Generalized transverse momentum dependent parton distributions (GTMDs), as mother funtions of transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs), encode the most general parton structure of hadrons. We calculate four twist-two time reversal odd GTMDs of pion in a scalar spectator model. We study the dependence of GTMDs on the longitudinal momentum fraction $x$ carried by the active quark and the transverse momentum $|\vec k_T|$ for different values of skewness $ξ$ defined as the longitudinal momentum transferred to the proton as well as the total momentum $|\vecΔ_T|$ transferred to the proton. In addition, the quasi-TMDs and quasi-GPDs of pion have also been investigated in this paper.
To facilitate lattice QCD calculations of nucleon structute, a set of quasi-parton distributions were recently introduced. These quasi-PDFs were shown to reduce to standard PDFs when the nucleon is boosted to high energies, $P_z\rightarrow \infty$. Since taking such limit is not feasible in lattice simulations, it is essential to provide guidance for what values of $P_z$ the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolariz…
We study the leading-twist quasi parton distribution function (quasi-PDF) and quasi generalize parton distribution (quasi-GPD) of the pion meson by using a spectator model. We consider the case the quasi functions are defined via inserting the matrix $γ^3$ in the spacial correlation functions. We obtain the analytical expressions for the quasi-PDF and quasi-GPD. The numerical results for them are calculated from the parameters obtained by fitting the model results to the known parametrization. Particularly, we investigate the hadron momentum dependence of the quasi functions as well as compare…
We revisit the connection between generalized parton distributions in impact parameter space and T-odd effects in single spin asymmetries of the semi-inclusive deep inelastic process. We show that nontrivial relations can be established only under very specific conditions, typically realized only in models that describe hadrons as two-body bound systems and involving a helicity-conserving coupling between the gauge boson and the spectator system. Examples of these models are the the scalar-diquark spectator model or the quark-target model for the nucleon, and relativistic models for the pion a…
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…
An Electron-Ion Collider (EIC) would enable next-generation measurements of deep-inelastic scattering (DIS) on the deuteron with detection of a forward-moving nucleon (p, n) and measurement of its recoil momentum ("spectator tagging"). Such experiments offer full control of the nuclear configuration during the high-energy process and can be used for precision studies of the neutron's partonic structure and its spin dependence, nuclear modifications of partonic structure, and nuclear shadowing at small x. We review the theoretical description of spectator tagging at EIC energies (light-front nu…
A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum $P_z$ is very large. Since taking the $P_z\to \infty$ limit is not feasible in lattice simulations, it is essential to provide guidance for what values of $P_z$ the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs…
We study the leading twist gluon generalized parton distributions (GPDs) and the gluon angular momentum inside the proton within a light-cone spectator model. Using the light-cone wave functions derived from the model, we provide the expressions of these distributions at the particular kinematical point $ξ=0$ in the overlap representation. The numerical results of the $H^g$, $E^g$, $\tilde{H}^g$, $H_T^g$ and $E_T^g$ as functions of $x$ at different $Δ_T$ are presented. Particularly, $H^g$, $\tilde{H}^g$ at non-zero $Δ_T$ are different from their forward counterparts, the unpolarized distributi…
All the leading-twist parton distribution functions are calculated in a spectator model of the nucleon, using scalar and axial-vector diquarks. Single gluon rescattering is used to generate T-odd distribution functions. Different choices for the diquark polarization states are considered, as well as a few options for the form factor at the nucleon-quark-diquark vertex. The results are listed in analytic form and interpreted in terms of light-cone wave functions. The model parameters are fixed by reproducing the phenomenological parametrization of unpolarized and helicity parton distributions a…
Recently the concept of quasi parton distributions (quasi-PDFs) for hadrons has been proposed. Quasi-PDFs are defined through spatial correlation functions and as such can be computed numerically using quantum chromodynamics on a four-dimensional lattice. As the hadron momentum is increased, the quasi-PDFs converge to the corresponding standard PDFs that appear in factorization theorems for many high-energy scattering processes. Here we investigate this new concept in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator mode…
We present a calculation of the twist-3 T-odd chiral-even fragmentation functions $G^{\perp}$ and $\tilde{G}^{\perp}$ using a spectator model. We consider the effect gluon exchange to calculate all necessary one-loop diagrams for the quark-quark and quark-gluon-quark correlation functions. We find that the gluon loops corrections generate non-zero contribution to these two fragmentation function. We numerically calculate their half-$k_T$ moments by integrating over the transverse momentum and also verify the equation of motion relation among $G^{\perp}$, $\tilde{G}^{\perp}$ and the Collins fun…
We show that for hadronic transverse energy $E_T$ in hadron-hadron collisions, the classic Collins-Soper-Sterman (CSS) argument for the cancellation of Glauber gluons breaks down at the level of two Glauber gluons exchanged between the spectators. Through an argument that relates the diagrams with these Glauber gluons to events containing additional soft scatterings, we suggest that this failure of the CSS cancellation actually corresponds to a failure of the `standard' factorisation formula with hard, soft and collinear functions to describe $E_T$ at leading power. This is because the observa…
Recent work suggests non-trivial relations between generalized parton distributions on the one hand and (naive time-reversal odd) transverse momentum dependent distributions on the other. Here we review the present knowledge on such type of relations. Moreover, as far as spectator model calculations are concerned, the existing results are considerably extended. While various relations between the two types of parton distributions can be found in the framework of spectator models, so far no non-trivial model-independent relations have been established.
Quasi parton distributions (quasi-PDFs) are currently under intense investigation. Quasi-PDFs are defined through spatial correlation functions and are thus accessible in lattice QCD. They gradually approach their corresponding standard (light-cone) PDFs as the hadron momentum increases. Recently, we investigated the concept of quasi-distributions in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. In the present work, we extend this study to the remaining six leading-twist GPDs. For large hadron momenta, all quas…
A microscopic treatment of cumulative phenomena based on perturbative QCD calculations of the corresponding quark diagrams near the threshold is presented. To sum all diagrams like these the special technique based on the recurrence relations was developed. The x-behaviour of the nuclear structure function $F_{2}(x)$ in the cumulative region x>1 was found to be roughly exponential, governed by an effective coupling constant, which depends on the QCD coupling constant and quark mass. Two mechanisms for cumulative particle production, direct and spectator ones, were analysed. It was shown that d…
We revisit the derivation of collinear factorization for Deep Inelastic Scattering at sub-asymptotic values of the four momentum transfer squared, where the masses of the particles participating in the interaction cannot be neglected. By using an inclusive jet function to describe the scattered quark final state, we can restrict the needed parton kinematic approximations just to the four-momentum conservation of the hard scattering process, and explicitly expand the rest of the diagram in powers of the unobserved parton transverse momenta rather than neglecting those. This procedure provides o…
We define in the framework of light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the $π^0$) up to twist 6. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 28 real GPDs, which are subject to constraints coming from the QCD equations of motion.
We investigate the quark Wigner distributions in a light-cone spectator model. The Wigner distribution, as a quasi-distribution function, provides the most general one-parton information in a hadron. Combining the polarization configurations, unpolarized, longitudinal polarized or transversal polarized, of the quark and the proton, we can define 16 independent Wigner distributions at leading twist. We calculate all these Wigner distributions for the $u$ quark and the $d$ quark respectively. In our calculation, both the scalar and the axial-vector spectators are included, and the Melosh-Wigner …
The present knowledge on non-trivial relations between generalized parton distributions on the one hand and transverse momentum dependent distributions on the other is reviewed. While various relations can be found in the framework of spectator models, so far no model-independent non-trivial relations have been established.
We define in a systematic way, based on the light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the pi0) up to twist 5. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 20 real GPDs, whose symmetry properties are explicitely given. The reduction of these GPDs to a minimal set is …
We present exploratory studies of the 3D proton tomography through polarized $T$-odd gluon TMDs at leading twist, obtained in a spectator-model framework. We embody in our approach a flexible parameterization for the spectator-mass spectral function, suited to catch both small- and moderate-$x$ effects. All these studies are relevant to unveil the gluon dynamics inside hadrons, which represents a core research line of studies at new-generation colliders, such as the Electron-Ion Collider, NICA-SPD, the High-Luminosity LHC, and the Forward Physics Facility.
We compute the leading-twist T-odd quasi-distributions of the proton in a spectator model with scalar and axial-vector diquarks: the quasi Sivers function $\tilde{f}_{1T}^\perp(x, k_T^2; P_z)$ and the quasi Boer-Mulders function $\tilde{h}_1^\perp(x, k_T^2; P_z)$. We obtain the quark-quark correlators in the four-dimensional Euclidian space by replacing $γ^+$ and $σ^{i+}$ in the light-cone frame with $γ_z$ and $σ_{iz}$. We show by analytical calculation that the results of $\tilde{f}_{1T}^\perp$ and $\tilde{h}_1^\perp$ derived from the correlators can reduce to the expressions of the correspon…
We investigate the quark angular momentum in a model with the nucleon being a quark and a spectator. Both scalar and axial-vector spectators are included. We perform the calculations in the light-cone formalism where the parton concept is well defined. We calculate the quark helicity and canonical orbital angular momentum. Then we calculate the gravitational form factors which are often related to the kinetic angular momentums, and find that even in a no gauge field model we cannot identify the canonical angular momentums with half the sum of gravitational form factors. In addition, we examine…
T-odd distributions like Sivers and Boer-Mulders functions are normally modeled using few-body models. In the present work I want to follow the completely opposite point of view, and study a high-energy proton-proton Drell-Yan where both the annihilating partons are wee, and one (at least) comes from a high-order Fok state of the parent proton, i.e. a state where a large number N of partons is present. I show that rescattering between active and spectator partons is modified, with suppression of those terms that are needed to build T-odd parton distributions.
Quantum chromodynamics is a fundamental non-abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state, $|θ\rangle$, is a linear superposition of the $n$-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in th…
We report on a calculation of the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively using overlaps of light-front wave functions (LFWFs).
We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon.
We present the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively using overlaps of light-front wave functions (LFWFs) in a simple model. We also present the chiral even GPDs in positon space in a phenomenological model.
We present a study of the chiral-odd generalized parton distributions for $u$ and $d$ quarks in a proton using the light front wave functions of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We obtain the GPDs in terms of overlaps of the LFWFs. Numerical results for chiral-odd GPDs in momentum as well as transverse position spaces considering both zero and nonzero skewness($ζ$) are presented. For nonzero skewness, the GPDs are also evaluated in longitudinal position space.
Lorentz invariance relations connecting twist-3 parton distributions with transverse momentum dependent twist-2 distributions have been proposed previously. These relations can be extracted from a covariant decomposition of the quark-quark correlator. It is argued, however, that the derivation of the Lorentz invariance relations fails if the path-ordered exponential is taken into account in the correlator. The model independent analysis is supplemented by an explicit calculation of the corresponding parton distributions in perturbative QCD with a quark target, and in a simple spectator model. …
We calculate the non-zero (naïve) T-odd transverse momentum dependent transversity distribution $h_1^{\perp}(x,\kp^2)$ of the pion in a quark-spectator-antiquark model. The final-state interaction is modelled by the approximation of one gluon exchange between the quark and the antiquark spectator. Using our model result we estimate the unsuppressed cos2$ϕ$ azimuthal asymmetry in unpolarized $π^-p$ Drell-Yan process. We find that the transverse momentum dependence of $h_1^{\perp}(x,\kp^2)$ of the pion is the same as that of $h_1^{\perp}(x,\kp^2)$ of the proton calculated from the quark-scalar-d…
QCD Wehrl and entanglement entropies in a gluon spectator model at small-$x$
Universidade Estadual de Campinas – Instituto de Física Gleb Wataghin（坎皮纳斯州立大学 - 格莱布·瓦塔金物理研究所）；Federal University of Rio Grande do Sul (UFRGS)（南里奥格兰德联邦大学）
Double Parton Scattering Effects on the Measurement of the W-Boson Mass
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Shanghai Institute of Satellite Engineering（上海卫星工程研究所）；State Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所粒子天体物理国家重点实验室）
Parton distributions contain factorizable final state interaction effects originating from the fast-moving struck quark interacting with the target spectators in deeply inelastic scattering. We show that these interactions give rise to gauge invariance of the transverse momentum-dependent parton distributions. As compared to previous analyses, our study demonstrates the existence of extra scaling contributions from transverse components of the gauge potential at the light-cone infinity. They form a transverse gauge link which is indispensable for restoration of the gauge invariance of parton d…
We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. The light-front wave function (LFWF) of this system gives a template for the quark spin-one diquark structure of the valence LFWF of the proton. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.
Using a physically motivated parameterization based on the reggeized diquark model we perform a flavor separation of the chiral-odd generalized parton distributions obtained from both $π^0$ and $η$ exclusive electroproduction. In our approach we exploit a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations that are relevant for a class of models that includes two-component models. We compare our results for $η$ production to the previously obtained $π^0$ results, and we make predictions for the transverse single spin asymmetry components w…
Exclusive $π^o$ electroproduction is suggested for extracting both the tensor charge and the transverse anomalous magnetic moment from experimental data. A connection between partonic degrees of freedom, given in terms of Generalized Parton Distributions, and Regge phenomenology is discussed. Calculations are performed using a physically motivated parametrization that is valid at values of the skewness, $ζ\neq 0$. Our method makes use of information from the nucleon form factor data, from deep inelastuc scattering parton distribution functions, and from lattice results on the Mellin moments of…
In the present work we have studied the chiral odd Generalized Parton Distributions (GPDs) in the impact parameter space by assuming a flexible parametrization in a quark-diquark model. In order to obtain the explicit contributions from the up and down quarks, we have considered both the scalar (spin-0) and the axial-vector (spin-1) configurations for the diquark. We have also studied the spin densities for the up and down quarks in this model for monopole, dipole and quadrupole contributions for unpolarized and polarized quarks in unpolarized and polarized proton.
We report progresses on leading-twist transverse-momentum-dependent (TMD) gluon distributions, calculated in a spectator-model framework for the parent nucleon. We encode in our formalism a fit-based parameterization for the spectator-mass density, suited to describe the gluon content of the proton in a wide range of $x$. We present preliminary results on the $f$-type Sivers function, a key ingredient to access relevant spin-asymmetries emerging when the nucleon is transversely polarized. These studies are helpful to shed light on the gluon dynamics inside nucleons and nuclei, which is one of …
We present a physically motivated parameterization of the chiral-odd generalized parton distributions. The parametrization is an extension of our previous one in the chiral-even sector which was based on the reggeized diquark model. While for chiral even generalized distributions a quantitative fit with uncertainty estimation can be performed using deep inelastic scattering data, nucleon electromagnetic, axial and pseudoscalar form factors measurements, and all available deeply virtual Compton scattering data, the chiral-odd sector is far less constrained. While awaiting the analysis of measur…
We present the general framework to calculate chiral-odd generalized parton distributions in the overlap representation using the Fock-state decomposition in the transverse spin basis. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon. Numerical results are obtained by applying the formalism to the case of light-cone wavefunctions of constituent quark models.
Within the framework of light-cone quantization we derive the overlap representation of generalized parton distributions for transversely polarized quarks using the Fock-state decomposition in the transverse-spin basis. We apply this formalism to the case of light-cone wave functions in a constituent quark model giving numerical results for the four chiral-odd generalized parton distributions in a region where they describe the emission and reabsorption of a quark by the nucleon. With the transversity distribution obtained in the forward limit of the generalized distribution, we provide some p…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
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)-…
