Quark Distribution Functions Research Articles

Sivers effect for pion and kaon production in semi-inclusive deep inelastic scattering

We study the Sivers effect in the transverse single spin asymmetries (SSA) for pion and kaon production in semi-inclusive deep inelastic scattering (SIDIS) processes. We perform a fit of \(\ensuremath A^{\sin(\phi_h-\phi_S)}_{UT}\) which, by including recent high-statistics experimental data for pion and kaon production from HERMES and COMPASS Collaborations, allows a new determination of the Sivers distribution functions for quarks and antiquarks with u , d and s flavours. Estimates for forthcoming SIDIS experiments at COMPASS and JLab are given.

Longitudinal parity-violating asymmetry in hadronic decays of weak bosons in polarized proton collisions

We investigate the possible measurement of parity-violating spin asymmetries in jet pair production in proton-proton collisions at the Brookhaven Relativistic Heavy Ion Collider (RHIC), with the goal to constrain longitudinally polarized quark and antiquark distribution functions. A measurable asymmetry could be observed in the vicinity of the massive weak $W$ boson resonance, where the parity-violating signal appears above the parity-conserving background and is enhanced by interference of the strong and electroweak production amplitudes. We discuss the potential for such measurements, perhaps the first opportunity to measure a parity-violating asymmetry in proton-proton collisions at RHIC. Sensitivity of this measurement to the polarization of down-type antiquarks is demonstrated.

Next-to-next-to-leading order QCD contributions to the flavor nonsinglet sector ofF2(x,Q2)

We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function ${F}_{2}(x,{Q}^{2})$. New parameterizations are derived for the nonsinglet quark distributions for the kinematic wide range of $x$ and ${Q}^{2}$. The analysis is based on the Jacobi polynomials expansion of the structure function. The higher twist contributions of proton and deuteron structure function are obtained in the large $x$ region. Our calculations for nonsinglet unpolarized quark distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$ and ${\ensuremath{\alpha}}_{s}({M}_{z}^{2})$ are determined.

Antihyperon polarization in high energyppcollisions with polarized beams

We study the polarization of the anti-Lambda particle in polarized high energy pp collisions at large transverse momenta. The anti-Lambda polarization is found to be sensitive to the polarization of the anti-strange sea of the nucleon. We make predictions using different parameterizations of the polarized quark distribution functions. The results show that the measurement of longitudinal anti-Lambda polarization can distinguish different parameterizations, and that similar measurements in the transversely polarized case can give some insights into the transversity distribution of the anti-strange sea of nucleon.

Measurement of transversity signals in two hadron production at COMPASS

The quark structure of the nucleon at the twist two level can be completely described with three quark distribution functions: the spin averaged distribution function q(x), the helicity distribution Δq(x) and the transverse spin distribution ΔTq(x). This last function, referred to as transversity, is chiral-odd and can only be measured in combination with another chiral-odd function. COMPASS is a fixed target experiment at the CERN SPS M2 beamline. Its target (6LiD) can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c µ+-beam. In transverse configuration ΔTq(x) can be measured in semi-inclusive deep-inelastic scattering (SIDIS), requiring the detection of hadronic products. A rather new probe of the transverse spin distribution function ΔTq(x) is the measurement of two hadron production, introducing the chiral odd interference fragmentation function H1∢(z, Mh2). Results are presented for the years 2003–2004 including particle identification by using the information of the RICH detector. The analysis was performed using all positive/negative charged pairs and z-ordered pairs.

Evidence for a transverse single-spin asymmetry in leptoproduction of π+π−pairs

A single-spin asymmetry was measured in the azimuthal distribution of pi(+)pi(-) pairs produced in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target. For the first time, evidence is found for a correlation between the transverse target polarization and the azimuthal orientation of the plane containing the two pions. The corresponding single-spin asymmetry is expected to be related to the product of the little-known quark transversity distribution function and an unknown naive-T-odd chiral-odd dihadron fragmentation function.

Transverse-momentum-dependent parton distribution function and jet transport in a nuclear medium

We show that the gauge-invariant transverse-momentum-dependent (TMD) quark distribution function can be expressed as a sum of all higher-twist collinear parton matrix elements in terms of a transport operator. From such a general expression, we derive the nuclear broadening of the transverse-momentum distribution. Under the maximal two-gluon correlation approximation, in which all higher-twist nuclear multiple parton correlations with the leading nuclear enhancement are given by products of twist-two nucleon parton distributions, we find the nuclear transverse-momentum distribution as a convolution of a Gaussian distribution and the nucleon TMD quark distribution. The width of the Gaussian, or the mean total transverse-momentum broadening squared, is given by the path integral of the quark transport parameter ${\stackrel{^}{q}}_{F}$ which can also be expressed in a gauge-invariant form and is given by the gluon distribution density in the nuclear medium. We further show that contributions from higher-twist nucleon gluon distributions can be resummed under the extended adjoint two-gluon correlation approximation and the nuclear transverse-momentum distribution can be expressed in terms of a transverse-scale-dependent quark transport parameter or gluon distribution density. We extend the study to hot medium and compare to dipole model approximation and $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory in the strong coupling limit. We find that multiple gluon correlations become important in the strongly coupled system such as $\mathcal{N}=4$ SYM plasma.

Predictions of the QCD Parton Model

The QCD parton model allows to establish approximate relations among transverse momentum dependent quark distribution functions and, simultaneously, to fix an energy scale, involved in the parametrization of the correlator, which determines the Q 2 dependence of the azimuthal asymmetries in inclusive reactions, like SIDIS and Drell-Yan. Some of the present data support such model predictions. We suggest further measurements of asymmetries and an alternative way of determining (approximately) the proton transversity.

X-dependence of the quark distribution functions in the χCQMconfig

Chiral constituent quark model with configuration mixing (χCQMconfig) is known to provide a satisfactory explanation of the “proton spin problem” and related issues. In order to enlarge the scope of χCQMconfig, we have attempted to phenomenologically incorporate x-dependence in the quark distribution functions. In particular, apart from calculating valence and sea quark distributions qval(x) and q(x), we have carried out a detailed analysis to estimate the sea quark asymmetries d(x)-ū(x), d(x)/ū(x) and $\frac{\overline{d}(x)-\overline{u}(x)}{u(x)-d(x)}$ as well as spin independent structure functions F2 p(x)-F2 n(x) and F2 n(x)/F2 p(x) as functions of x. We are able to achieve a satisfactory fit for all the above mentioned quantities simultaneously. The inclusion of effects due to configuration mixing have also been examined in the case F2 p(x)-F2 n(x) and F2 n(x)/F2 p(x) where the valence quark distributions dominate and it is found that it leads to considerable improvement in the results. Further, the valence quark structure has also be tested by extrapolating the predictions of our model in the limit x→1 where data is not available.

Longitudinal polarisation of Λ and Λ̄ hyperons in lepton–nucleon deep-inelastic scattering

We consider models for the spin transfers to Λ and Λ hyperons produced in lepton–nucleon deep-inelastic scattering. We make predictions for longitudinal Λ and Λ spin transfers for the COMPASS experiment and for HERA, and for the spin transfer to Λ hyperons produced at JLAB. We demonstrate that accurate measurements of the spin transfers to Λ and Λ hyperons with COMPASS kinematics have the potential to probe the intrinsic strangeness in the nucleon. We show that a measurement of Λ polarisation could provide a clean probe of the spin transfer from s quarks and provides a new possibility to measure the antistrange quark distribution function. COMPASS data in a domain of x that has not been studied previously will provide valuable extra information to fix models for the nucleon spin structure. The spin transfer to Λ hyperons, which could be measured by the COMPASS experiment, would provide a new tool to distinguish between the SU(6) and Burkardt–Jaffe (BJ) models for baryon spin structure. In the case of the HERA electron–proton collider experiments with longitudinally-polarised electrons, the separation between the target and current fragmentation mechanisms is more clear. It provides a complementary probe of the strange quark distribution and helps distinguish between the SU(6) and BJ models for the Λ and Λ spin structure. Finally, we show that the spin transfer to Λ hyperons measured in a JLAB experiment would be dominated by the spin transfer of the intrinsic polarised-strangeness in the remnant nucleon, providing an independent way to check our model predictions.

THE QCD PARTON MODEL: A USEFUL APPROXIMATION

Approximate relations among transverse momentum dependent quark distribution functions are established in the framework of the QCD parton model. The validity of such results survives QCD evolution effects, owing to the Politzer theorem on equations of motion. Furthermore the model fixes an energy scale, involved in the parametrization of the correlator, which determines the Q2 dependence of the azimuthal asymmetries in inclusive reactions. Some of the present data — in particular the sin 2ϕ single spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) and the cos ϕ asymmetry in unpolarized SIDIS — support model predictions. Further measurements of SIDIS and Drell–Yan asymmetries are suggested, in particular the SIDIS double spin asymmetry, which allows to determine approximately the proton transversity.

The Jacobi polynomials QCD analysis for the polarized structure function

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 distributions for the kinematic range $x \epsilon [10^{-8},1]$, $Q^2 \epsilon [1,10^6]$ GeV^2. The analysis is based on the Jacobi polynomials expansion of the polarized structure functions. Our calculations for polarized parton distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of $\Lambda_{QCD}$ and $\alpha_s(M_z)$ are determined.

Parton distribution function for quarks in ans-channel approach

We use an $s$-channel picture of hard hadronic collisions to investigate the parton distribution function for quarks at small momentum fraction $x$, which corresponds to very high energy scattering. We study the renormalized quark distribution at one loop in this approach. In the high-energy picture, the quark distribution function is expressed in terms of a Wilson-line correlator that represents the cross section for a color dipole to scatter from the proton. We model this Wilson-line correlator in a saturation model. We relate this representation of the quark distribution function to the corresponding representation of the structure function ${F}_{T}(x,{Q}^{2})$ for deeply inelastic scattering.

Semi-Inclusive Deep Inelastic Scattering processes from small to large PT

We consider the azimuthal and PT-dependence of hadrons produced in unpolarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes, within the factorized QCD parton model. It is shown that at small PT values, P T ≲ 1GeV/c, lowest-order contributions, coupled to unintegrated (transverse-momentum-dependent) quark distribution and fragmentation functions, describe all data. At larger PT values, P T ≳ 1GeV/c, the usual pQCD higher-order collinear contributions dominate. Having explained the full PT range of available data, we give new detailed predictions concerning the azimuthal and PT-dependence of hadrons which could be measured in ongoing or planned experiments by HERMES, COMPASS and JLab Collaborations.

Small-xBehavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep-Inelastic-Scattering Cross Sections

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln2s fit, A + beta ln2(s/s0), where s = (Q2/x)(1-x) + m2, and Q2 is the virtuality of the exchanged photon. Over a wide range in Q2 (0.11 < or = Q2 < or = 1200 GeV2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x-well beyond the range accessible experimentally. As Q2-->infinity, the structure function F2(p)(x,Q2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.

Modeling dihadron fragmentation functions

We present a model for dihadron fragmentation functions, describing the fragmentation of a quark into two unpolarized hadrons. We tune the parameters of our model to the output of the PYTHIA event generator for two-hadron semi-inclusive production in deep-inelastic scattering at HERMES. Once the parameters of the model are fixed, we make predictions for other unknown fragmentation functions and for a single-spin asymmetry in the azimuthal distribution of ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ pairs in semi-inclusive deep-inelastic scattering on a transversely polarized target at HERMES and COMPASS. Such asymmetry could be used to measure the quark transversity distribution function.

Transverse momentum dependence of the quark helicity distributions and the Cahn effect in double-spin asymmetryALLin semiinclusive DIS

Within the LO QCD parton model of Semi-Inclusive Deep Inelastic Scattering, $\ensuremath{\ell}N\ensuremath{\rightarrow}\ensuremath{\ell}hX$, with unintegrated quark distribution and fragmentation functions, we study the ${\mathbit{P}}_{hT}$ dependence of the double longitudinal-spin asymmetry ${A}_{LL}$. We include $1/Q$ kinematic corrections, which induce an azimuthal modulation of the asymmetry, analogous to the Cahn effect in unpolarized SIDIS. We show that a study of ${A}_{LL}$ and of the weighted DSA ${A}_{LL}^{\mathrm{cos}{\ensuremath{\phi}}_{h}}$ allows to extract the transverse momentum dependence of the unintegrated helicity distribution function ${g}_{1L}^{q}(x,{k}_{\ensuremath{\perp}})$ [or $\ensuremath{\Delta}q(x,{k}_{\ensuremath{\perp}})]$. Predictions, based on some models for the unknown functions, are given for ongoing COMPASS, HERMES and JLab experiments.

Contribution of radiative gluons and spin-one diquarks to theF2structure function

We calculate unpolarized quark distribution functions and the ${F}_{2}$ structure functions for the proton and the neutron. The calculations are preformed in the light-cone frame. For the bare nucleon we have used three different distributions, namely, the spin-0 diquark, the spin-0 plus spin-1 diquark, and the no diquark models. By using perturbative QCD an initial gluon distribution is generated inside the core nucleon. The physical nucleon is assumed to be a superposition of the bare nucleon plus the virtual light-cone Fock states of baryon octets and decuplets and pseudoscalar meson pairs. The initial distributions are evolved. The ${F}_{2}$ structure functions calculated from the evolved distributions are compared with NMC and ZEUS results along with a CTEQ6M fit. Also, it is shown that the meson cloud is a contributing factor to sea-quark asymmetry and to Gottfried sum-rule violation.

CHIRAL CONSTITUENT QUARK MODEL AND THE COUPLING STRENGTH OF η′

Using the latest data pertaining to [Formula: see text] asymmetry and the spin polarization functions, detailed implications of the possible values of the coupling strength of the singlet Goldstone boson η′ have been investigated in the χCQM with configuration mixing. Using Δu, Δ3, [Formula: see text] and [Formula: see text], the possible ranges of the coupling parameters a, α2a, β2a and ζ2a, representing respectively the probabilities of fluctuations to pions, K, η and η′, are shown to be 0.10 ≲ a ≲ 0.14, 0.2 ≲ α ≲ 0.5, 0.2 ≲ β ≲ 0.7 and 0.10 ≲|ζ|≲ 0.70. To further constrain the coupling strength of η′, detailed fits have been obtained for spin polarization functions, quark distribution functions and baryon octet magnetic moments corresponding to the following sets of parameters: a = 0.1, α = 0.4, β = 0.7, |ζ| = 0.65 (Case I); a = 0.1, α = 0.4, β = 0.6, |ζ| = 0.70 (Case II); a = 0.14, α = 0.4, β = 0.2, ζ = 0 (Case III) and a = 0.13, α = β = 0.45, |ζ| = 0.10 (Case IV). Case I represents the calculations where a is fixed to be 0.1, in accordance with earlier calculations, whereas other parameters are treated free and the Case IV represents our best fit. The fits clearly establish that a small nonzero value of the coupling of η′ is preferred over the higher values of η′ as well as when ζ = 0, the latter implying the absence of η′ from the dynamics of χCQM. Our best fit achieves an overall excellent fit to the data, in particular the fit for Δu, Δd, Δ8 as well as the magnetic moments μn, μΣ-, μΣ+ and μΞ- is almost perfect, the μΞ- being a difficult case for most of the similar calculations.

Nuclear effects in deep inelastic scattering of charged-current neutrino off nuclear target

The nuclear effects in the neutrino–nucleus charged-current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. The structure functions F2(x,Q2) and xF3(x,Q2) as well as differential cross sections are calculated by using CTEQ parton distribution functions and the EKRS and HKN nuclear parton distribution functions, and these are compared with the CCFR and NuTeV data. It is found that the corrections of the nuclear effect to the differential cross section for the charged-current antineutrino scattering on the nucleus are negligible, the EMC effect exists in the neutrino structure function F2(x,Q2) in the large x region, the shadowing and anti-shadowing effect occur in the distribution functions of valence quarks in the small and medium x region, respectively. It is also found that shadowing effects on F2(x,Q2) in the small x region in the neutrino–nucleus and the charged-lepton–nucleus deep inelastic scattering processes are different. It is clear that the neutrino–nucleus deep inelastic scattering data should further be employed in restricting the nuclear parton distributions.