The relative contributions to the valence nuclear EMC effect in the deuteron arising from off-shell effects and Fermi motion are examined in models which include nuclear binding and off-shell effects. Contrary to expectations, the effect of Fermi motion overwhelms the off-shell effects for nucleons in short-range correlations (SRCs), calling into question the hypothesized causal connection between SRCs and the EMC effect.
We demonstrate that measurement of tagged structure functions of the deuteron in (e,e'N) semi-inclusive reactions can discriminate between different hypotheses on the origin of the nuclear EMC effect. By choosing extreme backward kinematics for the spectator nucleon to minimize effects from the deuteron wave function and final state interactions, one can isolate the modifications in the structure of the bound nucleon within the impulse approximation. The same reaction can be used to extract the large-x neutron to proton structure function ratio.
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）
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…
We have determined the structure function ratio $R^d_{\rm EMC}=F_2^d/(F_2^n+F_2^p)$ from recently published $F_2^n/F_2^d$ data taken by the BONuS experiment using CLAS at Jefferson Lab. This ratio deviates from unity, with a slope $dR_{\rm EMC}^{d}/dx= -0.10\pm 0.05$ in the range of Bjorken $x$ from 0.35 to 0.7, for invariant mass $W>1.4$ GeV and $Q^2>1$ GeV$^2$. The observed EMC effect for these kinematics is consistent with conventional nuclear physics models that include off-shell corrections, as well as with empirical analyses that find the EMC effect proportional to the probability of sho…
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…
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…
We investigate the influence of modified nuclear parton distribution functions (PDFs) on high-pT hadron production at RHIC and LHC energies using a pQCD-improved parton model. For application at RHIC, we focus on the possible contribution of the EMC modification of the nuclear PDFs in the x > 0.3 region to the observed suppression of pi0 production at pT > 10 GeV/c in dAu collisions. We study three different parameterizations of the nuclear PDF modifications and find that they give consistent results for R_dAu(pT) for neutral pions in the region 10 GeV/c < pT < 20 GeV/c. We find that the EMC s…
We study nuclear effects on the deuteron in the deep inelastic regime using the newest available data analyzing their $Q^2$ dependence. We conclude that precise EMC ratios for large $Q^2$ (> 30, GeV$^2$) cannot be obtained without considering these nuclear effects. For this purpose we use a scheme which parametrizes these effects in a simple manner and compare our results with other recent proposals.
The deep inelastic scattering of leptons off nuclei is considered within the the Bethe-Salpeter formalism. It is shown that nuclear short-range structure can be expressed in terms of the nucleon structure functions and four-dimensional Fermi motion of the nucleons. The four-dimensional Fermi motion broadens the bound nucleon localization area, what lead to the observation of the nucleon structure change in nuclei -- EMC effect. The $\rm ^4He$ to deuteron structure functions ratio is found in good agreement with experimental data. It is shown that the pattern of the ratio is defined by dynamica…
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…
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…
By considering the $x$-dependence of $π^+$, $π^-$, $K^+$, $K^-$, $Λ$, $\barΛ$, $p$, $\bar{p}$ hadron productions in charged lepton semi-inclusive deep inelastic scattering off nuclear target (using Fe as an example) and deuteron D target, % at $Q^2=5$ GeV$^2$, we find that $(\barΛ^A/Λ^A)/(\barΛ^D/Λ^D)$ and $({\bar{p}}^A/{p}^A)/({\bar{p}}^A/p^A)$ are ideal to figure out the nuclear sea content, which is predicted to be different by different models accounting for the nuclear EMC effect.
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…
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…
Due to the lack of a free neutron target the structure function of the neutron cannot be measured directly and is therefore extracted from deuteron and proton DIS data. Because the deuteron is a bound nuclear system, in order to extract the neutron structure function, one needs to apply model dependent theoretical corrections which dominate the uncertainty at the large xB region. We present here a correlation between the magnitude of the EMC effect and the amount of two nucleon Short Range Correlation (2N-SRC) pairs in nuclei. Using this correlation we propose a phenomenological procedure to e…
We analyze experimental data of nuclear structure function ratios $F_2^A/F_2^D$ for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Parametrization of nuclear parton distribution is investigated in the leading order of $α_s$. The parton distribution are provided at $Q^2=1 GeV^2$ with a number of parameters, which are determined by a $χ^2$ analysis of the data on nuclear structure function. From the analysis, we propose parton distributions at $Q^2=1 GeV^2$ for nuclei from deuteron to heavy ones with …
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 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…
A clustering aspect is explained for the $^9$Be nucleus in charged-lepton deep inelastic scattering. Nuclear modifications of the structure function $F_2$ are studied by the ratio $R_{\rm EMC} = F_2^A /F_2^D$, where $A$ and $D$ are a nucleus and the deuteron, respectively. In a JLab experiment, an unexpectedly large nuclear modification slope $|dR_{\rm EMC}/dx|$ was found for $^9$Be, which could be related to its clustering structure. We investigated a mean conventional part of a nuclear structure function $F_2^A$ by a convolution description with nucleon momentum distributions calculated by a…
We test the hypothesis that configurations of a proton with a large-$x$ parton, $x_p \gtrsim 0.1$, have a smaller than average size. The QCD $Q^2$ evolution equations suggest that these small configurations also have a significantly smaller interaction strength, which has observable consequences in collisions with nuclei. We perform a global analysis of jet production data in proton- and deuteron-nucleus collisions at RHIC and the LHC. Using a model which takes a distribution of interaction strengths into account, we quantitatively extract the $x_p$-dependence of the average interaction streng…
Nuclear effects on longitudinal-transverse structure function ratio in the deuteron
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所）；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部理论中心）
Recently the ratio of neutron to proton structure functions F_2n/F_2p was extracted from a phenomenological correlation between the strength of the nuclear EMC effect and inclusive electron-nucleus cross section ratios at x>1. Within conventional models of nuclear smearing, this "in-medium correction" (IMC) extraction constrains the size of nuclear effects in the deuteron structure functions, from which the neutron structure function F_2n is usually extracted. The IMC data determine the resulting proton d/u quark distribution ratio, extrapolated to x=1, to be 0.23 +- 0.09 with a 90% confidence…
We report on the measurement of inclusive electron scattering off a carbon target performed with CLAS at Jefferson Laboratory. A combination of three different beam energies 1.161, 2.261 and 4.461 GeV allowed us to reach an invariant mass of the final-state hadronic system W~2.4 GeV with four-momentum transfers Q2 ranging from 0.2 to 5 GeV2. These data, together with previous measurements of the inclusive electron scattering off proton and deuteron, which cover a similar continuous two-dimensional region of Q2 and Bjorken variable x, permit the study of nuclear modifications of the nucleon str…
Short-Range Correlation Scaling of Nuclear Parton Modifications: Consistency Tests and Recoil-Tagged Charm-Production DIS
Lanzhou University（兰州大学）；Shanghai Jiao Tong University（上海交通大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Tianjin University（天津大学）
We present a systematic study of the leading twist structure functions of the deuteron, F_2^D, b_{1,2}^D and g_1^D in a fully relativistic approach. Our study is based on a realistic Bethe-Salpeter amplitude for the deuteron, which is obtained as a solution to the homogeneous Bethe-Salpeter equation with a realistic NN kernel. Particular effort is made to connect the structure functions to the densities of the appropriate charges and currents. This allows for a systematic comparison between the relativistic and nonrelativistic calculations, by analysing the same densities in both approaches. T…
Nucleon-nucleon potentials evolved to low momentum, which show great promise in few- and many-body calculations, have generally been formulated with a sharp cutoff on relative momenta. However, a sharp cutoff has technical disadvantages and can cause convergence problems at the 10-100 keV level in the deuteron and triton. This motivates using smooth momentum-space regulators as an alternative. We generate low-momentum interactions with smooth cutoffs both through energy-independent renormalization group methods and using a multi-step process based on the Bloch-Horowitz approach. We find greatl…
Nuclear modifications to the Drell-Yan dilepton production cross sections in p+A and A+A collisions in the leading twist approximation are caused by nuclear effects in the parton distributions of bound nucleons. For non-isoscalar nuclei, isospin corrections must also be considered. We calculate these effects for p+A and Pb+Pb collisions at CERN SPS energies. Our goal is to place constraints on nuclear effects in sea quark distributions in the region x > 0.2. We show that the net nuclear corrections remain small for p+A collisions at E_lab=450 GeV. However, in Pb+Pb collisions at E_lab=158 AGeV…
Valence-shell nucleon knock-out experiments, such as 12C(e,e'p)11B, measure less strength then is predicted by independent particle shell model calculations. The theoretical solution to this problem is to include the correlations between the nucleons in the nucleus in the calculations. Motivated by these results, many electron scattering experiments have tried to directly observe these correlations in order to gain new insight into the short-range part of the nucleon-nucleon potential. Unfortunately, many competing mechanisms can cause the same observable final-state as an initial-state correl…
Nucleon structure function ratios r(x) = F2A(x)/F2D(x) measured in the range of atomic masses A larger or equal 4 are analyzed with the aim to determine the pattern of the x and A dependence of F2(x) modifications caused by nuclear environment. It is found that the x and A dependence of the deviations of the r(x) from unity can be factorized in the entire range of x. The characteristic feature of the factorization is represented with the three cross-over points x_i, i = 1 -- 3 in which r(x) = 1 independently of A. In the range x lager than 0.7 the pattern of r(x) is fixed with x_3 = 0.84 +/- 0…
