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.
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.
An explicit model realizing parton-hadron duality and fitting the data is suggested. Complex nonlinear Regge trajectories are important ingredients of the model. The inclusion of $Δ$ and $N^*$ trajectories should account for all resonances in the direct channel. The exotic trajectory is responsible for the smooth background.
We summarize the current view on Parton-Hadron duality as it applies to B meson decays. It is emphasized that an OPE treatment is essential for properly formulating duality and its limitations. Duality violations are unlikely to become the limiting factor in describing semileptonic B width vis-a-vie higher order corrections. The consistent extraction of the b quark mass from B production and decays provides a striking example of the theoretical control achieved.
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.
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.
We present a model that realizes both resonance-Regge (Veneziano) and parton-hadron (Bloom-Gilman) duality. We first review the features of the Veneziano model and we discuss how parton-hadron duality appears in the Bloom-Gilman model. Then we review limitations of the Veneziano model, namely that the zero-width resonances in the Veneziano model violate unitarity and Mandelstam analyticity. We discuss how such problems are alleviated in models that construct dual amplitudes with Mandelstam analyticity (so-called DAMA models). We then introduce a modified DAMA model, and we discuss its properti…
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…
By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-$x$ behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large $Q^2$.
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.
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.
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 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…
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}…
Recent studies of the Q^2 dependence of ep scattering in the large x region and in the Q^2 range: 1 < Q^2 <leq 30 Gev^2, confirm the validity of the phenomenon of quark-hadron duality - the similarity of the deep inelastic (parton) and resonance (hadron) spectra - for values of the invariant mass, W^2 > 2.4 GeV^2 At lower values of W^2, duality is found to be significantly violated by an amount that cannot be parametrized in terms of the first few terms of a series of power corrections. We present a dynamical model that explains the Q^2 dependence of the data: at low W^2, non-partonic componen…
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…
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 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 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…
Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use the simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in two-point sum rules works fine, the duality in three-point sum rules may be 100%- violated, leading to completely unreliable predictions for the matrix elements in question. The implications for three-point QCD sum rules are discussed. A new estimate for the parameter $λ_1$ of HQET is given.
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 study the phenomenon of parton-hadron duality in both polarised and unpolarised electron proton scattering using the HERMES and the Jefferson Lab data, respectively. In both cases we extend a systematic perturbative QCD based analysis to the integrals of the structure functions in the resonance region. After subtracting target mass corrections and large x resummation effects, we extract the remaining power corrections up to order 1/Q^2. We find a sizeable suppression of these terms with respect to analyses using deep inelastic scattering data. The suppression appears consistently in both po…
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 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 mo…
A large variety of jet properties can be described perturbatively by evolving the parton cascade down to small scales of order of a few 100 MeV. We discuss two recent applications of this approach: 1. the soft limit of the particle spectrum which is nearly energy independent as expected for the soft gluon bremsstrahlung; further tests of this interpretation in $e^+e^-$ and DIS are presented; 2. the steep decrease of the distribution of rapidity gaps in $e^+e^-$ annihilation can be explained by the Sudakov formfactor for quark jets.
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.
We calculate the probability for rapidity gaps in the parton cascade for different approximations within the perturbative QCD and compare the results with recent measurements. The aim is to find out whether the dual connection between the parton and hadron final states -- observed so far in various inclusive measurements -- holds as well for the extreme kinematic configurations with colour sources separated by large rapidity gaps. A description of the data is possible indeed choosing the parameters of the cascade in the range suggested by recent analyses of the energy spectra (the $k_\perp$ cu…
The chirally-odd twist-3 parton distribution function e(x) of the nucleon is studied in the large-Nc limit in the framework of the chiral quark-soliton model. It is demonstrated that in spite of properties not shared by other distribution functions, namely the appearance of a delta(x)-singularity and quadratic divergences in e(x), an equally reliable calculation is possible. Among the most remarkable results obtained in this work is the fact that the coefficient of the delta(x)-singularity can be computed exactly in this model, avoiding involved numerics. Our results complete existing studies …
We calculate the off-forward structure function of the pion within a simple model where the size of the pion is accounted for using a momentum cut-off. Twist-two and twist-three generalized parton distributions are extracted. Relations between twist-three and twist-two contributions are obtained, the origin of which is not kinematical as they differ from those arising from the Wandzura-Wilczek approximation.
We extend a recent global analysis of nucleon parton distributions carried out at next-to-leading order (NLO) in the MSbar scheme to provide distributions in the so-called DIS scheme. We pay particular attention to the translation of the heavy quark distributions in going from the MSbar to the DIS scheme. We repeat the global analysis at leading order (LO) and comment on the major effects produced when going from LO to NLO. Finally we include in the global analysis a freely parameterised form of possible higher twist contributions to make an exploratory study of the size of these effects as a …
The twist three contributions to the $Q^2$-evolution of the spin-dependent structure function $g_2(x_{Bj},Q^2)$ are considered in the non-local operator product approach. Defining appropriate twist three distribution function we derive their evolution equation for the nonsinglet case in leading order approximation. In the limit $x_{Bj} \rightarrow 1$ as well as in the large $N_c$ limit we confirm the result that the evolution of the nonsinglet part of $g_2$ is governed by a Gribov-Lipatov-Altarelli-Parisi equation.
We discuss observables in multiparticle production for three kinds of limits of decreasing kinematical scales: 1. the transition jet \to hadron (limit y_{cut}\to 0 of the resolution parameter y_{cut}); 2. single particle inclusive distributions normalized at threshold \sqrt s\to 0 and 3. particle densities in the limit of low momentum p,p_T\to 0. The observables show a smooth behaviour in these limits and follow the perturbative QCD predictions, originally designed for large scales, whereby a simple prescription is supplemented to take into account mass effects. A corresponding physical pictur…
We formulate a consistent 1/N_c^2 expansion of the QCD evolution equations for the twist-three quark distributions g_2(x,Q^2), h_L(x,Q^2) and e(x,Q^2) based on the interpretation of the evolution as a three-particle quantum-mechanical problem with hermitian Hamiltonian. Each distribution amplitude can be decomposed in contributions of partonic components with DGLAP-type scale dependence. We calculate the 1/N_c^2 corrections to the evolution of the dominant component with the lowest anomalous dimension - the only one that survives in the large-N_c limit - and observe a good agreement with the e…
We study the orbital angular momentum contribution to the spin structure of the proton. It is well known that the quark and gluon spin contributions do not add up to the proton spin. We motivate the connection between the Generalized Transverse Momentum Distribution (GTMD) $F_{14}$, and orbital angular momentum by exploring the underlying quark proton helicity amplitude structure. The twist three Generalized Parton Distribution (GPD) $\tilde{E}_{2T}$, was shown to connect to OAM. We study these functions using a diquark model calculation. The GTMD $F_{14}$ is unique in that it can describe bot…
An approach is described to calculate Generalized Parton Distributions (GPDs) in Constituent Quark Models (CQM). The GPDs are obtained from wave functions to be evaluated in a given CQM. The general relations linking the twist-two GPDs to the form factors and to the leading twist quark densities are recovered. Results for the leading twist, unpolarized GPD in the Isgur and Karl model are presented.
The first moment the chirality-odd twist-3 parton distribution $e(x)$ is related to the pion-nucleon $σ$-term which is important for phenomenology. However, the possible existence of a singular contribution proportional to $δ(x)$ in the distribution prevents from the determination of the $σ$-term with $e(x)$ from experiment. There are two approaches to show the existence. The first one is based on an operator identity. The second one is based on a perturbative calculation of a single quark state with finite quark mass. We show that all contributions proportional to $δ(x)$ in the first approach…
We study the effect of parton angular momentum on the twist-four correction to the left-right asymmetry in the electron-deuteron parity-violating deep inelastic scattering (PVDIS). We show that this higher-twist correction is transparent to the dynamics of parton angular momentum needed to account for the Sivers and Boer-Mulders functions and spin-independent parton distribution functions. A sufficiently precise measurement of the PVDIS asymmetry may, thus, provide additional information about the parton dynamics responsible for nucleon spin.
We set up a framework for the study of the power-suppressed three-parton contribution to the pion electromagnetic form factor in the $k_T$ factorization theorem. It is first shown that the gauge dependence proportional to parton transverse momenta from the two-parton Fock state and the gauge dependence associated with the three-parton Fock state cancel each other. After verifying the gauge invariance, we derive the three-parton-to-three-parton $k_T$-dependent hard kernel at leading order of the coupling constant, and find that it leads to about 5% correction to the pion electromagnetic form fa…
Basing upon dual analytic models, we present arguments in favor of the parametrization of generalized parton distributions (GPD) in the form (x/g_0)^{(1-x)\tildeα(t)}, where \tildeα(t)=α(t)-α(0) is the nonlinear part of the Regge trajectory and g_0 is a parameter, g_0>1. For linear trajectories it reduces to earlier proposals. We compare the calculated moments of these GPD with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier-transforming the obtained GPD, we access the spatial distribution of protons in the trans…
