Generalized transverse momentum dependent parton distributions of the nucleon
S. Meissner, A. Metz, M. Schlegel
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4 pages; talk given by S. Meissner at the 16th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2008), London, UK, April 7 - 11, 2008
We present first results from our analysis of the most general quark-quark correlator of the nucleon, which can be parameterized in terms of so-called generalized transverse momentum dependent parton distributions. These results include the first complete parameterization of the nucleon GPDs and TMDs to all twists as well as new results on possible nontrivial relations between them.
We study the parton distribution of nucleon and nuclear EMC effect in a statistical model. We find when we choose the parameters appropriately, the predictions given by pure statistical laws can fit the experimental data well in most range of $x$, this reveal statistical law play an important role in the parton distribution of nucleon.
We demonstrate that perturbative QCD leads to positive 3D parton--parton correlations inside nucleon explaining a factor two enhancement of the cross section of multi-parton interactions observed at Tevatron at $x_i\ge 0.01$ as compared to the predictions of the independent parton approximation. We also find that though perturbative correlations decrease with $x$ decreasing, the nonperturbative mechanism kicks in and should generate correlation which, at $x$ below $10^{-3}$, is comparable in magnitude with the perturbative one for $x\sim 0.01$.
The consequences of a flavor broken SU(3)_f dynamical parton model are studied in the context of the elastic scattering of supersymmetric dark matter off nucleons. It is shown that the predictions of this model differ considerably from those of the commonly applied `standard' parton model. Some notable properties of the dynamical parton model are finally presented and discussed.
We have performed several fits to find the ratio $R=σ_{L}/σ_{T}$ in different phenomenological models. Our fits seem to leave no room for possible admixture of scalar partons inside the nucleon.
We present an exploratory study using generalized parton distributions of several observables related to transverse degrees of freedom in hadronic structure -- the nucleon transverse momentum, the transverse radius, or impact parameter, and the momentum transfer, $t$, dependence of the longitudinal variable $x$ -- in both nucleons and nuclei.
A model independent prediction is given for the nucleon spin contents, based only upon a reasonable theoretical postulate on the isosinglet anomalous gravitomagnetic moment of the nucleon.
The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.
Generalized parton distributions (GPDs) have become a standard QCD tool for analyzing and parametrizing the non perturbative parton structure of hadron targets. GPDs might be viewed as non-diagonal overlaps of light-cone wave functions and offer the opportunity to study the partonic content of the nucleon from a new perspective, allowing one to study the interplay between longitudinal and transverse partonic degrees of freedom. In particular, we will review some of the new information encoded in the GPDs through the definition of impact-parameter dependent parton distributions and form factors…
A fit to proton, neutron and deuteron spin asymmetries is presented and polarized parton distributions in nucleon are given. These densities have their roots in the MRS fit for unpolarized case. The integrals of polarized distributions are compared with the experimental figures. The role of polarized gluons is also discussed.
We study the generalized parton distributions, including the helicity-flip ones, using Nambu-Jona-Lasinio model based on a relativistic Faddeev approach with `static approximation'. Sum rules relating the generalized parton distributions to nucleon electromagnetic form factors are satisfied. Moreover, quark-antiquark contributions in the region $-ξ<x<ξ$ are non-vanishing. Our results are qualitatively similar to those calculated with Radyushkin's double distribution ansatz using forward parton distribution functions calculated in the NJL model as inputs.
We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a $Δ$ described within the constituent quark model in terms of three valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolari…
We discuss the relations between Generalized Parton Distributions (GPDs) and nucleon resonances. We first briefly introduce the concept of "transition" GPDs. Then we discuss a straightforward application to the modelization of the N-$Δ$ magnetic transition form factor. Finally, we discuss the experimental aspects of the subject and present first preliminary experimental investigations in this field.
The current status of global QCD analysis of parton distribution functions of the nucleon is reviewed. Recent progress made in determining various features of the parton structure of the nucleon, as well as outstanding open questions are discussed. These include: the small-$x$ and large-$x$ behavior of the partons, particularly the gluon; the differentiation of $u$ and $d$ quarks; the strangeness sea ($s+\bar{s}$), the strangeness asymmetry ($s-\bar{s}$); and the heavy quark distributions $c$ and $b$. Important issues about assessing the uncertainties of parton distributions and their physical…
We evaluate the differential cross section for the electroproduction of lepton pairs off a polarized nucleon target in the generalized Bjorken region to leading power accuracy in hard momentum. We discuss the importance of this process for phenomenology of generalized parton distributions. A special attention is given to the sensitivity of physical observables, i.e., diverse asymmetries, to their dependence on scaling variables that allows to map directly the functional two-dimensional surface of generalized parton distributions.
A new generation of (unpolarized) dynamical parton distribution functions of the nucleon is determined. After introducing basic elements of perturbative QCD, the dynamical model is discussed and compared with the approach to parton distributions used by most other groups ("standard"). Parton distributions sets (with uncertainties) at different orders (LO, NLO, NNLO), using different factorization schemes (\overline{MS}, DIS) and different treatments of heavy quark masses (FFNS, VFNS) are extracted and compared. The astrophysical implications of the dynamical predictions are outlined before foc…
Continuing with our analysis of parton distributions in the nucleon, we extend our light-front quark model in order to obtain both the helicity independent and helicity dependent parton distributions, analytically matching the results of global fits at the initial scale $μ\sim 1$ GeV, and which also contain the correct Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We also calculate the transverse parton, Wigner and Husimi distributions from a unified point of view, using our light-front wave functions and expressing them in terms of the parton distributions $q_v(x)$ and $δq_v(x)$. Our …
In the following, the subject of Deep Virtual Compton Scattering on the nucleon and its relation to the recently introduced concept of Generalized Parton Distributions are briefly reviewed. The general theoretical framework and the links between theory and experiment will be outlined and the recently published data which look promising for the development of this field will be discussed. Finally, the experimental prospectives of the domain will be presented.
The nucleon distribution amplitudes and the nucleon-to-pion transition distribution amplitudes are investigated at leading twist within the frame of a light-cone quark model. The distribution amplitudes probe the three-quark component of the nucleon light-cone wave function, while higher order components in the Fock-space expansion of the nucleon state are essential to describe the nucleon-to-pion transition distribution amplitudes. Adopting a meson-cloud model of the nucleon the nucleon-to-pion transition distribution amplitudes are calculated for the first time.
We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.
Reports on our latest extractions of parton distribution functions of the nucleon are given. First an overview of the recent JR14 upgrade of our unpolarized PDFs, including NNLO determinations of the strong coupling constant and a discussion of the role of the input scale in parton distribution analysis. In the second part of the talk recent results on the determination of spin-dependent PDFs from the JAM collaboration are reported, including a careful treatment of hadronic and nuclear corrections, as well as reports on the impact of present and future data in our understanding of the spin of …
We incorporate the perturbative evolution effects in the generalized parton distributions (GPDs) calculated in effective light-front quark model for the nucleon. The perturbative effects enters into formalism through the evolution of GPDs according to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-like (DGLAP) equation. We obtain the evolved GPDs in the momentum space and transverse impact parameter space. We observe that combining the light front quark model with the perturbative evolution effects, give the effective model for studying the phenomenological GPDs
We study the small-$x$ evolution equation for the gluon generalized parton distribution (GPD) $E_g$ of the nucleon. It is shown that $E_g$ at vanishing skewness exhibits the Regge behavior identical to the BFKL Pomeron, despite its association with nucleon helicity-flip processes. We also consider the effect of gluon saturation and demonstrate that $E_g$ gets saturated in the same way as its helicity-nonflip counterpart $H_g$. Our result has a direct impact on the modeling of $E_g$ as well as the small-$x$ contribution to nucleon spin sum rules.
The proton's transverse polarization structure is examined in terms of the Lorentz-covariant Pauli-Lubanski vector in QCD. We find that there are contributions from leading, subleading, and next-to-subleading partonic contributions in the light-front system of coordinates. The subleading and next-to-subleading contributions are related to the leading one through Lorentz symmetry. And the leading contribution obeys a simple partonic angular momentum sum rule that gives a clear physical interpretation to a relation known previously.
The distribution of the spin of the nucleon among its constituents can be parametrized in the form of polarized parton distribution functions for quarks and gluons. Using all available data on the polarized structure function $g_1(x,Q^2)$, we determine these distributions both at leading and next-to-leading order in perturbation theory. We suggest three different, equally possible scenarios for the polarized gluon distribution, which is found to be only loosely constrained by current experimental data. We examine various possibilities of measuring polarized parton distributions at future exper…
It is known that some of the deeply-virtual-Compton-scattering observables, for instance, the beam-charge asymmetry in the hard electroproduction of real photons on the nucleon, are extremely sensitive to the magnitude of D-term appearing in the parameterization of the generalized parton distributions. We report a theoretical analysis of both the isoscalar and isovector parts of the nucleon D-term within the framework of the chiral quark soliton model, without recourse to the derivative expansion type approximation used in previous works.
We discuss some recent developments concerning the nucleon's helicity parton distribution functions: New preliminary data from jet production at RHIC suggest for the first time a non-vanishing polarization of gluons in the nucleon. SIDIS measurements at COMPASS provide better constraints on the strange and light sea quark helicity distributions. Single-longitudinal spin asymmetries in W-boson production have been observed at RHIC and will ultimately give new insights into the light quark and anti-quark helicity structure of the nucleon.
Examining the structure functions of nucleons by introducing new Ansatz and their consequences on parton distribution functions in higher approximation
We discuss building models for nucleon generalized parton distributions (GPDs) H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD+D-term" construction should be amended by an extra term, ξE^1_+(x,ξ) built from the α/βmoment of the DD e(β,α) that generates GPD E(x,ξ). Unlike the D-term, this function has support in the whole -1 \leq x \leq 1 region, and in general does not vanish at the border points |x|=ξ.
I discuss the physical interpretation of GPDs in the limit $ξ=0$, where the $t$ dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also provides a physical interpretation for Ji's angular momentum sum rule.
The cross section for ultra-high energy neutrino-nucleon scattering is very sensitive to the parton distributions at very small values of Bjorken x ($x \leq 10^{-4})$. We numerically investigate the effects of modifying the behavior of the gluon distribution function at very small $x$ in the DGLAP evolution equation. We then use the Color Glass Condensate formalism to calculate the neutrino-nucleon cross section at ultra-high energies and compare the result with those based on modification of DGLAP evolution equation.
It is well established that the nucleon form factors can be related to Generalized Parton Distributions (GPDs) through sum-rules. On the other hand, GPDs can be expressed in terms of Parton Distribution Functions (PDFs) according to Diehl's model. In this work, we use this model to calculate polarized GPDs for quarks ($\widetilde{H}_q$) using the available polarized PDFs obtained from the experimental data, and then study the axial form factor of nucleon. We determine parameters of the model using standard $χ^2$ analysis of experimental data. It is shown that some parameters should be readjust…
We review recent progress in calculating the twist--2 parton distribution functions at a low normalization point in the large--$N_c$ limit, where the nucleon can be described as a soliton of the effective chiral lagrangian. This field-theoretic approach preserves all general requirements on the distribution functions (positivity, normalization etc.). In particular, it allows to calculate the polarized and unpolarized antiquark distributions at the low normalization point.
We present a phenomenological unpolarized Parton Distribution Functions for diquarks based on a soft-wall light front AdS/QCD quark-diquark nucleon model. From a probed model consistent with the Drewll-Yan-West relation and quark counting rule, we have performed a fit of some free parameters using known phenomenological quark PDF data. The model considers the entire set of possible diquarks within the nucleon valence, in the present work we focus on the spin-0 $ud_0$, spin-1 $ud_1$ and spin-1 $uu_1$ diquarks into the valence of protons. The diquark PDFs obtained are able to used in proton-prot…
We study the effects of light gluinos with mass below about 1 GeV on the nucleon parton densities and the running of alpha_(S). It is shown that from the available high-statistics DIS data no lower bound on the gluino mass can be derived. Also in the new kinematical region accessible at HERA the influence of such light gluinos on structure f unctions is found to be very small and difficult to detect. For use in more direct searches involving final state signatures we present a radiative estimate of the gluino distribution in the nucleon.
By working out the kinematics of double parton scattering at short relative transverse distances, we obtain an explicit link between the transverse centres of mass, of the two hard partonic interactions, and the contributions to the process, due to pairs of interacting partons generated by perturbative splitting. One my thus foresee the interesting possibility of discriminating experimentally between contributions to the double parton scattering cross section, due to interacting parton pairs originated by independent evolution, and contributions, due to interacting parton pairs generated by sp…
An up-to-date global QCD analysis of high energy lepton-hadron and hadron-hadron interactions is performed to better determine the gluon and quark parton distributions in the nucleon. Improved experimental data on inclusive jet production, in conjunction with precise deep inelastic scattering data, place good constraints on the gluon over a wide range of x; while new data on asymmetries in Drell-Yan processes contribute to better determine the d/u ratio. Comparisons with results of other recent global analyses are made, and the differences are described. Open issues and the general problem of …
Generalized parton distributions (GPDs) with purely transverse momentum transfer can be interpreted as Fourier transforms of the distribution of partons in impact parameter space. The helicity-flip GPD $E(x,0,-\Dps)$ is related to the distortion of parton distribution functions in impact parameter space if the target is not a helicity eigenstate, but has some transverse polarization. This transverse distortion can be used to develop an intuitive explanation for various transverse single spin asymmetries.
A physical model for parton densities in hadrons, based on Gaussian momentum fluctuations of partons and hadronic baryon-meson fluctuations, is presented. The model has previously been shown to describe proton structure function data, and is now applied to sea quark asymmetries and shown to describe the dbar-ubar asymmetry of the proton. By considering fluctuations involving strange quarks, the model gives an asymmetry between the momentum distributions of s and sbar, which would reduce the significance of the NuTeV anomaly.
We consider the collinear limit of QCD amplitudes at one-loop order, and their factorization properties directly in colour space. These results apply to the multiple collinear limit of an arbitrary number of QCD partons, and are a basic ingredient in many higher-order computations. In particular, we discuss the triple collinear limit and its relation to flavour asymmetries in the QCD evolution of parton densities at three loops. As a phenomenological consequence of this new effect, and of the fact that the nucleon has non-vanishing quark valence densities, we study the perturbative generation …
The scale factor $σ_{eff}$, which characterizes double parton collisions in high energy hadron interactions, is a direct manifestation of the distribution of the interacting partons in transverse space, in such a way that different distributions give rise to different values of $σ_{eff}$ in different double parton collision processes. We work out the value of the scale factor in a few reactions of interest, in a correlated model of the multi-parton density of the proton recently proposed.
A physical model is presented for the non-perturbative parton distributions in the nucleon. This is based on quantum fluctuations of the nucleon into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons. The hadronic fluctuations, here developed in terms of hadronic chiral perturbation theory, occur with high probability and generate sea quarks as well as dynamical effects also for valence quarks and gluons. The resulting parton momentum distributions $f(x,Q_0^2)$ at low momentum transfers are evolved with conventional DGLAP equations from perturbative QCD t…
We extend to the strange quarks and antiquarks, the statistical approach of parton distributions and we calculate the strange quark asymmetry $s-\bar s$. We find that the asymmetry is small, positive in the low $x$ region and negative in the high $x$ region. In this framework, the polarized strange quarks and antiquarks distributions, which are obtained simultaneously, are found to be both negative for all $x$ values.
A leading order QCD analysis of spin asymmetries in polarized deep inelastic lepton nucleon scattering is presented within the framework of the radiative parton model. Two resulting sets of plausible leading order spin dependent parton distributions are presented, respecting the fundamental positivity constraints down to the low resolution scale $Q^2=μ_{LO}^2=0.23$ GeV$^2$. The $Q^2$ dependence of the spin asymmetries $A_1^{p,n,d}(x,Q^2)$ is investigated in the range $1 \leq Q^2 \leq 20$ GeV$^2$ and shown to be non-negligible for $x$-values relevant for the analysis of present data and possibl…
We discuss the parton branching (PB) evolution equation for transverse momentum dependent (TMD) parton distribution functions (PDFs), especially we concentrate on the angular ordering constrain and its effect on the TMD distributions. We discuss application of the PB TMDs to precise prediction of Drell-Yan transverse momentum spectrum at LHC, stressing the role of angular ordering in the low transverse momentum region. We compare the PB implementation of the angular ordering condition with the Kimber-Martin-Ryskin-Watt (KMRW), both at the analytical and numerical level.
The strangeness degrees of freedom in the parton structure of the nucleon are explored in the global analysis framework, using the new CTEQ6.5 implementation of the general mass perturbative QCD formalism of Collins. We systematically determine the constraining power of available hard scattering experimental data on the magnitude and shape of the strange quark and anti-quark parton distributions. We find that current data favor a distinct shape of the strange sea compared to the isoscalar non-strange sea. A new reference parton distribution set, CTEQ6.5S0, and representative sets spanning the …
The cross section for transverse momentum dependent double parton scattering involves transverse momentum dependent double parton distributions (DTMDs). In the region of perturbative transverse momentum the DTMDs can be matched onto collinear double parton distributions. We present the framework and results for this matching, as well as the evolution equations for DTMDs in the region of large distance between the two partons. We discuss explicit results for one-loop matching coefficients and evolution kernels.
Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GP…
The new parameterization of the generalized parton distributions t-dependence is proposed. It allows one to reproduce sufficiently well the electromagnetic form factors of the proton and neutron at small and large momentum transfer. The description of the data obtained by the Rosenbluth method and the polarization method are compared. The results obtained by the latter method are shown to be compatible with the correspondent neutron data. The impact parameter dependence of the neutron charge density is examined. The quark contributions to gravitational form factors of the nucleons are obtained…
We present a connection between the modifications induced by the nuclear medium of the nucleon form factors and of the deep inelastic structure functions, obtained using the concept of generalized parton distributions. Generalized parton distributions allow us to access elements of the partonic structure that are common to both the hard inclusive and exclusive scattering processes in nuclei.
We give a brief overview of the General Parton Distributions(GPDs), including their properties, connections to conventional quantities, and relationships to physical observables. We also perform a systematic analysis on the non-forward matrix elements of twist-two quark and gluon helicity-flip operators and explain their relationships to the GPDs. We systematically count the number of independent nucleon form factors in non-forward scattering (of matrix elements of these operators), by matching the allowed quantum numbers with their crossing channel counterparts and time reversal symmetry cons…
We give an interpretation of the $u$ and $d$ quarks contributions to the nucleon electromagnetic form factors for values of the four-momentum transfer in the multi-GeV region where flavor separated data have been recently made available. The data show, in particular, a suppression of $d$ quarks with respect to $u$ quarks at large momentum transfer. %and constant ratios of the flavor dependent Pauli to Dirac form factors ratios. This trend can be explained using a reggeized diquark model calculation of generalized parton distributions, thus providing a correlation between momentum and coordinat…
The Dirac and Pauli form factors of the proton and neutron are obtained in the framework of the generalized parton distributions (GPDs) with some simple momentum transfer dependence. It is shown that both sets of the existing experimental data of the form factors, obtained by the Rosenbluth and polarization transfer, can be described by changing only the slope of the GPDs $E$. The description of neutron form factors is substantially better when the proton data obtained by the studies of polarization transfer are used.
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.
We present a model calculation of the generalized parton distributions where the nucleon is described by a quark core surrounded by a mesonic cloud. In the one-meson approximation, we expand the Fock state of the physical nucleon in a series involving a bare nucleon and two-particle, meson-baryon, states. We discuss the role of the different Fock-state components of the nucleon by deriving a convolution formalism for the unpolarized generalized parton distributions, and showing predictions at different kinematics.
It is shown that, based only on two empirically known facts besides two reasonable theoretical postulates, we are inevitably led to a conclusion that the quark orbital angular momentum carries nearly half of the total nucleon spin. We also perform a model analysis to find that the quark spin fraction $ΔΣ$ is extremely sensitive to the pion mass, which may resolve the discrepancy between the observation and the prediction of the recent lattice QCD simulation carried out in the heavy pion region.
We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta. The evolution of these distributions with change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon. Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through distinct a…
We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution to calculate the diferential cross-section of $π^0$-production for intermediate values of transverse momentum in $p-p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained u…
We study the impact of transverse-momentum dependent parton distributions on detailed features of multi-jet final states, focusing on angular jet correlations in DIS data.
