Off-shell Nucleon Research Articles

Nuclear effects in the deuteron and global QCD analyses

We report the results of a new global QCD analysis, which includes deep-inelastic $e/\mu$ scattering data off proton and deuterium, as well as Drell-Yan lepton pair production in proton-proton and proton-deuterium collisions and $W^\pm/Z$ boson production data from $pp$ and $p \bar p$ collisions at the LHC and Tevatron. Nuclear effects in the deuteron are treated in terms of a nuclear convolution approach with bound off-shell nucleons within a weak binding approximation. The off-shell correction is controlled by a universal function of the Bjorken variable $x$ describing the modification of parton distributions in bound nucleons, which is determined in our analysis along with the parton distribution functions of the proton. A number of systematic studies are performed to estimate the uncertainties arising from the use of various deuterium datasets, from the modeling of higher twist contributions to the structure functions, from the treatment of target mass corrections, as well as from the nuclear corrections in the deuteron. We obtain predictions for the ratios $F_2^n/F_2^p$, and $d/u$, focusing on the region of large $x$. We also compare our results with the ones obtained by other QCD analyses, as well as with the recent data from the MARATHON experiment.

Off-shell Nucleons in Intermediate Energy Physics

I discuss some issues pertaining to vertices involving virtual (i.e. off-mass-shell) nucleons, namely, in which processes off-shell vertices appear, their transformation properties under field redefinitions, and the attempts that have been made to esti- mate their effects in electromagnetic processes at intermediate energies.

Covariant spectator theory of np scattering: Deuteron form factors

This paper uses the covariant spectator theory to calculate the deuteron electromagnetic form factors, yielding impressive quantitative results for deuteron observables. Special attention is given to a consistent treatment of currents generated by the nuclear force models obtained from the 2008 high-precision fits to the $N\phantom{\rule{0}{0ex}}N$ scattering data. Noteworthy results are (1) the neutron charge form factor prediction and (2) determination of two off-shell nucleon form factors that contribute to electron-deuteron scattering.

Nuclear effects in the proton-deuteron Drell-Yan process

We compute the nuclear corrections to the proton-deuteron Drell-Yan cross section for inclusive dilepton production, which, when combined with the proton-proton cross section, is used to determine the flavor asymmetry in the proton sea, $\overline{d}\ensuremath{\ne}\overline{u}$. In addition to nuclear smearing corrections that are known to be important at large values of the nucleon's parton momentum fraction ${x}_{N}$, we also consider dynamical off-shell nucleon corrections associated with the modifications of the bound nucleon structure inside the deuteron, which we find to be significant at intermediate and large ${x}_{N}$ values. We also provide estimates of the nuclear corrections at kinematics corresponding to existing and planned Drell-Yan experiments at Fermilab and J-PARC which aim to determine the $\overline{d}/\overline{u}$ ratio for $x\ensuremath{\lesssim}0.6$.

Measurement of the structure function of the nearly free neutron using spectator tagging in inelasticH2(e,e′ps)Xscattering with CLAS

Much less is known about neutron structure than that of the proton due to the absence of free neutron targets. Neutron information is usually extracted from data on nuclear targets such as deuterium, requiring corrections for nuclear binding and nucleon off-shell effects. These corrections are model dependent and have significant uncertainties, especially for large values of the Bjorken scaling variable x. The Barely Off-shell Nucleon Structure (BONuS) experiment at Jefferson Lab measured the inelastic electron deuteron scattering cross section, tagging spectator protons in coincidence with the scattered electrons. This method reduces nuclear binding uncertainties significantly and has allowed for the first time a (nearly) model independent extraction of the neutron structure function. A novel compact radial time projection chamber was built to detect protons with momentum between 70 and 150 MeV/c. For the extraction of the free neutron structure function $F_{2n}$, spectator protons at backward angle and with momenta below 100 MeV/c were selected, ensuring that the scattering took place on a nearly free neutron. The scattered electrons were detected with Jefferson Lab's CLAS spectrometer. The extracted neutron structure function $F_{2n}$ and its ratio to the deuteron structure function $F_{2d}$ are presented in both the resonance and deep inelastic regions. The dependence of the cross section on the spectator proton momentum and angle is investigated, and tests of the spectator mechanism for different kinematics are performed. Our data set can be used to study neutron resonance excitations, test quark hadron duality in the neutron, develop more precise parametrizations of structure functions, as well as investigate binding effects (including possible mechanisms for the nuclear EMC effect) and provide a first glimpse of the asymptotic behavior of d/u as x goes to 1.

Nuclear quasielastic electron scattering limits nucleon off-mass shell properties

The use of quasielastic electron nucleus scattering is shown to provide significant constraints on models of the proton electromagnetic form factor of off-shell nucleons. Such models can be constructed to be consistent with constraints from current conservation and low-energy theorems, while also providing a contribution to the Lamb shift that might potentially resolve the proton radius puzzle in muonic hydrogen. However, observations of quasielastic scattering limit the overall strength of the off-shell form factors to values that correspond to small contributions to the Lamb shift.

Final-state interactions in semi-inclusive deep inelastic scattering off the deuteron

Semi-inclusive deep inelastic scattering off the deuteron with production of a slow nucleon in recoil kinematics is studied in the virtual nucleon approximation, in which the final-state interaction (FSI) is calculated within generalized eikonal approximation. The cross section is derived in a factorized approach, with a factor describing the virtual photon interaction with the off-shell nucleon and a distorted spectral function accounting for the final-state interactions. One of the main goals of the study is to understand how much the general features of the diffractive high-energy soft rescattering accounts for the observed features of FSI in deep inelastic scattering (DIS). Comparison with the Jefferson Lab data shows good agreement in the covered range of kinematics. Most importantly, our calculation correctly reproduces the rise of the FSI in the forward direction of the slow nucleon production angle. By fitting our calculation to the data we extracted the $W$ and ${Q}^{2}$ dependencies of the total cross section and slope factor of the interaction of DIS products, $X$, off the spectator nucleon. This analysis shows the $\mathit{XN}$-scattering cross section rising with $W$ and decreasing with an increase of ${Q}^{2}$. Finally, our analysis points at a largely suppressed off-shell part of the rescattering amplitude.

Re-study of Nucleon Pole Contributionin J/ψ→NN̄π Decay

We re-study nucleon pole contribution in J/ψ→NN̄π decays by including the imaginary part for thepropagator of the off-shell nucleon with energy above πNthreshold. It is found that when including the imaginary part inthe propagator, the branching ratio of the decay width willdescend about 11% compared with the result without including theimaginary part, no matter whether including the off-shell formfactors or not. It also leads to a phase of up to 25° forthe off-shell nucleon propagator at invariant mass around 1400MeV. This effect needs to be considered for detailed partial waveanalysis of N* resonances around this mass region.

Ratio of the proton electromagnetic form factors from meson dressing

The Dressed K-matrix Model, developed previously for low- and intermediate-energy Compton scattering, is generalized to calculate the photon-nucleon vertex with a virtual photon and an off-shell nucleon. Using this model, the ratio of the proton electromagnetic form factors is computed. The calculated ratio is in excellent agreement with the ratio measured in polarized electron-proton scattering.

Time-like compton scattering and the Bethe-Heitler process

Arguments are presented for p(γ, e + e −)p measurements to obtain new information about the off-shell time-like nucleon form factors, especially in the o meson region governing the oN couplings g oNN V,T . Theoretical predictions based upon a Quantum Hadrodynamic model and vector meson dominance are highlighted for both the proton form factor and the time-like Compton scattering cross section. The Bethe-Heitler process is also calculated but is only important at low momentum transfer ¦t¦ permitting a novel high |t| φ enhancement in the Compton cross section related to nucleon strangeness to emerge.

Scattering of GeV electrons in the framework of the relativistic hartree approximation

The high momentum transfer electron-nucleus scattering cross section is evaluated within the plane wave impulse approximation (PWIA) supplemented by the relativistic Hartree approximation (RHA). Binding effects on the struck nucleon are introduced through the scalar and vector meson-exchange fields within the framework of quantum hadrodynamics. This model naturally satisfies the current conservation, with the off-shell nucleons behaving as being on the mass shell but having an effective mass. The nucleon inelastic response is included via different parameterizations of the structure function measured at SLAC, while the smearing of the Fermi surface is introduced through a momentum distribution obtained from a perturbative nuclear matter calculation. Recent CEBAF data on inclusive scattering of 4.05 GeV electrons on 56Fe are well reproduced for all measured geometries by the first time. Scaling effects are analyzed as well, and the scaling properties of the nuclear response in terms of the y variable associated to the PWIA within the RHA framework are discussed. The theoretical scaling function obtained in our approach also significantly improves previous PWIA calculations within the multi-GeV electron scattering regime, and describes properly the CEBAF scaling data.

New Fermi smearing approach for scattering of multi-GeV electrons by nuclei

The cross section for electron scattering by nuclei at high momentum transfers is calculated within the Fermi smearing approximation (FSA), where binding effects on the struck nucleon are introduced via the relativistic Hartree approximation (RHA). The model naturally preserves current conservation, since the response tensor for an off-shell nucleon conserves the same form that for a free one but with an effective mass. Different parameterizations for the inelastic nucleon structure function, are analyzed. The smearing at the Fermi surface is introduced through a momentum distribution obtained from a perturbative nuclear matter calculation. Recent CEBAF data on inclusive scattering of 4.05 GeV electrons on $^{56}$Fe are well reproduced for all measured geometries for the first time, as is evident from the comparison with previous calculations.

Off-shell effects on particle production

We investigate the observable effects of off-shell propagation of nucleons in heavy-ion collisions at SIS energies. Within a semiclassical Boltzmann-Uehling-Uhlenback transport model we find a strong enhancement of subthreshold particle production when off-shell nucleons are propagated.

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T c pseudogap formation is visible in the spectral function and below T c a superfluid gap also appears.

Probing few-body systems with bremsstrahlung

A series of bremsstrahlung measurements have been performed at KVI with the 190 MeV polarized proton beam of the new superconducting cyclotron, AGOR. The aim of these measurements is to investigate the dynamics of interactions involving intermediate off-shell nucleons. Nucleon-nucleon bremsstrahlung is the most fundamental process used for such studies as it involves the strong interaction between two nucleons and the well-known electromagnetic interaction. The present experiment provides the most accurate data on the proton-proton system. In addition the first exclusive proton-proton virtual-bremsstrahlung data ever is presented. The accuracy of the real bremsstrahlung data is high enough to investigate higher-order effects such as the virtual Δ-isobar and meson-exchange currents. None of the microscopic calculations is able to describe the data both in magnitude and in shape. The virtual-bremsstrahlung data are integrated over the detector acceptance. This same integration is done for two different soft-photon calculations for comparison.

Temperature-Dependent Imaginary Part of the Off-Shell Nucleon Self-Energy and the Second Order Correction of Real Part of the Nucleon Self-Energy

The imaginary part of the off-shell nucleon self-energy at finite temperature in nuclear matter, where the polarization and correlation contributions of exchanges of the meson are taken into account, is investigated based on Walecka's meson-nucleon model and thermofield dynamics. The second order correction of temperature-dependent real part of the nucleon self-energy is calculated in terms of the dispersion relation. The Schrödinger equivalent potential of relativistic microscopic optical potential of a nucleon at finite temperature in nuclear medium is also studied.

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L HBChPT through O( q 3) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L HBChPT for on-shell nucleons, through O( q 3). The extension of the method (to obtain on-shell L HBChPT within HBChPT) to higher orders is also discussed.

Nuclear effects in the F3 structure function for finite and asymptotic Q2

We study nuclear effects in the structure function F 3 which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q −2 series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F 3. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q −2 correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q 2 and x dependence of nuclear structure functions is found.

Inclusive quasielastic scattering of polarized electrons from polarized nuclei

The inclusive quasielastic response functions that appear in the scattering of polarized electrons from polarized nuclei are computed and analyzed for several closed-shell-minus-one nuclei with special attention paid to 39K. Results are presented using two models for the ejected nucleon — when described by a distorted wave in the continuum shell model or by a plane wave in PWIA with on- and off-shell nucleons. Relativistic effects in kinematics and in the electromagnetic current have been incorporated throughout. Specifically, the recently obtained expansion of the electromagnetic current in powers only of the struck nucleon's momentum is employed for the on-shell current and the effects of the first-order terms (spin-orbit and convection) are compared with the zeroth-order (charge and magnetization) contributions. The use of polarized inclusive quasielastic electron scattering as a tool for determining near-valence nucleon momentum distributions is discussed.

Polarized deep-inelastic scattering from nuclei: A relativistic approach.

We discuss spin-dependent, deep-inelastic scattering from nuclei within a covariant framework. In the relativistic impulse approximation this is described in terms of the amplitude for forward, virtual-photon scattering from an off-mass-shell nucleon. The general structure of the off-shell nucleon hadronic tensor is derived, and the leading behavior of the off-shell nucleon structure functions computed in the Bjorken limit. The formalism, which is valid for nucleons bound inside nuclei with spin 1/2 or 1, is applied to the case of the deuteron. \textcopyright{} 1996 The American Physical Society.