Transverse-mass spectra of protons, pions and kaons produced in collisions of heavy nuclei are analyzed within the model of 3-fluid dynamics. It was demonstrated that this model consistently reproduces these spectra in wide ranges of incident energies E_{lab}, from 4A GeV to 160A GeV, rapidity bins and centralities of the collisions. In particular, the model describes the "step-like" dependence of kaon inverse slopes on the incident energy. The key point of this explanation is interplay of hydrodynamic expansion of the system with its dynamical freeze-out.
In the wounded nucleon model, a proton-nucleus (p+A) collision is a superposition of independent nucleon-nucleon collisions. We use this model to calculate the average transverse momentum of pions, kaons and protons in high energy p+A collisions. For the same number of produced particles, because the number of participants differs, in the wounded nucleon model the transverse momentum of hadrons can differ between p+p and p+A collisions. In this model we find that the average transverse momentum in high multiplicity p+A collisions depends weakly on the number of produced particles, and underest…
Using recent experimental data, we analyze the electromagnetic transition from the nucleon to the P11(1440) resonance. From the resulting empirical transition form factors, we map out the quark transverse charge densities which induce the N to P11(1440) transition. It is found that the transition from the proton to its first radially excited state is dominated by up quarks in a central region of around 0.5 fm and by down quarks in an outer band which extends up to about 1 fm.
Through an impulse approximation analysis of single spin Sivers and Collins asymmetries in the Bjorken limit, the possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized 3He is illustrated. The analysis is generalized to finite momentum transfers in a light-front Poincare' covariant framework, defining the light-front spin-dependent spectral function of a J=1/2 system. The definition of the light-front spin-dependent spectral function for constituent quarks in the nucleon allows us to show that, with…
The transverse densities in a fast-moving nucleon offer a model-independent framework for analyzing the spatial structure of the pion cloud and its role in current matrix elements. We calculate the chiral large-distance component of the charge density using a dispersion representation of the form factor and discuss its partonic interpretation. The non-chiral core is dominant up to surprisingly large distances ~2 fm. The chiral component can be probed in precision low-Q^2 elastic eN scattering or in peripheral deep-inelastic processes which resolve its quark/gluon content.
We study the sensitivity of isospin dependence of nucleon-nucleon cross section and symmetry energy on the collective transverse in-plane flow. We find that collective transverse flow in Ca+Ca reactions shows great sensitivity to isospin dependence of nn cross section and symmetry energy.
In the light-front description of nucleon structure the electromagnetic form factors are expressed in terms of frame-independent transverse densities of charge and magnetization. Recent work has studied the transverse densities at peripheral distances b = O(M_pi^{-1}), where they are governed by universal chiral dynamics and can be computed in a model-independent manner. Of particular interest is the comparison of the peripheral charge and magnetization densities. We summarize (a) their interpretation as spin-independent and -dependent current matrix elements; (b) the leading-order chiral effe…
We investigate the transverse quark spin densities of the nucleon with the lowest moment within the framework of the SU(3) chiral quark-soliton model, emphasizing the strange quark spin density. Based on previous results of the vector and tensor form factors, we are able to determine the impact-parameter dependent probability densities of transversely polarized quarks in an unpolarized nucleon as well as those of unpolarized quarks in a transversely polarized nucleon. We find that the present numerical results for the transverse spin densities of the up and down quarks are in good agreement wi…
We present a systematic study of generalized transverse-momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. We present such simultaneous modeling by considering a light-cone wave function overlap representation of the GTMDs. We construct the different quark-quark correlation functions from the 3-quark Fock components within both the light-front constituent quark model as well as wit…
We investigate the medium modification of the generalized vector form factors of the nucleon, which include the electromagnetic and energy-momentum tensor form factors, based on an in-medium modified $π$-$ρ$-$ω$ soliton model. We find that the vector form factors of the nucleon in nuclear matter fall off faster than those in free space, which implies that the charge radii of the nucleon become larger in nuclear medium than in free space. We also compute the corresponding transverse charge densities of the nucleon in nuclear matter, which clearly reveal the increasing of the nucleon size in nuc…
We calculate the photon production cross section arising from the hard scattering of partons in nucleon-nucleon collisions by taking into account the intrinsic parton transverse momentum distribution and the next-to-leading-order contributions. As first pointed out by Owens, the inclusion of the intrinsic transverse momentum distribution of partons leads to an enhancement of photon production cross section in the region of photon transverse momenta of a few GeV/c for nucleon-nucleon collisions at a center-of-mass energy of a few tens of GeV. The enhancement increases as $\sqrt{s}$ decreases. S…
We investigated the transverse charge densities in the nucleon in nuclear matter within the framework of the in-medium modified Skyrme model. The medium modification of the nucleon electromagnetic form factors are first discussed. The results show that the form factors in nuclear matter fall off faster than those in free space, as the momentum transfer increases. As a result, the charge radii of the nucleon become larger, as the nuclear matter density increases. The transverse charge densities in the nucleon indicate that the size of the nucleon tends to bulge out in nuclear matter. This salie…
The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances $b = O(M_π^{-1})$ the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representa…
We review the current status and future perspectives of theory and experiments of transverse spin phenomena in high-energy scattering processes off nucleon targets and related issues in nucleon structure and QCD. Systematic exploration of transverse spin effects requires measurements in polarized deep-inelastic scattering, polarized pp collisions, and e+e- annihilations. Sophisticated QCD-based techniques are also needed to analyze the experimental data sets.
We present a complete study of the leading-twist quark Wigner distributions in the nucleon, discussing both the $\mathsf T$-even and $\mathsf T$-odd sector, along with all the possible configurations of the quark and nucleon polarizations. We identify the basic multipole structures associated with each distribution in the transverse phase space, providing a transparent interpretation of the spin-spin and spin-orbit correlations of quarks and nucleon encoded in these functions. Projecting the multipole parametrization of the Wigner functions onto the transverse-position and the transverse-momen…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse-momentum dependent parton distributions. They depend on both the transverse position and the three-momentum of the quark relative to the nucleon, and therefore combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. We focus the discussion on the distributio…
This work presents the first calculation in lattice QCD of three moments of spin-averaged and spin-polarized generalized parton distributions in the proton. It is shown that the slope of the associated generalized form factors decreases significantly as the moment increases, indicating that the transverse size of the light-cone quark distribution decreases as the momentum fraction of the struck parton increases.
Recent progress on the extraction of electromagnetic properties of nucleon resonance excitation through pion photo- and electroproduction is reviewed. Cross section data measured at MAMI, ELSA, and CEBAF are analyzed and compared to the analysis of other groups. On this basis, we derive longitudinal and transverse transition form factors for most of the four-star nucleon resonances. Furthermore, we discuss how the transition form factors can be used to obtain empirical transverse charge densities. Contour plots of the thus derived densities are shown for the Delta, Roper, S11, and D13 nucleon …
We study the nucleon's partonic angular momentum (AM) content at peripheral transverse distances $b = \mathcal{O}(M_π^{-1})$, where the structure is governed by chiral dynamics. We compute the nucleon form factors of the energy-momentum tensor in chiral effective field theory (ChEFT) and construct the transverse densities of AM at fixed light-front time. In the periphery the spin density is suppressed, and the AM is predominantly orbital. In the first-quantized representation of ChEFT in light-front form, the field-theoretical AM density coincides with the quantum-mechanical orbital AM density…
QCD-based scaling arguments predict the predominance of longitudinal over transverse electroproduction of pions by terms $\propto Q^2$. However, data from JLAB, Cornell and DESY, covering a wide kinematical range $1 < Q^2 < 11\, {\rm GeV}^2$ and $2\, {\rm GeV} < W < 4\, {\rm GeV}$, do not show this expected behavior. At the same time standard descriptions of pion-electroproduction on nucleons have given a very good description of the longitudinal components of the cross sections. However, these very same models have failed grossly in describing the transverse component. We discuss here a commo…
The transverse mass spectra of light mesons produced in Au-Au collisions at 200 GeV/nucleon are analyzed in Tsallis statistics. In high energy collisions, it has been found that the spectra follow a generalized scaling law. We applied Tsallis statistics to the description of different particles using the scaling properties. The calculated results are in agreement with experimental data of PHENIX Collaboration. And, the temperature of emission sources is extracted consistently.
We discuss the general formalism for the calculation in light-front quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon, parametrized in terms of generalized transverse momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. The corresponding distributions in impact-parameter space are the Wigner functions which provide multidimensional images of t…
Color Lorentz force on a transversely polarized quark in the nucleon
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Iowa State University（爱荷华州立大学）
We present a calculation of the Mellin moments of the nucleon transverse quark spin densities extracted from the unpolarized and transversity generalized form factors. We use three $N_F=2+1+1$ ensembles of twisted mass fermions with quark masses tuned to their physical values and lattice spacings $a\sim 0.08$~fm, $a\sim 0.07$~fm and $a\sim 0.06$~fm and extrapolate the form factors to the continuum limit. Besides isovector densities we also include results for the tensor charge for each quark flavor using the ensemble with $a\sim 0.08$~fm for which we include the disconnected contributions.
Predictions for electron induced proton knockout from the $p_{1/2}$ and $p_{3/2}$ shells in $^{16}$O are presented using various approximations for the relativistic nucleonic current. Results for the differential cross section, transverse-longitudinal response ($R_{TL}$) and left-right asymmetry $A_{TL}$ are compared at $|Q^2|=0.8$ (GeV/c)$^2$ corresponding to TJNAF experiment 89-003. We show that there are important dynamical and kinematical relativistic effects which can be tested by experiment.
We show that exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions can be systematically studied in QCD factorization approach if the photon's transverse momentum $q_T$ with respect to the colliding pion is much greater than $Λ_{\rm QCD}$. We demonstrate that the leading power non-perturbative contributions to the scattering amplitudes of this exclusive process are process-independent and can be systematically factorized into universal pion's distribution amplitudes (DAs) and nucleon's generalized parton distributions (GPDs), which are convoluted with co…
Several observables of unbound nucleons which are to some extent sensitive to the medium modifications of nucleon-nucleon elastic cross sections in neutron-rich intermediate energy heavy ion collisions are investigated. The splitting effect of neutron and proton effective masses on cross sections is discussed. It is found that the transverse flow as a function of rapidity, the $Q_{zz}$ as a function of momentum, and the ratio of halfwidths of the transverse to that of longitudinal rapidity distribution $R_{t/l}$ are very sensitive to the medium modifications of the cross sections. The transver…
We have implemented the Tsallis q-statistics in the Weibull model of particle production known as the q-Weibull distribution to describe the transverse-momentum (pT ) distribution of the charged hadrons at mid-rapidity measured at RHIC and LHC energies. The model describes the data remarkably well for the entire pT range measured in nucleus-nucleus and nucleon-nucleon collisions. The proposed distribution is based on the non-extensive Tsallis q-statistics which replaces the usual thermal equilibrium assumption of hydrodynamical models. The parameters of the distribution can be related to the v…
The nucleon's peripheral transverse charge and magnetization densities are computed in chiral effective field theory. The densities are represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft pion-nucleon intermediate states. The orbital motion of the pion causes a large left-right asymmetry in a transversely polarized nucleon. The effect attests to the relativistic nature of chiral dynamics [pion momenta k = O(M_pi)] and could be observed in form factor measurements at low momentum transfer.
Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\…
The transverse momentum dependence of J/Psi suppression in relativistic heavy ion collisions is calculated from initial state gluon rescattering not only with nucleons but also with prompt gluons produced in nucleon-nucleon collisions in the early phase of the reaction. The second mechanism is new and turns out to be important in a description of the data for central collisions.
Forward rapidity $J/ψ$ meson production in proton-nucleus collisions can be an important constraint of descriptions of the small-$x$ nuclear wavefunction. In an earlier work we studied this process using a dipole cross section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data and consistently extrapolated to the nuclear case using a standard Woods-Saxon distribution. In this paper we present further calculations of these cross sections, studying the mean transverse momentum of the meson and the dependence on collision centrality. We also extend the calculation to backward …
Light-Front Transverse Nucleon Charge and Magnetisation Densities
Universidad de Huelva（韦尔瓦大学）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗森多夫亥姆霍兹中心）；Anhui Normal University（安徽师范大学）；Nanjing University（南京大学）；Institute for Nonperturbative Physics, Nanjing University（南京大学非微扰物理研究所）；Univ. Pablo de Olavide（巴勃罗·德·奥拉维德大学）
We calculate the amplitude for exclusive neutrino production of a charmed meson on an unpolarized target, in the colinear QCD approach where generalized parton distributions (GPDs) factorize from perturbatively calculable coefficient functions. We demonstrate that the transversity chiral odd GPDs contribute to the transverse cross section if the hard amplitude is calculated up to order mc/Q. We show how to access these GPDs through the azimuthal dependence of the nu N -> mu D N differential cross section.
Background: The transverse densities $ρ_{1, 2}(b)$ describe the distributions of electric charge and magnetic moment at fixed light-front time and connect the nucleon's elastic form factors with its partonic structure. The dispersive representation of the form factors $F_{1, 2}(t)$ expresses the densities in terms of exchanges of hadronic states in the $t$-channel and permits their analysis using hadronic physics methods. Purpose: Compute the densities at peripheral distances $b = \mathcal{O}(M_π^{-1})$, where they are generated predominantly by the two-pion states in the dispersive representa…
The transverse momentum spectra of the produced hadrons have been compared to a model which is based on the assumption that a nucleus-nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze out temperature. The freeze-out temperature in nucleus-nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon-nucleon collision. The successive collisions in the nuclear reaction leads to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse ra…
We first describe a new way to access the chiral odd transversity parton distribution in the proton through the photoproduction of lepton pairs. The basic ingredient is the interference of the usual Bethe-Heitler or Drell-Yan amplitudes with the amplitude of a process, where the photon couples to quarks through its chiral-odd distribution amplitude, which is normalized to the magnetic susceptibility of the QCD vacuum. We also show how the chiral-odd transversity generalized parton distributions (GPDs) of the nucleon can be accessed experimentally through the exclusive electro - or photoproduct…
We review the status of our understanding of nucleon structure based on the modelling of different kinds of parton distributions. We use the concept of generalized transverse momentum dependent parton distributions and Wigner distributions, which combine the features of transverse-momentum dependent parton distributions and generalized parton distributions. We revisit various quark models which account for different aspects of these parton distributions. We then identify applications of these distributions to gain a simple interpretation of key properties of the quark and gluon dynamics in the…
For the first time, mass dependence of balance energy only for heavier systems has been studied. Our results are in excellent agreement with the data which allow us to predict the balance energy of U+U, for the first time, around 37-39 MeV/nucleon. Also our results indicate a hard equation of state along with nucleon-nucleon cross-section around 40 mb.
A complete theoretical study is presented for the disappearance of flow, for the first time, by analyzing 15 reactions with masses between 47 and 476 units. We demonstrate that the effect of nucleon-nucleon cross-section reduces to insignificant level for heavier colliding nuclei in agreement with previous studies. A stiff equation of state with nucleon-nucleon cross-sections of 35-40 mb is able to explain all the measured balance energies within few percent. A power law is also given for the mass dependence of the disappearance of flow which is in excellent agreement with experimental data.
Nucleon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of nonlocal three quark operators between a nucleon and a meson states, arise within the collinear factorized description of hard exclusive electroproduction of mesons off nucleons in the backward direction. Below we address the problem of modelling pion to nucleon TDAs. We suggest a factorized Ansatz for quadruple distributions with input from the soft pion theorem for pi N TDAs. In order to satisfy the polynomiality property in its full form the spectral representation is complemented with a D-term like …
At the very first stage of an ultra-relativistic nucleus-nucleus collision new particles are produced in individual nucleon-nucleon collisions. In the transverse plane, all particles from a single $NN$ collision are initially located at the same position. The subsequent transverse radial expansion of the system creates strong position-momentum correlations and leads to characteristic rapidity, transverse momentum, and azimuthal correlations among the produced particles.
The observation of the violation of Lam-Tung relation in the $πN$ Drell-Yan process triggered many theoretical speculations. The TMD Boer-Mulders functions characterizing the correlation of transverse momentum and transverse spin for partons in unpolarized hadrons could nicely account for the violation. The COMPASS experiment at CERN will measure the angular distributions of dimuons from the unpolarized Drell-Yan process over a wide kinematic region and study the beam particle dependence. Significant statistics is expected from a successful run in 2015 which will bring further understanding of…
We study the transverse flow throughout the mass range from $^{20}Ne+^{20}Ne$ to $^{131}Xe+^{131}Xe$ as a function of the impact parameter. We find that at smaller impact parameters the flow is negative while going through the impact parameter, transverse flow vanishes at a particular colliding geometry named GVF. We find that the mass dependence of GVF is insensitive to the equation of state and momentum dependent interactions whereas it is quite sensitive to the cross section. So it can act as a useful tool to pin down the nucleon nucleon cross section.
Within a transport model, we study the neutron-proton differential transverse flow and its excitation function in central $^{132}$Sn + $^{124}$Sn collisions at 270 MeV/nucleon. To more accurately evaluate effects of the high-density behavior of symmetry energy \esym on this observable, we also consider the uncertainties of \esym around the saturation density $ρ_{0}$. It is shown that the neutron-proton differential transverse flow and its excitation function are mainly sensitive to the slope $L$ of \esym at $ρ_{0}$. However, the effects of low-density behavior of \esym on this observable shoul…
Recent analyses of backward meson electroproduction support the validity of a collinear QCD factorization framework for these hard exclusive reactions. This opens a way to the extraction of nucleon-to-meson transition distribution amplitudes (TDAs) from the experimental data. Similarly to the generalized parton distributions, TDAs - after the Fourier transform in the transverse plane - carry valuable information on the transverse location of hadron constituents. We address the properties of integrated nucleon-to-meson TDAs in the impact parameter representation. We argue that the emerging pict…
We study the transverse flow for systems having various N/Z ratios. We find the transverse flow is sensitive to N/Z ratio and, in fact, increases with N/Z of the system. The relative contribution of symmetry energy and isospin dependence of nucleon-nucleon cross section is also investigated. We find the greater sensitivity of symmetry energy in the lighter systems compared to heavier ones.
Transverse Charge Distribution as a Probe of Nucleon Transversity
Fudan University（复旦大学）；Beijing Normal University（北京师范大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Peking University（北京大学）
The physical nucleon is modeled as a bare nucleon surrounded by a pion cloud using a psuedoscalar pion-nucleon coupling to examine its implications for the neutron form factor, F_1, and the corresponding transverse charge density in the infinite momentum frame. Two versions, one with a tunable Pauli-Villars parameter, and one with light-front cloudy-bag pion-nucleon form factors, are examined. A qualitative agreement with the experimental form factor (negative definite for all Q^2) and transverse charge density are achieved when the nucleon is treated as having a finite extent. The bare nucleo…
Regge-pole based descriptions of pion-electroproduction on nucleons have given a very good description of the longitudinal components of the cross sections. However, these very same models grossly underestimate the transverse components. A related problem appears in QCD-based scaling arguments that predict the predominance of longitudinal over transverse electroproduction of pions by terms $\propto Q^2$. However, data from JLAB, Cornell and DESY, covering a wide kinematical range $1 < Q^2 < 11\, {\rm GeV}^2$ and $2\, {\rm GeV} < W < 4\, {\rm GeV}$, do not show this expected behavior. We addres…
We study the relative contribution of the symmetry energy and isospin dependence of the nucleon-nucleon cross section to the collective transverse in-plane flow for the reactions of Ca+Ca having N/Z varying from 1.0, 1.6 and 2.0. We see that role of symmetry energy to the flow increases with N/Z of the system.
Existence of nuclear modifications on longitudinal-transverse structure-function ratio
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Southern Center for Nuclear Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；Faculty of Science, Japan Women’s University（日本女子大学理学部）；KEK Theory Center, Institute of Particle and Nuclear Studies, KEK（高能加速器研究机构粒子与核研究所学部理论中心）
We use a Glauber-like approach to describe very energetic nucleus-nucleus collisions as a sequence of binary nucleon-nucleon collisions. No free parameters are needed: all the information comes from simple parametrizations of nucleon-nucleon collision data. Produced mesons are assumed not to interact with each other or with the original baryons. Comparisons are made to published experimental measurements of baryon rapidity and transverse momentum distributions, negative hadron rapidity and transverse momentum distributions, average multiplicities of pions, kaons, hyperons, and antihyperons, an…
At the very first stage of an ultra-relativistic nucleus-nucleus collision new particles are produced in individual nucleon-nucleon collisions. In the transverse plane, all particles from a single $NN$ collision are initially located at the same position. The subsequent thermalization and transverse radial expansion of the system create strong position-momentum correlations and lead to characteristic rapidity, transverse momentum, and azimuthal correlations among the produced particles.
We study the balance energy as a function of the composite mass of the system. The results are in very good agreement with data over a wide range of masses from very light (Ne+Al) to very heavy (Au+Au) for hard equation of state and nucleon-nucleon cross-section of 40 mb strength.
In this dissertation we apply the pionless effective field theory to low energy neutron deuteron elastic scattering process. We calculated some of the polarization observables in neutron deuteron scattering to next-to-next-to-next-to-leading-order, in particular the transverse asymmetry $A_y$. All of the previous calculations have the same characteristic feature of under-predicting this observable, this is known as the $A_y$-puzzle. At this order of the pionless EFT new two-body $P$-wave interaction terms enter into the Lagrangian. This interaction terms give crucial contributions to the $A_y$…
We present a parametrization of the observed enhancement in the transverse electron quasielastic (QE) response function for nucleons bound in carbon as a function of the square of the four momentum transfer ($Q^2$) in terms of a correction to the magnetic form factors of bound nucleons. The parametrization should also be applicable to the transverse cross section in neutrino scattering. If the transverse enhancement originates from meson exchange currents (MEC), then it is theoretically expected that any enhancement in the longitudinal or axial contributions is small. We present the prediction…
I discuss relativistic models of few-nucleon systems, with particular emphasis on calculations of electron-deuteron scattering and the comparison of these calculations with recent data from Jefferson Lab.
We investigate the nuclear effects on the transverse and longitudinal responses in the deep inelastic region due to the nuclear binding and nucleon Fermi motion. We display the role of the transverse-longitudinal admixture due to the transverse nucleon momentum. The mixing effect is appreciable at small Q^2 values, and gradually disappears at large Q^2 values. The nuclear modification is then dominated by the binding and Fermi-motion effects which are contained in the spectral function.
