Short range correlations and the EMC effect

Nucleon-nucleon correlations inside atomic nuclei: synergies, observations and theoretical models

While the main features of atomic nuclei are well described by nuclear mean-field models, there is a large and growing body of evidence which indicates an important additional role played by spatially-correlated nucleon-nucleon structures. The role of nucleonic structures was first suggested by Heidmann in 1950 to explain the pick-up reactions of energetic nucleons. Since then, a steady flux of new experimental evidence has confirmed the presence of similar structures inside atomic nuclei, dominated by correlations between pairs of nucleons. The role of these internal nucleon-nucleon correlations has been established using various energetic probes like photons, pions, leptons and hadrons. These correlated structures are essential for understanding the interaction of particles with nuclei and their presence provides an explanation of many specific nuclear phenomena, including backscattered protons, copious deuteron production, sub-threshold particle production, neutrino interactions with nuclei and the European Muon Collaboration effect. On the theoretical side, these measurements have stimulated a large number of phenomenological models specifically devised to address these enigmatic observations. While reviews exist for specific interactions, there is currently no published commentary which systematically encompasses the wide range of experimental signatures and theoretical frameworks developed thus far. The present review draws together the synergies between a wide range of different experimental and theoretical studies, summarizes progress in this area and highlights outstanding issues for further study.

New Perspectives on Spectroscopic Factor Quenching from Reactions

The evolution of single-particle strengths as the neutron-to-proton asymmetry changes informs us of the importance of short- and long-range correlations in nuclei and has therefore been extensively studied for the last two decades. Surprisingly, the strong asymmetry dependence of these strengths and their extreme values for highly asymmetric nuclei inferred from knockout reaction measurements on a target nucleus are not consistent with what is extracted from electron-induced, transfer, and quasi-free reaction data, constituting a two-decade old puzzle. This work presents the first consistent analysis of one-nucleon transfer and one-nucleon knockout data, in which theoretical uncertainties associated with the nucleon-nucleus effective interactions considered in the reaction models are quantified using a Bayesian analysis. Our results demonstrate that, taking into account these uncertainties, the spectroscopic strengths of loosely bound nucleons extracted from both probes agree with each other and, although there are still discrepancies for deeply bound nucleons, the slope of the asymmetry dependence of the single-particle strengths inferred from transfer and knockout reactions are consistent within 1σ. Both probes are consistent with a small asymmetry dependence of these strengths. The uncertainties obtained in this work represent a lower bound and are already significantly larger than the original estimates.

New Structure in the Deuteron

We demonstrate that a paradigm shift from considering the deuteron as a system of a bound proton and neutron to that of a pseudovector system in which we observe a proton and neutron results in the possibility of probing a new "incomplete" P-statelike structure on the light front (LF). This occurs at extremely large internal momenta, which can be achieved in a high energy transfer electrodisintegration of the deuteron. Investigating the deuteron on the light front, where the vacuum fluctuations are suppressed, we found that this new structure, together with the conventional S and D states, is leading order in transferred energy of the reaction and thus not suppressed on the light front. The incompleteness of the observed P state results in a violation of the angular condition that can happen only if the deuteron contains non-nucleonic structures, such as Δ Δ, N^{*}N or hidden color components. We demonstrate that experimentally verifiable signatures of incomplete P states are angular anisotropy of the light front momentum distribution of the nucleon in the deuteron, as well as an enhancement of the tensor polarization strength beyond the S- and D-wave predictions at large internal momenta in the deuteron.

Measurement of the Nucleon F_{2}^{n}/F_{2}^{p} Structure Function Ratio by the Jefferson Lab MARATHON Tritium/Helium-3 Deep Inelastic Scattering Experiment

The ratio of the nucleon F_{2} structure functions, F_{2}^{n}/F_{2}^{p}, is determined by the MARATHON experiment from measurements of deep inelastic scattering of electrons from ^{3}H and ^{3}He nuclei. The experiment was performed in the Hall A Facility of Jefferson Lab using two high-resolution spectrometers for electron detection, and a cryogenic target system which included a low-activity tritium cell. The data analysis used a novel technique exploiting the mirror symmetry of the two nuclei, which essentially eliminates many theoretical uncertainties in the extraction of the ratio. The results, which cover the Bjorken scaling variable range 0.19<x<0.83, represent a significant improvement compared to previous SLAC and Jefferson Lab measurements for the ratio. They are compared to recent theoretical calculations and empirical determinations of the F_{2}^{n}/F_{2}^{p} ratio.

Lattice QCD Constraints on the Parton Distribution Functions of ^{3}He

The fraction of the longitudinal momentum of ^{3}He that is carried by the isovector combination of u and d quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to m_{π}∼800  MeV. With a naive extrapolation to the physical quark masses, this constraint is consistent with, and more precise than, determinations from global nuclear parton distribution function fits through the nnnpdf framework. It is thus concretely demonstrated that lattice QCD calculations of light nuclei have imminent potential to enable more precise determinations of the u and d parton distributions in light nuclei and to reveal the QCD origins of the EMC effect.

Neutron Valence Structure from Nuclear Deep Inelastic Scattering

Mechanisms of spin-flavor SU(6) symmetry breaking in quantum chromodynamics (QCD) are studied via an extraction of the free neutron structure function from a global analysis of deep inelastic scattering (DIS) data on the proton and on nuclei from A=2 (deuterium) to 208 (lead). Modification of the structure function of nucleons bound in atomic nuclei (known as the EMC effect) are consistently accounted for within the framework of a universal modification of nucleons in short-range correlated (SRC) pairs. Our extracted neutron-to-proton structure function ratio F_{2}^{n}/F_{2}^{p} becomes constant for x_{B}≥0.6, equaling 0.47±0.04 as x_{B}→1, in agreement with theoretical predictions of perturbative QCD and the Dyson-Schwinger equation, and in disagreement with predictions of the scalar diquark dominance model. We also predict F_{2}^{^{3}He}/F_{2}^{^{3}H}, recently measured, as yet unpublished, by the MARATHON Collaboration, the nuclear correction function that is needed to extract F_{2}^{n}/F_{2}^{p} from F_{2}^{^{3}He}/F_{2}^{^{3}H}, and the theoretical uncertainty associated with this extraction.

Direct Observation of Proton-Neutron Short-Range Correlation Dominance in Heavy Nuclei

We measured the triple coincidence A(e,e^{'}np) and A(e,e^{'}pp) reactions on carbon, aluminum, iron, and lead targets at Q^{2}>1.5  (GeV/c)^{2}, x_{B}>1.1 and missing momentum >400  MeV/c. This was the first direct measurement of both proton-proton (pp) and neutron-proton (np) short-range correlated (SRC) pair knockout from heavy asymmetric nuclei. For all measured nuclei, the average proton-proton (pp) to neutron-proton (np) reduced cross-section ratio is about 6%, in agreement with previous indirect measurements. Correcting for single-charge exchange effects decreased the SRC pairs ratio to ∼3%, which is lower than previous results. Comparisons to theoretical generalized contact formalism (GCF) cross-section calculations show good agreement using both phenomenological and chiral nucleon-nucleon potentials, favoring a lower pp to np pair ratio. The ability of the GCF calculation to describe the experimental data using either phenomenological or chiral potentials suggests possible reduction of scale and scheme dependence in cross-section ratios. Our results also support the high-resolution description of high-momentum states being predominantly due to nucleons in SRC pairs.

The sea of quarks and antiquarks in the nucleon

The quark and gluon structure of the proton has been under intense experimental and theoretical investigation for five decades. Even for the distributions of the well-studied valence quarks, challenges such as the value of the down quark to up quark ratio at high fractional momenta remain. Much of the sea of quark-antiquark pairs emerges from the splitting of gluons and is well described by perturbative evolution in quantum chromodynamics. However, experiments confirm that there is a non-perturbative component to the sea that is not well understood and hitherto has been difficult to calculate with ab initio non-perturbative methods. This non-perturbative structure shows up, perhaps most directly, in the flavor dependence of the sea antiquark distributions. While some of the general trends can be reproduced by models, there are features of the data that do not seem to be well described. This article discusses the experimental situation, the status of calculations and models, and the directions where these studies will progress in the near future.

Exclusive studies on short range correlations in nuclei

Short Range Correlations (SRC) are brief fluctuations of high relative momentum nucleon pairs. Properties of SRC have important consequences for nuclear physics, high energy physics, atomic physics, and astrophysics. SRC pairs form some of the densest states of cold matter achievable on Earth, making them an ideal system to study the partonic and nucleonic degrees of freedom in nuclear systems. Hard exclusive breakup reactions, where high-energy probes scatter on SRC pairs, are used to study such properties of SRC pairs as isospin decomposition, nuclear mass and asymmetry dependence, c.m. momentum distribution. Thomas Jefferson National Accelerator Facility (JLab) plays a key role in the SRC program. CLAS (CEBAF Large Acceptance Spectrometer), located in Hall B at JLab, has almost 4πcoverage and is capable of measuring exclusive reactions of the type A(e, e’pp). We will discuss the recent experimental results from JLab and future experiments planned at JLab as well as at JINR.

Center of Mass Motion of Short-Range Correlated Nucleon Pairs studied via the A(e,e^{'}pp) Reaction

Short-range correlated (SRC) nucleon pairs are a vital part of the nucleus, accounting for almost all nucleons with momentum greater than the Fermi momentum (k_{F}). A fundamental characteristic of SRC pairs is having large relative momenta as compared to k_{F}, and smaller center of mass (c.m.) which indicates a small separation distance between the nucleons in the pair. Determining the c.m. momentum distribution of SRC pairs is essential for understanding their formation process. We report here on the extraction of the c.m. motion of proton-proton (pp) SRC pairs in carbon and, for the first time in heavier and ansymetric nuclei: aluminum, iron, and lead, from measurements of the A(e,e^{'}pp) reaction. We find that the pair c.m. motion for these nuclei can be described by a three-dimensional Gaussian with a narrow width ranging from 140 to 170  MeV/c, approximately consistent with the sum of two mean-field nucleon momenta. Comparison with calculations appears to show that the SRC pairs are formed from mean-field nucleons in specific quantum states.

The gluon structure of hadrons and nuclei from lattice QCD

I discuss recent lattice QCD studies of the gluon structure of hadrons and light nuclei. After very briefly highlighting new determinations of the gluon contributions to the nucleon’s momentum and spin, presented by several collaborations over the last year, I describe first calculations of gluon generalised form factors. The generalised transversity gluon distributions are of particular interest since they are purely gluonic; they do not mix with quark distributions at leading twist. In light nuclei they moreover provide a clean signature of non-nucleonic gluon degrees of freedom, and I present the first evidence for such effects, based on lattice QCD calculations. The planned Electron-Ion Collider, designed to access gluon structure quantities, will have the capability to test this prediction, and measure a range of gluon observables including generalised gluon distributions and transverse momentum dependent gluon distributions, within the next decade.

Short-Range Correlations and the EMC Effect in Effective Field Theory

We show that the empirical linear relation between the magnitude of the EMC effect in deep inelastic scattering on nuclei and the short-range correlation scaling factor a_{2} extracted from high-energy quasielastic scattering at x≥1 is a natural consequence of scale separation and derive the relationship using effective field theory. While the scaling factor a_{2} is a ratio of nuclear matrix elements that individually depend on the calculational scheme, we show that the ratio is independent of this choice. We perform Green's function Monte Carlo calculations with both chiral and Argonne-Urbana potentials to verify this and determine the scaling factors for light nuclei. The resulting values for ^{3}He and ^{4}He are in good agreement with experimental values. We also present results for ^{9}Be and ^{12}C extracted from variational Monte Carlo calculations.

Parity-violating deep inelastic scattering and the flavor dependence of the EMC effect

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 nontrivial flavor-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 flavor dependence of the EMC effect. Indeed, for nuclei like lead and gold we find that these flavor-dependent effects are large.

Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei

We provide a perspective on studies aimed at observing the transition between hadronic and quark-gluonic descriptions of reactions involving light nuclei. We begin by summarizing the results for relatively simple reactions such as the pion form factor and the neutral pion transition form factor as well as that for the nucleon and end with exclusive photoreactions in our simplest nuclei. A particular focus will be on reactions involving the deuteron. It is noted that a firm understanding of these issues is essential for unravelling important structure information from processes such as deeply virtual Compton scattering as well as deeply virtual meson production. The connection to exotic phenomena such as color transparency will be discussed. A number of outstanding challenges will require new experiments at modern facilities on the horizon as well as further theoretical developments.

How well do we know the neutron structure function?

We present a detailed analysis of the uncertainty in the neutron F(2n) structure function extracted from inclusive deuteron and proton deep-inelastic scattering data. The analysis includes experimental uncertainties as well as uncertainties associated with the deuteron wave function, nuclear smearing, and nucleon off-shell corrections. Correctly accounting for the Q(2) dependence of the data and calculations and restricting the nuclear corrections to microscopic models of the deuteron, we find a significantly smaller uncertainty in the extracted F(2n)/F(2p) ratio than in previous analyses. In addition to yielding an improved extraction of the neutron structure function, this analysis also provides an important baseline that can be compared to future, model-independent extractions of neutron structure to examine nuclear medium effects in the deuteron.