Narrow Results

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.

The present knowledge about nontrivial relations between generalized parton distributions for a spin-1/2 hadron on the one hand and transverse momentum dependent distributions on the other is reviewed. While various relations can be found in the framework of simple spectator models, so far no model-independent nontrivial relations have been established. In fact, by relating the two types of parton distributions to the fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2 hadron, we argue that none of the nontrivial relations can be promoted to a model-independent status.

We describe the determination of the strong coupling constant and of the charm-quark mass m_c(m_c) in the -scheme, based on the QCD analysis of the unpolarized World deep-inelastic scattering data. At NNLO the values of and are obtained and are compared with other determinations, and also clarifying discrepancies.

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the $u$ and $d$ 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 $Q^2=5$GeV². The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of $m_u/m_d=0.5$ at $Q^2=5$GeV² are, respectively, estimated by 1.3% and 2.0% at $x\simeq 1$ in comparison with those for $m_u/m_d=1.0$, while those for the kaon are approximately about 0.3% and 0.5% at $x\simeq 1$, 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.

Ultrahigh energy neutrinos can provide important information about the distant astronomical objects and the origin of the Universe. Precise knowledge about neutrino interactions and production rates is essential for estimating background, expected fluxes and detection probabilities. In this paper we review the applications of the high energy QCD to the calculations of the interaction cross-sections of the neutrinos. We also study the production of the ultrahigh energy neutrinos in the atmosphere due to the charm and beauty decays.

According to a rederivation — due to Collins and Qiu — the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound |Δ f(x, Q)| < f(x, Q) between polarized and unpolarized distributions, or positivity of the helicity distributions, for any Q. We reanalyze this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in α_s, which we illustrate. We also elaborate on some of the formal properties of the Collins–Qiu form and comment on the underlying regularization, introduce a Kramers–Moyal expansion of the equation and briefly analyze its Fokker–Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution q_V and for the transverse spin distribution h₁.

The role of global QCD analysis of parton distribution functions (PDFs) in collider physics at the Tevatron and LHC is surveyed. Current status of PDF analyses are reviewed, emphasizing the uncertainties and the open issues. The stability of NLO QCD global analysis and its prediction on "standard candle" W/Z cross sections at hadron colliders are discussed. The importance of the precise measurement of various W/Z cross sections at the Tevatron in advancing our knowledge of PDFs, hence in enhancing the capabilities of making significant progress in W mass and top quark parameter measurements, as well as the discovery potentials of Higgs and New Physics at the Tevatron and LHC, is emphasized.

The extension of the statistical parton distributions to include their transverse momentum dependence (TMD) is revisited by considering that the proton target has a finite longitudinal momentum. The TMD will be generated by means of a transverse energy sum rule. The new results are mainly relevant for electron–proton inelastic collisions in the low Q² region. We take into account the effects of the Melosh–Wigner rotation for the helicity distributions.

Jet production at hadron colliders provides powerful constraints on the parton distribution functions (PDFs) of the proton, in particular on the gluon PDF. Jet production can also be used to extract the QCD coupling ${\alpha }_s(Q)$ and to test its running with the momentum transfer up to the TeV region. In this review, I summarize the information on PDFs and the strong coupling that has been provided by Run I LHC jet data. First of all, I discuss why jet production is directly sensitive to the gluon and quark PDFs at large-x, and then review the state-of-the-art perturbative calculations for jet production at hadron colliders and the corresponding fast calculations required for PDF fitting. Then I present the results of various recent studies on the impact on PDFs, in particular the gluon, that have been performed using as input jet measurements from ATLAS and CMS. I also review the available determinations of the strong coupling constant based on ATLAS and CMS jet data, with emphasis on the fact that LHC jet data provides, for the first time, a direct test of the ${\alpha }_s(Q)$ running at the TeV scale. I conclude with a brief outlook on possible future developments.

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 $M(z,p)$ of the parton fields is a function ${ℳ}(\nu ,-z^2)$ of Lorentz invariants $\nu =-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution ${ℳ}(\nu ,-z^2)$ from Euclidean separations $z$ accessible on the lattice. Another basic feature is the use of the ratio $𝔐(\nu ,-z^2)\equiv {ℳ}(\nu ,-z^2)/{ℳ}(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $𝔐(\nu ,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,{\mu }^2)$ using matching relations. The $\nu$-dependence of $𝔐(\nu ,-z^2)$ governs the $x$-dependence of parton densities $f(x,{\mu }^2)$. 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.

Dedicated to the memory of our colleague, Harald Fritzsch, who, together with Murray Gell-Mann, introduced the color quantum number as the exact symmetry responsible for the strong interaction, thus establishing quantum chromodynamics (QCD) as a fundamental non-Abelian gauge theory. A basic understanding of hadron properties, however, such as confinement and the emergence of a mass scale, from first principles QCD has remained elusive: Hadronic characteristics are not explicit properties of the QCD Lagrangian and perturbative QCD, so successful in the large transverse momentum domain, is not applicable at large distances. In this article, we shall examine how this daunting obstacle is overcome in holographic QCD with the introduction of a superconformal symmetry in anti de Sitter (AdS) space which is responsible for confinement and the introduction of a mass scale within the superconformal group. When mapped to light-front coordinates in physical spacetime, this approach incorporates supersymmetric relations between the Regge trajectories of meson, baryon and tetraquark states which can be visualized in terms of specific $SU{(3)}_C$ color representations of quarks. We will also briefly discuss here the implications of holographic models for QCD color transparency in view of the present experimental interest.

In this paper, we study the contribution of color correlations to Double Parton Scattering (DPS). We show that there is a specific class of Feynman diagrams related to so-called $1\to 2$ processes when the contribution of these color correlations is not Sudakov suppressed with the transverse scales. The effective absence of Sudakov suppression gives hope that although they are small relative to color singlet correlations, they eventually can be observed.

We review the basic concepts of the Poincare group in light cone quantum mechanics and light cone field theory. We discuss recent progress in light cone representations of the Bethe–Salpeter equation, with application to the pion form factor, and the quark Schwinger–Dyson equation. Applications are discussed for deeply virtual Compton scattering, particularly for skewed parton distributions of the pion, and rare B to lepton pair decays. Meson light cone wave functions and recent experimental studies of light cone wave functions are also covered. This review was motivated by the LANL Light Cone 2002 International Workshop.

The nonlinear Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations with parton recombination corrections are used to dynamically evaluate the proton's parton distribution functions starting from a low scale μ², where the nucleon consists of valence quarks. We find that the resulting negative nonlinear corrections can improve the perturbative stability of the QCD evolution equation at low Q². Our resulting parton distributions, with four free parameters, are compatible with the existing databases. This approach provides a powerful tool to connect the quark models of the hadron and various nonperturbative effects at the scale μ² with the measured structure functions at the high scale Q² ≫ μ².

Recent work unambiguously resolves the level of charge symmetry violation in moments of parton distributions using (2 + 1)-flavor lattice QCD. We introduce the methods used for that analysis by applying them to determine the strong contribution to the proton–neutron mass difference. We also summarize related work which reveals that the fraction of baryon spin which is carried by the quarks is in fact structure-dependent rather than universal across the baryon octet.

The introduction talk given at the beginning of QCD Evolution workshop held in Thomas Jefferson National Accelerator Facility (Jefferson Lab) on May 14 -17, 2012.

Azimuthal asymmetries in high-energy processes, most pronounced showing up in combination with single or double (transverse) spin asymmetries, can be understood with the help of transverse momentum dependent (TMD) parton distribution and fragmentation functions. These appear in correlators containing expectation values of quark and gluon operators. TMDs allow access to new operators as compared to collinear (transverse momentum integrated) correlators. These operators include nontrivial process dependent Wilson lines breaking universality for TMDs. Making an angular decomposition in the azimuthal angle, we define a set of universal TMDs of definite rank, which appear with process dependent gluonic pole factors in a way similar to the sign of T-odd parton distribution functions in deep inelastic scattering or the Drell-Yan process. In particular, we show that for a spin 1/2 quark target there are three pretzelocity functions.

We discuss the quark phase-space or Wigner distributions of the nucleon which combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-front constituent quark model. We show how the quark orbital angular momentum can be extracted from the Wigner distributions and compare it with alternative definitions.

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs), in short referred to as TMDs, also take into account the transverse momentum (pT) of the partons. Just as the pT-integrated analogues we want to link them to quark and gluon matrix elements using Operator Product Expansion methods in QCD, involving operators of definite twist. The TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Using the expression for TMDs involving nonlocal matrix elements of quark and gluon fields there is a gauge link dependence, which also introduces an inherent process dependence. Using transverse moments, which are specific pT-weightings, we can establish the link with quark and gluon fields including the higher twist ones. We introduce (a finite number of) universal TMDs of definite rank and show how the process dependent TMDs can be written as combinations of these universal functions.

We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.