Quark Distribution Functions Research Articles

Quark counting, Drell-Yan West, and the pion wave function

The relation between the pion's quark distribution function, q(x), its light-front wave function, and the elastic charge form factor, F(Δ2), is explored. The square of the leading-twist pion wave function at a special probe scale, ζH, is determined using models and Poincaré covariance from realistic results for q(x). This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship between q(x) and F(Δ2) is proposed. Published by the American Physical Society 2024

Dense QCD2 with matrix product states

We study one-flavor SU(2) and SU(3) lattice QCD in (1 + 1) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

TMD factorisation for diffractive jets in photon-nucleus interactions

Using the colour dipole picture and the colour glass condensate effective theory, we study the diffractive production of two or three jets via coherent photon-nucleus interactions at high energy. We consider the hard regime where the photon virtuality and/or the transverse momenta of the produced jets are much larger than the saturation momentum Qs of the nuclear target. We show that, despite this hardness, the leading-twist contributions are controlled by relatively large parton configurations, with transverse sizes R ~ 1/Qs, which undergo strong scattering and probe gluon saturation. We demonstrate that these leading-twist contributions admit transverse-momentum dependent (TMD) factorisation, in terms of quark and gluon diffractive TMD distribution functions, for which we obtain explicit expressions from first principles. We go beyond our previous work by evaluating the contributions involving the quark diffractive distributions and by establishing that their DGLAP evolution emerges via controlled calculations within the colour dipole picture. We find the same expression for the quark diffractive TMD in two different processes (semi-inclusive diffraction and the diffractive production of quark-gluon dijets), thus demonstrating its universality.

Flavor asymmetry of light sea quarks in proton: a light-front spectator model

We formulate a light-front spectator model for the proton that incorporates the presence of light sea quarks. In this particular model, the sea quarks are seen as active partons, whereas the remaining components of the proton are treated as spectators. The proposed model relies on the formulation of the light-front wave function constructed by the soft wall AdS/QCD. The model wave functions are parameterized by fitting the unpolarized parton distribution functions of light sea quarks from the CTEQ18 global analysis. We then employ the light-front wave functions to obtain the sea quarks generalized parton distribution functions, transverse momentum dependent parton distributions, and their asymmetries, which are accessible in the upcoming Electron-Ion-Colliders. We investigate sea quarks’ spin and orbital angular momentum contributions to the proton spin.

Intrinsic charm quark valence distribution of the proton

We provide a first quantitative indication that the wave function of the proton contains unequal distributions of charm quarks and antiquarks, i.e., a nonvanishing intrinsic valence charm distribution. A significant nonvanishing valence component cannot be perturbatively generated; hence, our results reinforce previous evidence that the proton contains an intrinsic (i.e., not radiatively generated) charm quark component. We establish our result through a determination of the parton distribution functions of charm quarks and antiquarks in the proton. We propose two novel experimental probes of this intrinsic charm valence component: D-meson asymmetries in Z+c-jet production at the LHCb experiment and flavor-tagged structure functions at the Electron-Ion Collider. Published by the American Physical Society 2024

Heavy quark diffusion and radiation at intermediate momentum

Heavy quark diffusion and radiation are discussed in an intermediate-momentum regime where finite mass effects can be significant. Diffusion processes are described in the Fokker-Planck approximation for soft momentum transfer, while radiative ones are taken into account by nearly collinear gluon emission from a single scattering in the Boltzmann equation. There are also radiative corrections to the transverse momentum diffusion coefficient, which are O(g2) suppressed more than the leading-order diffusion coefficient but logarithmically enhanced. Numerical results show that the heavy quark distribution function depends on the energy loss mechanism so that the medium modifications by diffusion and radiation are distinguishable. The nuclear modification factor is estimated by employing the heavy quark diffusion coefficient which is constrained by lattice quantum chromodynamics data. The suppression factor exhibits a transition from diffusion at low momentum to radiation at high momentum. The significance of the radiative effects at intermediate momentum depends on the diffusion coefficient and the running coupling constant. Published by the American Physical Society 2024

Developing predictions for pion fragmentation functions

Exploiting crossing symmetry, the hadron scale pion valence quark distribution function is used to predict the kindred elementary valence quark fragmentation function (FF). This function defines the kernel of a quark jet fragmentation equation, which is solved to obtain the full pion FFs. After evolution to a scale typical of FF fits to data, the results for quark FFs are seen to compare favourably with such fits. However, the gluon FF is markedly different. Notably, although FF evolution equations do not themselves guarantee momentum conservation, inclusion of a gluon FF which, for four quark flavours, distributes roughly 11% of the total light-front momentum fraction, is sufficient to restore momentum conservation under evolution. Overall, significant uncertainty is attached to FFs determined via fits to data; hence, the features of the predictions described herein could potentially provide useful guidance for future such studies.

Impact of charge symmetry breaking on gluon and sea quark distributions in the pion and kaon

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the [Formula: see text] and [Formula: see text] quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of [Formula: see text][Formula: see text]GeV2. The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of [Formula: see text] at [Formula: see text][Formula: see text]GeV2 are, respectively, estimated by 1.3% and 2.0% at [Formula: see text] in comparison with those for [Formula: see text], while those for the kaon are approximately about 0.3% and 0.5% at [Formula: see text], respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.

Pion parton distribution functions with the nonrelativistic constituent quark model

We calculate the valence quark distribution functions of the π meson using the non-relativistic chiral constituent quark model. The π wave function is obtained by solving the two-body Schrödinger equation within the framework of constituent quark model. We transform the π wave function from the rest frame to the light cone or infinite momentum frame based on the Lorentz boost. The valence quark distributions at the initial evolution scale are obtained. The QCD evolution is given with the DGLAP equations with parton-parton recombination corrections. With tuning the valence up (down) quark mass to 70 MeV, the calculated valence up quark distributions at Q2=20 GeV2 are in good agreement with the E615 experimental data. The structure functions F2π(x,Q2) of pion are also calculated which consist with the H1 experimental data. The proposed mechanisms here could be also used to study other hadrons.

Searching for a 0(980)-meson parton distribution function

In this paper, we calculate the scalar a 0(980)-meson leading-twist wave function by using the light-cone harmonic oscillator model (LCHO), where the model parameters are determined by fitting the ξ-moments of its light-cone distribution amplitudes. Then, the a 0(980)-meson leading-twist light-cone distribution amplitudes with three different scales ζ = (1.0, 2.0, 5.2)GeV are given. After constructing the relationship between the a 0(980)-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wave function, we exhibit the and with different scales. Furthermore, we also calculate the Mellin moments of the a 0(980)-meson’s valence quark distribution function with n = (1, 2, 3), i.e. , and . Finally, the scale evolution for the ratio of the Mellin moments are presented.

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.

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F2nF2p for mirror nuclei He3 and H3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions ${x}_{B}\ensuremath{\rightarrow}0$ and ${x}_{B}\ensuremath{\rightarrow}1$. The extrapolated ${F}_{2}$ ratio as quark momentum fraction ${x}_{B}\ensuremath{\rightarrow}1$ is $\frac{{F}_{2}^{n}}{{F}_{2}^{p}}\ensuremath{\rightarrow}0.4\ifmmode\pm\else\textpm\fi{}0.05$ and this value is compared to theoretical predictions. The extrapolated ratio when ${x}_{B}\ensuremath{\rightarrow}0$ favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high-${x}_{B}$, the proton quark distribution function ratio $d/u$ is derived from the ${F}_{2}$ ratio and found to be $d/u\ensuremath{\rightarrow}1/6$. Our extrapolated values for both the $\frac{{F}_{2}^{n}}{{F}_{2}^{p}}$ ratio and the $d/u$ parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. One such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated ${F}_{2}$ ratio at ${x}_{B}=1$.

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.

T-even transverse momentum dependent gluon fragmentation functions in a spectator model

We present a model calculation of transverse momentum dependent (TMD) gluon fragmentation functions in both spin-1/2 and spin-0 hadrons. Our approach is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle. So far, such spectator models have been restricted to TMD distribution functions of quarks and gluon as well TMD fragmentation function of quarks. The effective coupling between the gluon-hadron-spectator system is described by a vertex composed of two form factors. We obtain analytical expressions for the four T-even TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and kT-dependence of the fragmentation functions. Our analysis reveals the non-negligible impact of these fragmentation functions, which could potentially be explored in forthcoming experimental measurements.

Detailed study of quark-hadron duality in spin structure functions of the proton and neutron

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross section. The overlap region between these two pictures, where both yield similar predictions, is referred to as quark-hadron duality and has been extensively studied in reactions involving unpolarized hadrons. Some limited information on this phenomenon also exists for polarized protons, deuterons, and $^{3}\mathrm{He}$ nuclei, but not yet for neutrons.Purpose: In this paper, we present comprehensive and detailed results on the correspondence between the extrapolated deep inelastic structure function ${g}_{1}$ of both the proton and the neutron with the same quantity measured in the nucleon resonance region. Thanks to the fine binning and high precision of our data, and using a well-controlled perturbative QCD (pQCD) fit for the partonic prediction, we can make quantitative statements about the kinematic range of applicability of both local duality and global duality.Method: We use the most updated QCD global analysis results at high $x$ from the Jefferson Lab Angular Momentum Collaboration to extrapolate the spin structure function ${g}_{1}$ into the nucleon resonance region and then integrate over various intervals in the scaling variable $x$. We compare the results with the large data set collected in the quark-hadron transition region by the CLAS Collaboration, including, for the first time, deconvoluted neutron data, integrated over the same intervals. We present this comparison as a function of the momentum transfer ${Q}^{2}$.Results: We find that, depending on the integration interval and the minimum momentum transfer chosen, a clear transition to quark-hadron duality can be observed in both nucleon species. Furthermore, we show, for the first time, the approach to scaling behavior for ${g}_{1}$ measured in the resonance region at sufficiently high momentum transfer.Conclusions: Our results can be used to quantify the deviations from the applicability of pQCD for data taken at moderate energies and can help with extraction of quark distribution functions from such data.

Twist-2 light-quark distribution functions in a singly heavy baryon in the largeNclimit

AbstractA singly heavy baryon can be considered as a state consisting of the Nc − 1 light valence quarks that create the pion mean field in the large Nc limit. In the limit of the infinitely heavy quark mass, a heavy quark inside a singly heavy baryon is regarded as a mere static color source. It is required only to make the singly heavy baryon a color singlet. Thus, the Nc − 1 valence quarks govern quark dynamics inside the singly heavy baryon. Within this pion mean field framework, we investigate the twist-2 unpolarized and longitudinally polarized light-quark distribution functions inside charmed and bottom baryons at a low renormalization point. We observe that the light quarks inside a heavy baryon carry less momentum than those inside a nucleon. This feature is more prominent as the heavy quark mass increases. We discuss the baryon sum rule, momentum sum rule, and the Bjorken spin sum rule for singly heavy baryons. We also discuss the inequality conditions for the quark distribution functions. In addition, we present the results for the light-quark quasi-distribution functions.

D ∗ jet fragmentation function paradox and combination mechanism

In the framework of the perturbative Quantum Chromodynamics factorization, the production of a hadron includes contributions from fragmentation as well as combination, with the latter being of higher twist. In particular, the heavy meson production can be via the combination of a heavy quark with a light one, and the cross section can be factorized to be the convolution of the combination matrix element, the light quark distribution function, and the hard partonic sub-cross section of the heavy quark production. The partonic distribution and the combination matrix element are functions of a scaling variable, respectively, which is the momentum fraction of the corresponding quark with respect to the heavy meson. We studied the D *± production in jet via combination in pp collision at the LHC. The total result is comparable with the experimental data. The combination matrix elements can be further studied in various hadron production processes.

Kinetics of the Chiral Phase Transition in a Quark–Meson \(\sigma \) Model

Using the two-particle irreducible (2PI) $\Phi$-functional formalism for self-consistent approximations of a linear-$\sigma$ model for quarks and mesons in and out of equilibrium, the build-up of fluctuations of net-baryon number during the time evolution of an expanding fireball is studied within a kinetic theory for the order parameter ($\sigma$ field) and quark distribution functions. Initializing the system with purely Gaussian fluctuations a fourth-order cumulant is temporarily built up due to the evolution of the $\sigma$-field. This is counterbalanced, however, by the dissipative evolution due to collisions between quarks, anti-quarks, mesons, and the mean field, depending on the speed of the fireball expansion.

Semi-inclusive diffractive deep inelastic scattering at small x

Inspired by a recent study of Iancu, Mueller and Triantafyllopoulos [1] and earlier papers by Golec-Biernat and Wusthoff [2,3], we propose semi-inclusive diffractive deep inelastic scattering (SIDDIS) to investigate the gluon tomography in the nucleon and nuclei at small-$x$. The relevant diffractive quark and gluon parton distribution functions (DPDF) can be computed in terms of the color dipole S-matrices in the fundamental and adjoint representations, respectively. Novel correlations from the gluon tomography in the dipole S-matrix can be experimentally studied through the DPDFs in these processes at the future electron-ion collider (EIC).

Analytical solution of the DGLAP equations using the generating function method

Recently, we generated the evolution equations of the parton distribution functions (PDF) usually used in the hadrons phenomenology by the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space. The evolution equations obtained from the stochastic modeling are the same as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, but they are acquired by a mathematical procedure based on the non-equilibrium statistical mechanics and Markov processes. In this paper, we present a new analytical solution of the parton evolution equation (DGLAP equation) for the non-singlet quark distribution function using the generating function method. This method is a general technique for solving the master equation of Markov processes.