Isospin-dependent nuclear forces play a fundamental role in nuclear structure. In relativistic models of nuclear structure constructed at the quark level these isovector nuclear forces affect the u and d quarks differently, leading to non-trivial flavour dependent modifications of the nuclear parton distributions. We explore the effect of isospin dependent forces for parity-violating deep inelastic scattering on nuclear targets and demonstrate that the cross-sections for nuclei with N /= Z are sensitive to the flavour dependence of the EMC effect. Indeed, for nuclei like lead and gold we find that these flavour dependent effects are large.
We determine nuclear structure functions and quark distributions for $^7$Li, $^{11}$B, $^{15}$N and $^{27}$Al. For the nucleon bound state we solve the covariant quark-diquark equations in a confining Nambu--Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. W…
A recent theoretical model predicts that the modification of quark distributions in the nuclear medium (EMC effect) depends on the flavor of the quarks. We investigate $W$-boson production in proton-nucleus collision as a possible tool to test this theoretical prediction. Several experimental observables in $W$ production sensitive to the flavor-dependent EMC effect are identified. Calculations for these experimental observables at the RHIC and LHC energies are presented using the recent flavor-dependent EMC model.
The deep inelastic scattering cross section for scattering from bound nucleons differs from that of free nucleons.This phenomena, first discovered 30 years ago, is known as the EMC effect and is still not fully understood. Recent analysis of world data showed that the strength of the EMC effect is linearly correlated with the relative amount of Two-Nucleon Short Range Correlated pairs (2N-SRC) in nuclei. The latter are pairs of nucleons whose wave functions overlap, giving them large relative momentum and low center of mass momentum, where high and low is relative to the Fermi momentum of the …
Recent developments in understanding the influence of the nucleus on deep-inelastic structure functions, the EMC effect, are reviewed. A new data base which expresses ratios of structure functions in terms of the Bjorken variable $x_A=AQ^2/(2M_A q_0)$ is presented. Information about two-nucleon short-range correlations from experiments is also discussed and the remarkable linear relation between short-range correlations and teh EMC effect is reviewed. A convolution model that relates the underlying source of the EMC effect to modification of either the mean-field nucleons or the short-range co…
It has been recently confirmed that the magnitude of the EMC effect measured in electron deep inelastic scattering is linearly related to the Short Range Correlation scaling factor obtained from electron inclusive scattering. By using a $x$-rescaling approach we are able to understand the interplay between the quark-gluon and hadronic degrees of freedom in the discussion of the EMC effect.
Pion-induced Drell-Yan processes are proposed as a potential tool to measure the flavor dependence of the EMC effect, that is, the flavor-dependent modification of quark distributions in the nuclear medium. Existing pionic Drell-Yan data are compared with calculations using a recent model for nuclear quark distributions that incorporates flavor-dependent nuclear effects. While no firm conclusions can yet be drawn, we demonstrate that existing Drell-Yan data seem to imply a flavor dependence of the EMC effect. We highlight how pion-induced Drell-Yan experiments on nuclear targets can access imp…
The break-up of the deuteron during deeply-virtual Compton scattering, gamma* d --> gamma(*) n p, is explored. In the effective field theory describing nucleon dynamics at momenta below the pion mass, the EMC effect results from four-nucleon interactions with the twist-2 operators, appropriate for describing forward, and near-forward, matrix elements in the two-nucleon system. We point out that the break-up of the deuteron to low-energy final states during deeply-virtual Compton scattering is a process with which to explore strong-interaction physics closely related to that responsible for the…
A linear correlation is shown quantitatively between the magnitude of the EMC effect measured in electron deep inelastic scattering (DIS) and the nuclear residual strong interaction energy (RSIE) obtained from nuclear binding energy subtracting the Coulomb energy contribution. This phenomenological relationship is used to extract the size of in-medium correction (IMC) effect on deuteron and to predict the EMC slopes $|dR_{EMC}/dx|$ of various nuclei. We further investigate the correlations between RSIE and other quantities which are related to the EMC effect. The observed correlations among RS…
This paper shows quantitatively that the magnitude of the EMC effect measured in electron deep inelastic scattering (DIS) at intermediate $x_B$, $0.35\le x_B\le 0.7$, is linearly related to the Short Range Correlation (SRC) scaling factor obtained from electron inclusive scattering at $x_B\ge 1.$. The observed phenomenological relationship is used to extract the ratio of the deuteron to the free $pn$ pair cross sections, the DIS cross section for a free neutron, and $F_2^n/F_2^p$, the ratio of the free neutron to free proton structure functions. We speculate that the observed correlation is be…
The ratios of the in-medium to free nucleon structure functions for the unpolarized and polarized cases are obtained using the MIT bag model for the free case, along with the QMC model to incorporate the in-medium modifications of the structure functions. As discussed in earlier work, the observed nuclear EMC effect is reasonably well described. This gives us confidence to investigate the predictions of the model for the polarized EMC effect, the ratio $g_1^*(x)/g_1(x)$ for a bound proton to that of a free proton. This ratio is found to be substantially different from unity and very similar in…
Recent data on the EMC effect from Jefferson Lab experiment E03103 suggest that the nuclear dependence of the high x quark distribution may depend on the local nuclear environment, rather than being a purely bulk effect. We briefly discuss the analysis and results of the E03103 experiment focusing on the light nuclei and high x region. In addition, we also discuss a future experiment at the upgraded 12 GeV Jefferson Lab facility which will further investigate the role of the local nuclear environment and the influence of detailed nuclear structure on the modification of quark distributions.
Using QCD-inspired time dependent cross sections for pre-hadrons we provide a combined analysis of available experimental data on hadron attenuation in DIS off nuclei as measured by HERMES with 12 and 27 GeV and by EMC with 100 and 280 GeV lepton beam energies. We extract the complete four-dimensional evolution of the pre-hadrons using the JETSET-part of PYTHIA. We find a remarkable sensitivity of nuclear attenuation data to the details of the time-evolution of cross sections. Only cross sections evolving linearly in time describe the available data in a wide kinematical regime. Predictions fo…
Recent data for the slope of the EMC-ratio in the intermediate $x$-region for {\em light} nuclei, with $3 \leq A \leq 12$, have the potential to shed new light on the origin of the EMC effect. Here we study the role of nuclear binding using the scaling variable ${\tilde y}$, best suited to take into account this effect, and the understanding of the average nucleon removal energies, $\bar{E}$, provided by state-of-the-art calculations based on nuclear many body theory. We find an excellent correlation between the new EMC data at $x \sim 0.5$ and $\bar{E}$ for nuclei with $A$ from 3 to $\infty$,…
We discuss theoretical issues related to the extraction of deep inelastic~(DIS) structure function of neutron from inclusive DIS scattering off the deuteron at large Bjorken x. Theoretical justification is given to the consideration of only $pn$ component of the deuteron wave function and consistency with both the baryonic number and light-cone momentum conservation sum rules. Next we discuss the EMC type effects and argue that in all cases relevant to the nuclear DIS reactions at large x the main issue is the medium modification of the properties of bound nucleon rather than the non-nucleonic…
A proposal approved by the Jefferson Lab PAC to study semi-inclusive deep inelastic scattering (DIS) off the deuteron, tagged with high momentum recoiling protons or neutrons emitted at large angle relative to the momentum transfer. This experiment aims at studying the virtuality dependence of the bound nucleon structure function as a possible cause to the EMC effect and the EMC-SRC correlations. The experiment was approved in 2011 for a total run time of 40 days.
Using effective field theory, we investigate nuclear modification of nucleon parton distributions (for example, the EMC effect). We show that the universality of the shape distortion in nuclear parton distributions (the factorisation of the Bjorken x and atomic number (A) dependence) is model independent and emerges naturally in effective field theory. We then extend our analysis to study the analogous nuclear modifications in isospin and spin dependent parton distributions and generalised parton distributions.
Double parton scattering off nuclei and the double-EMC effect
Università degli Studi di Perugia（佩鲁贾大学）；INFN Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Université de Liège（列日大学）；Università di Roma Tor Vergata（罗马第二大学）；INFN Sezione di Roma Tor Vergata（意大利国家核物理研究所罗马第二大学分部）；Istituto Nazionale di Fisica Nucleare Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）
The quark exchange model (QEM) is reformulated for the $A=12$ and $14$ systems to obtain the constituent quark distributions of $^{12}C$ and $^{14}N$ nuclei, respectively. Afterwards, the different types of the point-like parton distribution functions (PDFs), i.e., the valence quarks, the sea quarks and the gluons, are extracted from the constituent quark model (CQM), at the hadronic scale $Q_0^2=0.34$ $GeV^2$ to generate the constituent quark exchange model (CQEM = QEM $\oplus$ CQM) PDFs. From the resulted PDFs, the structure functions and the European Muon Collaboration (EMC) ratios of the a…
Applying exact QCD sum rules for the baryon charge and energy-momentum we demonstrate that if nucleons are the only degrees of freedom of nuclear wave function, the structure function of a nucleus would be the additive sum of the nucleon distributions at the same Bjorken x = AQ^2/2(p_Aq)< 0.5 up to very small Fermi motion corrections if x>0.05. Thus the difference of the EMC ratio from one reveals the presence of non-nucleonic degrees of freedom in nuclei. Using exact QCD sum rules we show that the ratio R_A(x_p,Q^2) used in experimental studies, where x_p = Q^2/2q_0 m_p deviates from one even…
Since the discovery that the ratio of inclusive charged lepton (per-nucleon) cross sections from a nucleus A to the deuteron is not unity - even in deep inelastic scattering kinematics - a great deal of experimental and theoretical effort has gone into understanding the phenomenon. The EMC effect, as it is now known, shows that even in the most extreme kinematic conditions the effects of the nucleon being bound in a nucleus can not be ignored. In this paper we collect the most precise data available for various nuclear to deuteron ratios, as well as provide a commentary on the current status o…
We investigate the gluonic structure of nuclei within a mean-field model of nuclear structure based upon the modification of the structure of a bound nucleon, with the nucleon described by the Nambu--Jona-Lasinio model. This approach has been shown to reproduce the European Muon Collaboration (EMC) effect, involving the ratio of the spin-independent structure functions of a heavier nucleus to that of the deuteron. It also predicts a significant nuclear modification for the spin structure functions, known as the polarized EMC effect. Here we report sizeable nuclear modifications of the gluon di…
Gamow-Teller transitions in nuclei tell us that the nucleon's axial charge $g_A^{(3)}$ is quenched in large nuclei by about 20%. This result tells us that the spin structure of the nucleon is modified in nuclei and disfavours models of the medium dependence of parton structure based only on nucleon short range correlations in nuclei. For polarized photoproduction the Gerasimov-Drell-Hearn integral is expected to be strongly enhanced in medium.
We report the results of a Monte Carlo global QCD analysis of unpolarized parton distribution functions (PDFs), including for the first time constraints from ratios of $^3$He to $^3$H structure functions recently obtained by the MARATHON experiment at Jefferson Lab. Our simultaneous analysis of nucleon PDFs and nuclear effects in $A=2$ and $A=3$ nuclei reveals the first indication for an isovector nuclear EMC effect in light nuclei. We find that while the MARATHON data yield relatively weak constraints on the $F_2^n/F_2^p$ neutron to proton structure function ratio and on the $d/u$ PDF ratio, …
We present calculation of influence caused by nucleon Fermi motion on the parton distributions in nuclei. Our approach is based on the model where momenta of valence partons have some primordial distribution inside the hadron at rest, which is either provided by a statistical considerations or calculated using spherically symmetric Gaussian distribution with a width derived from the Heisenberg uncertainty relation. The sea parton contribution emerges from the similar Gaussian distribution with a width dictated by the presence of virtual pions in hadron. We show that the influence of Fermi moti…
We present our results for a flavor-dependent EMC effect based on the nIMParton nuclear PDFs, in which the $x$-dependence is described with a nucleon swelling model. The nuclear correction from nucleon swelling is considered through a modification of the initial valence quark distributions instead of a dynamical rescaling. To probe the flavor-dependence of the model, the experimental observables are calculated applying nIMParton nuclear modifications for various experiments: parity-violating deep inelastic scattering on nuclear target, pion-induced Drell-Yan, and W-boson production in proton-n…
The semi-inclusive deep inelastic scattering of electrons off the deuteron ($^2H \equiv D$) and $^3He$ with detection of slow protons and deuterons, respectively, i.e. the processes $D(e,e'p)X$ and $^3He(e,e'D)X$, are calculated within the spectator mechanism, taking into account the final state interaction of the hadronizing quark with the detected protons and deuterons, respectively. It is shown that by a proper choice of the kinematics the origin of the EMC effect and the details of the interaction between the hadronizing quark and the nuclear medium can be investigated at a level which can…
The EMC- and Cronin-effects are explained by a unitarized evolution equation, where the shadowing and antishadowing corrections are dynamically produced by gluon fusions. For this sake, an alternative form of the GLR-MQ-ZRS equation is derived. The resulting integrated and unintegrated gluon distributions in proton and nuclei are used to analyze the contributions of the initial parton distributions to the nuclear suppression factor in heavy ion collisions. A simulation of the fractional energy loss is extracted from the RHIC and LHC data, where the contributions of the nuclear shadowing and an…
High energy lepton scattering has been the primary tool for mapping out the quark distributions of nucleons and nuclei. Data on the proton and deuteron have shown that there is a fundamental connection between the low and high energy regimes, referred to as quark-hadron duality. We present the results of similar studies to more carefully examine scaling, duality, and in particular the EMC effect in nuclei. We extract nuclear modifications to the structure function in the resonance region, and for the first time demonstrate that nuclear effects in the resonance region are identical to those mea…
The EMC effect in deuterium and helium-3 is studied using a convolution formalism that allows isolating the impact of high-momentum nucleons in short-ranged correlated (SRC) pairs. We assume that the modification of the structure function of bound nucleons is given by a universal (i.e. nucleus independent) function of their virtuality, and find that the effect of such modifications is dominated by nucleons in SRC pairs. This SRC-dominance of nucleon modifications is observed despite the fact that the bulk of the nuclear inelastic scattering cross-section comes from interacting with low-momentu…
It is widely discussed in the literature that the wave function of the nucleon bound in a nucleus is modified due to the interaction with the surrounding medium. We argue that the modification should strongly depend on the momentum of the nucleon. We study such an effect in the case of the point-like configuration component of the wave function of a nucleon bound in a nucleus A, considering the case of arbitrary final state of the spectator A-1 system. We show that for non relativistic values of the nucleon momentum, the momentum dependence of the nucleon deformation appears to follow from rat…
Nuclear structure functions and EMC effect in a relativistic deuteron
University of Science and Technology of China（中国科学技术大学）；Lebedev Physical Institute（列别捷夫物理研究所）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽理论物理基础科学中心）
In this article we employ the nuclear EMC effect to extract the parton distribution functions (PDFs) inside the Lead (Pb) and Gold (Au) nuclei. Extracted PDFs are utilized to obtain the transverse momentum dependent (TMD) ones, using the computing codes like Pythia 8 or MCFM-10. Through this procedure TMDPDFs for charm and bottom quarks in Au at $\sqrt{s_{NN}}=200\;GeV$, Pb at $\sqrt{s_{NN}}=2.76\;TeV$ and $\sqrt{s_{NN}}=5.02\;TeV$ are calculated. To evaluate the validity of results and investigate the influence of nuclear EMC effect, the numerated TMDs are used as input to estimate heavy quar…
The recent x>1 (e,e') and correlation experiments at momentum transfer Q^2 \ge 2 GeV^2 confirm presence of short-range correlations (SRC) in nuclei mostly build of nucleons. Recently we evaluated in a model independent way the dominant photon contribution to the nuclear structure. Taking into account this effect and using definition of x consistent with the exact kinematics of eA scattering (with exact sum rules) results in the significant reduction of R_A(x,Q^2)=F_{2A}(x,Q^2)/F_{2N}(x,Q^2) ratio which explains \sim 50% of the EMC effect for x\le 0.55 where Fermi motion effects are small. The …
The EMC effect is studied by using the GLR-MQ-ZSR equation with minimum number of free parameters, where the nuclear shadowing effect is a dynamical evolution result of the equation, and nucleon swelling and Fermi motion in the nuclear environment deform the input parton distributions. Parton distributions of both proton and nucleus are predicted in a unified framework. We show that the parton recombination as a higher twist correction plays an essential role in the evolution of parton distributions either of proton or nucleus. We find that the nuclear antishadowing contributes a part of enhan…
Quark light cone momentum distributions in nuclear matter and the structure function of a bound nucleon are investigated in the framework of the Nambu-Jona-Lasinio model. This framework describes the nucleon as a relativistic quark-diquark state, and the nuclear matter equation of state by using the mean field approximation. The scalar and vector mean fields in the nuclear medium couple to the quarks in the nucleon and their effect on the spin independent nuclear structure function is investigated in detail. Special emphasis is placed on the important effect of the vector mean field and on a f…
A light front formalism for deep inelastic lepton scattering from finite nuclei is developed. In particular, the nucleon plus momentum distribution and a finite system analog of the Hugenholtz-van Hove theorem are presented. Using a relativistic mean field model, numerical results for the plus momentum distribution and ratio of bound to free nucleon structure functions for Oxygen, Calcium and Lead are given. We show that we can incorporate light front physics with excellent accuracy while using easily computed equal time wavefunctions. Assuming nucleon structure is not modified in-medium we fi…
Photons as well as quarks and gluons are constituents of the infinite momentum frame (IMF) wave function of an energetic particle. They are mostly equivalent photons whose amplitude follows from the Lorentz transformation of the particle rest frame Coulomb field into the IMF and from the conservation of the electromagnetic current. We evaluate in a model independent way the dominant photon contribution \propto α_{em}(Z^2/A^{4/3})\ln(1/R_{A}m_{N}x) to the nuclear structure functions as well as the term \propto α_{em}Z/A. In addition we show that the definition of x consistent with the exact kin…
A simple statistical model in terms of light-front kinematic variables is used to explain the nuclear EMC effect in the range $x \in [0.2,~0.7]$, which was constructed by us previously to calculate the parton distribution functions (PDFs) of the nucleon. Here, we treat the temperature $T$ as a parameter of the atomic number $A$, and get reasonable results in agreement with the experimental data. Our results show that the larger $A$, the lower $T$ thus the bigger volume $V$, and these features are consistent with other models. Moreover, we give the predictions of the quark distribution ratios, …
We discuss the electromagnetic form factors, axial form factors, and structure functions of a bound nucleon in the quark-meson coupling (QMC) model. Free space nucleon form factors are calculated using the improved cloudy bag model (ICBM). After describing finite nuclei and nuclear matter in the quark-based QMC model, we compute the in-medium modification of the bound nucleon form factors in the same framework. Finally, limits on the medium modification of the bound nucleon $F_2$ structure function are obtained using the calculated in-medium electromagnetic form factors and local quark-hadron …
The observed correlation between the EMC effect and the contribution of short-range correlations (SRCs) in nuclei suggests that the modification of the quark distributions of bound protons and neutrons might occur within SRCs. This raises the possibility that the EMC effect may have an isospin dependence arising from the np dominance of SRCs. We discuss previous attempts to test this possibility and perform a new analysis of existing data. We find no experimental support for the observation of an isospin dependence of the EMC effect.
The atomic nucleus is made of protons and neutrons (nucleons), that are themselves composed of quarks and gluons. Understanding how the quark-gluon structure of a nucleon bound in an atomic nucleus is modified by the surrounding nucleons is an outstanding challenge. Although evidence for such modification, known as the EMC effect, was first observed over 35 years ago, there is still no generally accepted explanation of its cause. Recent observations suggest that the EMC effect is related to close-proximity Short Range Correlated (SRC) nucleon pairs in nuclei. Here we report the first simultane…
An excellent description of both spin-independent and spin-dependent quark distributions and structure functions has been obtained with a modified Nambu-Jona-Lasinio model, which is free of unphysical thresholds for nucleon decay into quarks - hence incorporating an important aspect of confinement. We utilize this model to investigate nuclear medium modifications to structure functions and find that we are readily able to reproduce both nuclear matter saturation and the experimental F^A_2N / F_2N ratio, that is, the EMC effect. Applying this framework to determine g^A_1p, we find that the rati…
We sketch an approximate method to quantify the number of correlated pairs in any nucleus $A$. It is based on counting independent-particle model (IPM) nucleon-nucleon pairs in a relative $S$-state with no radial excitation. We show that IPM pairs with those quantum numbers are most prone to short-range correlations and are at the origin of the high-momentum tail of the nuclear momentum distributions. Our method allows to compute the $a_2$ ratios extracted from inclusive electron scattering. Furthermore, our results reproduce the observed linear correlation between the number of correlated pai…
The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering has a strongly "isophobic" nature. This surprising observation suggests short-range correlations between neighboring $n$ and $p$ nucleons in nuclear wavefunctions that are much stronger compared to $p-p$ or $n-n$ correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation of the isophobic nature of the EMC effect: the diffractive dissociation on a nu…
The problem of understanding the nuclear effects observed in lepton-nucleus deep-inelastic-scattering (the EMC effect) is still with us. Standard nuclear models (those using only hadronic degrees of freedom) are not able to account for the EMC effect. Thus it is necessary to understand how the nuclear medium modifies quark wave functions in the nucleus. Possibilities for such modifications, represented by the quark meson coupling model, and the suppression of point-like-configurations are discussed, and methods to experimentally choose between these are reviewed.
A neutron or proton excess in nuclei leads to an isovector-vector mean-field which, through its coupling to the quarks in a bound nucleon, implies a shift in the quark distributions with respect to the Bjorken scaling variable. We show that this result leads to an additional correction to the NuTeV measurement of sin^2(Theta_W). The sign of this correction is largely model independent and acts to reduce their result. Explicit calculation within a covariant and confining Nambu--Jona-Lasinio model predicts that this vector field correction accounts for approximately two-thirds of the NuTeV anoma…
Diquark formation across a short-range nucleon-nucleon pair is proposed as the underlying QCD physics of short-range correlations (SRC) in nuclei. SRC pairs have been proposed as the cause of distorted quark behavior in nuclei; experimentally observed quark momentum distribution distortions termed the EMC effect. The strong spatial overlap of SRC pairs brings nucleon constituents within range of inter-nucleon QCD potentials and any bonds formed - such as the diquark bond - affects their distributions. In this SRC model, diquarks form in the $\rm 3_C \otimes 3_C \rightarrow \bar{3}_C$ channel o…
We determine the quark distributions and structure functions for both unpolarized and polarized DIS of leptons on nucleons and nuclei. The scalar and vector mean fields in the nucleus modify the motion of the quarks inside the nucleons. By taking into account this medium modification, we are able to reproduce the experimental data on the unpolarized EMC effect, and to make predictions for the polarized EMC effect. We discuss examples of nuclei where the polarized EMC effect could be measured. We finally present an extension of our model to describe fragmentation functions.
An approach for a Poincaré covariant description of nuclear structure and of lepton scattering off nuclei is proposed within the relativistic Hamiltonian dynamics in the light-front form. Indeed a high level of accuracy is needed for a comparison with the increasingly precise present and future experimental data at high momentum transfer. Therefore, to distinguish genuine QCD effects or effects of medium modified nucleon structure functions from conventional nuclear structure effects, the commutation rules between the Poincaré generators should be satisfied. For the first time in this paper a …
Weinstein, et. al [1] [PRL 106, 052301 (2011)] and Hen, et. al [2] [PRC 85, 047301 (2012)] observed a correlation between the EMC effect and the amount of short range correlated (SRC) pairs in nuclei which implies that quark distributions are different in SRC pairs as compared with free nucleons. Schmookler, et. al [3] [Nature 566, 354 (2019)] bolstered this by showing that the EMC data can be explained by a universal modification of the structure of nucleons in neutron-proton SRC pairs and presented the first data-driven extraction of this universal modification function (UMF). Arrington and …
