We evaluate both chirally even and odd generalized parton distributions(GPDs) in the leading twist in a recently proposed quark-diquark model for the proton where the light front wavefunctions are constructed from the soft-wall AdS/QCD prediction. The GPDs in transverse impact parameter space give the spin densities for different quark and proton polarizations. For longitudinally polarized proton only chiral even GPDs contribute but for transversely polarized proton both chiral even and chiral odd GPDs contribute to the spin densities. We present a detail study of the spin densities in this model.
Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction $x$ of the hadron with $x >1$ or $x<-1$. The studied twist-4 parton distributions of collinear factoization are power-divergent for $\vert x\vert >1$. The corresponding transverse momentum dependent parton distributions have also no parton interpretation. They are finite. The implications of our results are discussed.
Within the framework of the generalized factorization in pQCD, we investigate the multiple parton scattering and induced parton energy loss at twist-6 in deeply inelastic e-A scattering with the helicity amplitude approximation. It is shown that twist-6 processes will give rise to additional nuclear size dependence of the parton energy loss due to LPM interference effect while its contribution is power suppressed.
The genuine twist-3 quark-gluon contributions to the Generalized Parton Distributions (GPDs) are estimated in the model of the instanton vacuum. These twist-3 effects are found to be parametrically suppressed relative to the ``kinematical'' twist-3 ones due to the small packing fraction of the instanton vacuum. We derive exact sum rules for the twist-3 GPDs.
We investigate the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in very good agreement with deep inelastic scattering experimental data from HERA.
We report on the results of a recent work, where we explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (LCWFs). These WFs provide one with a reasonable description of both polarized and unpolarized parton densities at large values of the Bjorken variable. Twist-3 parton distributions are then constructed as convolution integrals of qqqg and usual three-quark WFs.
Associated with the use of conventional integrated parton densities are kinematic approximations on parton momenta which result in unphysical differential distributions for final-state particles. We argue that it is important to reformulate perturbative QCD results in terms of fully unintegrated parton densities, differential in all components of the parton momentum.
Diffractive parton distributions of the proton are determined from fits to diffractive data from HERA. In addition to the twist--2 contribution, the twist--4 contribution from longitudinally polarised virtual photons is considered, which is important in the region of small diffractive masses. A new prediction for the longitudinal diffractive structure function is presented which differs significantly from that obtained in the pure twist--2 analyses.
We show that in the large N_c limit four-quark twist-4 distributions in the pion can be expressed in terms of twist-2 pion distribution amplitude. This allows us to compute the isospin-2 structure function of the pion F_2^{I=2}(x_B) in the large N_c limit. The method can be easily applied to other mesons as well.
Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau-Pomeranchuk-Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, $A\to \infty$, as assumed in previous studies. Due to the correlative nature of the twist-fo…
We discuss the calculation of the evolution kernels ΔW_ζ(X,Z) for the leading-twist nonforward parton distributions G_ζ(X,t) sensitive to parton helicities. We present our results for the kernels governing evolution of the relevant light-ray operators and describe a simple method allowing to obtain from them the components of the nonforward kernels ΔW_ζ(X,Z).
The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for the axial-vector quasi- and pseudodistributions.
We investigate the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in excellent agreement with deep inelastic scattering experimental data from HERA.
In order to study twist-3 and transverse momentum dependent parton distributions, we use light-front time-ordered pQCD at order $α_s$ to calculate various distribution functions for a dressed quark target. This study enables us to investigate in detail the existing relations between twist-3 and transverse momentum dependent parton distributions. Our calculation shows explicitly that two versions of such relations, considered to be equivalent, occur in the literature which need to be distinguished. Moreover, we examine sum rules for higher twist distributions. While the Burkhardt-Cottingham sum…
Collinear and transverse momentum dependent (TMD) parton densities are obtained from fits to precision measurements of deep inelastic scattering (DIS) cross sections at HERA. The parton densities are evolved by DGLAP evolution with next-to-leading-order (NLO) splitting functions using the parton branching method, allowing one to determine simultaneously collinear and TMD densities for all flavors over a wide range in $x$, $μ^2$ and $k_t$, relevant for predictions at the LHC. The DIS cross section is computed from the parton densities using perturbative NLO coefficient functions. Parton densiti…
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 extend the counting of generalized form factors presented in PRD63(2000) by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity flip) operator is given in terms of generalized form factors.
We study the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA.
Rapidity divergences occur when parton densities in a gauge theory are defined in the most natural way, as expectation values of partonic number operators in light-front quantization. I review these and other related divergences, and show how the definitions of parton densities can be modified to remove the divergences. A modified definition is not only essential for many phenomenological applications of QCD, but also concerns the treatment of parton densities in non-perturbative approaches. The necessity of modifications in the definition of a parton density also entails corrections in the fo…
We present a determination of parton densities at NLO obtained with the Parton Branching method using precision measurements of deep inelastic scattering cross sections at HERA. The two sets of parton densities shown in this work are obtained with the same angular angular ordering condition for the evolution scale and they differ in the chosen scale for the strong coupling evaluation, for which we consider two scenarios: the evolution scale, and the transverse momentum qT from the angular ordering prescription. The transverse momentum dependent densities obtained with the Parton Branching meth…
We determine diffractive parton distributions of the proton from DGLAP based fits to HERA data including the twist--4 contribution from longitudinal polarized virtual photons, which is known to be important in the region of large beta. The biggest impact of this contribution is on the diffractive gluon distribution and on the diffractive longitudinal structure function to be determined from HERA data.
Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $δ$-function at $x=0$. We confirm and clarify this result by constructing $h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating $h_L(x,Q^2)$ using light-front time-ordered pQCD to ${O}(α_S)$ on a quark target.
A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the CASCADE package for the full TMD parton shower, final state shower and…
I give an account of a new definition of transverse-momentum-dependent parton densities. The new definition solves a number of difficulties and inconsistencies in earlier definitions.
We explore the physics of the parton-hadron duality in the nucleon structure functions appearing in lepton-nucleon scattering. We stress that the duality allows one to extract the higher-twist matrix elements from data in the resonance region, and learn about the properties of resonances if these matrix elements are known. As an example, we construct the moments of $F_2(x, Q^2)$ for the low and medium $Q^2$ region, and from which we study the interplay between higher twists and the resonance contributions.
We constructed two sets of twist-3 correlation functions that are responsible for generating the novel single transverse-spin asymmetry in the QCD collinear factorization approach. We derive evolution equations for these universal three-parton correlation functions. We calculate evolution kernels relevant to the gluonic pole contributions to the asymmetry at the order of $α_s$. We find that all evolution kernels are infrared safe as they should be and have a lot in common to the DGLAP evolution kernels of unpolarized parton distributions. By solving the evolution equations, we explicitly demon…
We review the current status of collinear and Transverse Momentum Dependent densities based on the Parton Branching method. We investigate the performance of the PB-TMD evolution as well as PB-TMD parton shower with different configurations of the hard process in the four- and five-flavour schemes.
In the paper we include Bose-Einsten correlations for identical gluons, in the evolution of the double parton densities at low $x$ (high energies). We show that these correlations result in a faster increase of the double densities, in comparison with the product of two single parton densities. In addition, we find that the typical momentum in the double parton cross section, is of the order of the hard scales in the process, including the saturation momentum. This result is in agreement with recently published experimental data.
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.
We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the four-particle nucleon WFs involving three valence quarks and a gluon with total orbital momentum zero, and estimate their normalization (WF at the origin) using QCD sum rules. We demonstrate that these WFs provide one with a reasonable description of both polarized and unpolarized gluon parton densities at large values of Bjorken variable x > 0.5. Twist-three parton di…
Partons are defined as the quanta in a Fock space description of a hadron. Gluon saturation is described in the Weizsäcker-Williams approximation for a large nucleus. The elements of DGLAP and BFKL evolution are given with the BFKL equation derived in a large-$N_c$ dipole formalism. A more general discussion of saturation is given in terms of a dipole scattering on a nucleon or nucleus. Possible evidence for saturation at HERA is discussed.
The combined HERA data for the inclusive deep inelastic scattering (DIS) cross sections for the momentum transfer $Q^2 > 1$ GeV$^2$ are fitted within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) framework at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy, complemented by a QCD-inspired parameterisation of twist 4 corrections. A modified form of the input parton density functions is also included, motivated by parton saturation mechanism at small Bjorken $x$ and at a low scale. These modifications lead to a significant improvement of the data description…
We investigate the helicity dependent twist-two and twist-three generalized parton distributions in light-front Hamiltonian QCD for a massive dressed quark target. Working in the kinematical region $ξ< x <1$, we obtain the splitting functions for the evolutions of twist-two quark and gluon distributions in a straightforward way. For the twist-three distribution, we find that all contributions are proportional to the quark mass and thus the twist-three distribution is directly related to the chiral symmetry breaking dynamics in light-front QCD. We also show that the off-forward Wandzura-Wilczek…
In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $δ$-functions in parton distribution functions. It is explained why one might expect a small violation in sum rules for the twist-3 distribution functions $g_T(x)$ and $h_L(x)$ when the sum-rules are applied to $x\neq 0$ data only. The non-perturbative predictions are studied in the context of a one-loop model.
Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $δ$-function at $x=0$. We confirm and clarify this result by constructing $h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating $h_L(x,Q^2)$ using light-front time-ordered pQCD to ${\cal O}(α_S)$ on a quark target. A $δ(x)$ term is also found in $e(x,Q^2)$, but not in $g_T(x,Q^2)$, to this order in ${\cal O}…
Transverse momentum dependent parton distribution functions, also abbreviated as TMDs, offer a three-dimensional picture of hadrons by taking the intrinsic transverse momentum of the parton into consideration. Hence, they are very important for us to understand the structure of hadrons. In this article, we calculate and summarize all TMDs of quark through the spectator model, from twist-2 to twist-4. Especially, we give complete results of TMDs at twist-4. We adopt a general analytical framework to calculate TMDs, with both scalar and axial-vector spectators being considered. All TMDs are calc…
We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $α_s$-order of QCD perturbation theory.
We discuss how the operator product expansion (OPE) can be used to derive asymptotic expressions for certain integrals. This yields operator matrix elements (OME's) which determine the matching conditions for $\bar{\rm MS}$ parton densities across heavy flavour thresholds. Then we construct four and five-flavour densities from a three-flavour set via the AP equation using LO and NLO splitting functions.
In this paper, the twist-3 two parton corrections in charmless $B\to PP$ decays are shown to be factorizable under the QCD factorization approach. The factorizability of the twist-3 two parton corrections is constructed on the following findings. Under the energetic meson limit, the pseudoscalar distribution amplitude for a light pseudoscalar meson is allowed to be non-constant by the equations of motion for the quark. The non-constant pseudoscalar distribution amplitude is then used to regularize the end-point divergences in the hard spectator corrections at twist-3 order. By retaining the mo…
We study the twist-3 corrections to the neutrino induced deeply virtual meson production due to the chiral odd transversity Generalized Parton Distribution (GPD). We found that in contrast to pion electroproduction, in neutrino-induced processes these corrections are small. This occurs due to large contribution of unpolarized GPDs $H,\, E$ to the twist-2 amplitude in neutrinoproduction. Our results are important for analyses of the pion and kaon production in the Minerva experiment at FERMILAB.
We present recent results on transverse momentum dependent parton densities in the limit of small Bjorken x. A definition of an unintegrated seaquark density is proposed which can be used within the CCFM Monte-Carlo event generator CASCADE. We further discuss aspects of the determination of a NLO BFKL unintegrated gluon density.
We perform the NLO QCD analysis of the world data on inclusive deep inelastic scattering cross sections of charged leptons off the proton and the deuterium targets. The parton distributions, the value of strong coupling constant $α_{\rm s}$, and the twist 4 contributions to the structure functions $F_2$ and $F_{\rm L}$ are extracted with the complete account for the correlations of data points due to the systematic errors. Sensitivity of the $α_{\rm s}$ value and the high twist contribution to the procedures of accounting for the systematic errors is studied. The impact of theoretical uncertai…
We update the theoretical predictions for the t-tbar production cross-section at the Tevatron, taking into account the most recent determinations of systematic uncertainties in the extraction of the proton parton densities.
In this talk the relation between the semiclassical approach and the concept of diffractive parton densities is discussed. The proton rest frame calculation is organized in a way that exhibits the hard partonic cross section and the diffractive parton density as the two fundamental ingredients. The latter one is a non-perturbative quantity which, in the present model, is explicitly given by integrals of non-Abelian eikonal factors in the colour background field.
We prove collinear factorization theorem for the process $πγ^*\toπ$ at the twist-3 level in the covariant gauge by means of the Ward identity, concentrating on the two-parton case. It is shown that soft divergences cancel and collinear divergences are grouped into the pseudo-scalar and pseudo-tensor two-parton twist-3 pion distribution amplitudes. The delicate summation of a complete set of diagrams for achieving factorization in momentum, spin, and color spaces is emphasized. The proof is then extended to the exclusive semileptonic decay $B\toπl\barν$, assuming the hard scale to be of $O(\sqr…
We draw attention to some problems in the combined use of high-Q^2 deep inelastic scattering (DIS) data and low-Q^2 hyperon β-decay data in the determination of the polarized parton densities. We explain why factorization schemes like the JET or AB schemes are the simplest in which to study the implications of the DIS parton densities for the physics of the low-Q^2 region.
Collider data can play an important role in determining the parton distribution functions of the nucleon. I outline a formalism which makes it possible to use next-to-leading order calculations in such an extraction, while minimizing the amount of numerical computation required.
The feasibility of an experimental determination of the parton distributions of virtual photons at high energy $ep$ colliders is studied in the context of the DESY-HERA collider. Recently proposed parton densities of virtual photons are utilized to evaluate the appropriate production processes and their relevant kinematical regions. It is demonstrated that high $E_T$ jet production with $E_T\,\simeq 5-7\, {\rm{GeV}}$ and $b\bar{b}$ production can probe the parton distributions of virtual photons up to virtualities of a few ${\rm{GeV}}^2$. A useful leading order parametrization of our proposed …
We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions $h_L(x)$ and $e(x)$, and also the twist-two transversity distribution $δq(x)$. The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the $h_L$ quasi(pseudo)-…
We present a program to measure the parton densities in the pomeron using diffractive deep inelastic scattering and diffractive photoproduction, and to test the resulting parton densities by applying them to other processes such as the diffractive production of jets in hadron-hadron collisions. Since QCD factorization has been predicted NOT to apply to hard diffractive scattering, this program of fitting and using parton densities might be expected to fail. Its success or failure will provide useful information on the space-time structure of the pomeron.
Collider data can play an important role in determining the parton distribution functions of the nucleon. I present a formalism which makes it possible to use next-to-leading order calculations in such a determination, while minimizing the amount of numerical computation required.
We introduce the chiral-even and chiral-odd quark distributions as forward matrix elements of related bilocal quark operators with well-defined (geometric) twist. Thereby, we achieve a Lorentz invariant classification of these distributions which differ from the conventional ones by explicitly taking into account the necessary trace terms. The relations between both kinds of distribution functions are given and the mismatch between their different definition of twist is discussed. Wandzura-Wilczek--like relations between the conventional distributions (based on dynamical twist) are derived by …
We present a solution of the DGLAP evolution equations, written in terms of Sudakov form factors to describe the branching and no-branching probabilities, using a parton branching Monte Carlo method. We demonstrate numerically that this method reproduces the semi-analytical solutions. We show how this method can be used to determine Transverse Momentum Dependent (TMD) parton distribution functions, in addition to the usual integrated parton distributions functions. We discuss numerical effects of the boundary of soft gluon resolution scale parameter on the resulting parton distribution functio…
We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton d…
Higher twist corrections to the structure function F_2 at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. We present an analytical parameterization of the contributions from the twist-two and higher twist operators of the Wilson operator product expansion. Higher twist terms are evaluated using two different approaches, one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA.
