. In particular, if the sum of the free masses of the valence quarks in a meson is less than the meson mass, M q +M q ′ <M m , the structure functions do not vanish at ω −1=1, while for baryons our analysis does not add anything new to the well-known results on their structure functions. Also, if M m >M q +M q ′ , the Callan-Gross relation is violated to an extent dependent on the parametrization of the residue functions of the pole contributions to the quark-meson amplitudes. Our formalism prevents a meson creating a quark-antiquark pair on-mass-shell when M m>M q+M q ′ .

Asymptotic power laws for hadron calorimeter experiments

This is a study of asymptotic QCD predictions for collisions in which a finite fraction of the available energy is carried by hadrons into an angular region Ω whose complement is Ω a or Ω b or Ω a UΩ b , Ω a being fixed cones about the directions of motion of the initial particles. Apart from slow (logarithmic) corrections the asymptotic power laws derived from the covariant parton model appear to be justified provided certain conditions on Ω a and/or Ω b and the energy deposited in them are met.