Deep Inelastic Region Research Articles

Resonant contributions to polarized proton structure functions

Nucleon resonance contributions to the polarized proton ${g}_{1}$ and ${g}_{2}$ structure functions are computed from resonance electroexcitation amplitudes extracted from CLAS exclusive meson electroproduction data. Including resonances in the mass range up to 1.75 GeV, and taking into account the interference between excited states, we compare the resonant contributions with the polarized proton structure function and polarization asymmetry data from Jefferson Lab 6 GeV measurements. All resonance-like structure observed in the polarized structure functions and asymmetries can be attributed to the resonant contributions, confirming their essential role in the behavior of ${g}_{1}$ and ${g}_{2}$ in the resonant region over the entire range ${Q}^{2}<7.5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$ covered by the measurements. Comparing the resonance contributions with the ${g}_{1}$ and ${g}_{2}$ structure functions computed from parton distribution functions extrapolated from the deep-inelastic region, we also quantify the degree to which quark-hadron duality holds for ${g}_{1}$ and ${g}_{2}$ and their moments.

Mean-field and two-body nuclear effects in inclusive electron scattering on argon, carbon, and titanium: The superscaling approach

We compare the predictions of the SuSAv2 model including two-particle two-hole meson-exchange currents with the recent JLab data for inclusive electron scattering on three different targets (C, Ar and Ti). The agreement is very good over the full energy spectrum, with some discrepancy seen only in the deep inelastic region. The 2p2h response, peaked in the dip region between the quasielastic and $\Delta$-resonance peak, is essential to reproduce the data. We also analyze the $k_F$ (Fermi momentum) dependence of the data in terms of scaling of second kind, showing that the 2p2h response scales very differently from the quasielastic one, in full accord with what is predicted by the model. The results represent a valuable test of the applicability of the model to neutrino scattering processes on different nuclei.

The complete [formula omitted] non-singlet heavy flavor corrections to the structure functions [formula omitted], [formula omitted], [formula omitted] and the associated sum rules

We calculate analytically the flavor non-singlet O(αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep(x,Q2) and g1,2ep(x,Q2) and charged current non-singlet structure functions F1,2,3ν(ν¯)p(x,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross–Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O(αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2≫mc,b2. We also study the target mass corrections to the above sum rules.

High-xstructure function of the virtually free neutron

The pole extrapolation method is applied to the semi-inclusive inelastic electron scattering off the deuteron with tagged spectator protons to extract the high-x structure function of the neutron. This approach is based on the extrapolation of the measured cross sections at different momenta of the spectator proton to the non-physical pole of the bound neutron in the deuteron. The advantage of the method is in the possibility of suppression of the nuclear effects in a maximally model-independent way. The neutron structure functions obtained in this way demonstrate a surprising x dependence at $x\ge 0.6$ and $1.6 \leq Q^2 \leq 3.38$ GeV$^2$, indicating a possible rise of the neutron to proton structure function ratio. If the observed rise is valid in the true deep inelastic region then it may indicate new dynamics in the generation of high-x quarks in the nucleon. One such mechanism we discuss is the possible dominance of short-range isosinglet quark-quark correlations that can enhance the d-quark distribution in the proton.

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.

Comparative study of nuclear effects in polarized electron scattering from3He

We present a detailed analysis of nuclear effects in inclusive electron scattering from polarized ${}^{3}$He nuclei for polarization asymmetries, structure functions, and their moments, in both the nucleon-resonance and deep-inelastic regions. We compare the results of calculations within the weak binding approximation at finite ${Q}^{2}$ with the effective polarization ansatz often used in experimental data analyses and explore the impact of $\ensuremath{\Delta}$ components in the nuclear wave function and nucleon off-shell corrections on extractions of the free neutron structure. Using the same framework we also make predictions for the ${Q}^{2}$ dependence of quasielastic scattering from polarized ${}^{3}$He, data which can be used to constrain the spin-dependent nuclear smearing functions in ${}^{3}$He.

ConstrainedγZinterference corrections to parity-violating electron scattering

We present a comprehensive analysis of gamma-Z interference corrections to the weak charge of the proton measured in parity-violating electron scattering, including a survey of existing models and a critical analysis of their uncertainties. Constraints from parton distributions in the deep-inelastic region, together with new data on parity-violating electron scattering in the resonance region, result in significantly smaller uncertainties on the corrections compared to previous estimates. At the kinematics of the Qweak experiment, we determine the gamma-Z box correction to be ReBox^V_{gamma-Z} = (5.57 +- 0.36) x 10^{-3}. The new constraints also allow precise predictions to be made for parity-violating deep-inelastic asymmetries on the deuteron.

Measurement of the NeutronF2Structure Function via Spectator Tagging with CLAS

We report on the first measurement of the F(2) structure function of the neutron from the semi-inclusive scattering of electrons from deuterium, with low-momentum protons detected in the backward hemisphere. Restricting the momentum of the spectator protons to ≲100 MeV/c and their angles to ≳100° relative to the momentum transfer allows an interpretation of the process in terms of scattering from nearly on-shell neutrons. The F(2)(n) data collected cover the nucleon-resonance and deep-inelastic regions over a wide range of Bjorken x for 0.65<Q(2)<4.52 GeV(2), with uncertainties from nuclear corrections estimated to be less than a few percent. These measurements provide the first determination of the neutron to proton structure function ratio F(2)(n)/F(2)(p) at 0.2≲x≲0.8 with little uncertainty due to nuclear effects.

Non-perturbative momentum dependence of the coupling constant and hadronic models

Models of hadron structure are associated with a hadronic scale which allows by perturbative evolution to calculate observables in the deep inelastic region. The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We use this new development to understand why perturbative treatments are working reasonably well despite the smallness of the hadronic scale.

Deep exclusive electroproduction ofπ+from data measured with the HERMES detector at DESY

Deeply virtual electroproduction of pions in an exclusive reaction p(e,e{sup '}{pi}{sup +})n is studied using a two-component model that includes soft hadronic and hard partonic reaction mechanisms. The results are compared with the experimental data measured at HERMES in the deep inelastic region for values of Q{sup 2}>1 GeV{sup 2} and W{sup 2}>10 GeV{sup 2}. At forward angles the {pi}{sup +} cross section is longitudinal and is dominated by exchange of Regge poles, with {pi} being the dominant trajectory. The off-forward region with -t>1 GeV{sup 2} is transverse and shows the dominance of partonic subprocesses. An implication of the present results for the future JLab facilities is briefly discussed.

New method for extracting neutron structure functions from nuclear data

We propose a new method for extracting neutron structure functions from inclusive structure functions of nuclei. Unlike earlier approaches, the new method is applicable to both spin-averaged and spin-dependent structure functions. We test the reliability of the method on unpolarized F_2 and polarized g_1 structure functions of the deuteron in both the nucleon resonance and deep inelastic regions. The new method is able to reproduce known input functions of almost arbitrary shape to very good accuracy with only several iterations.

Virtual Compton scattering and neutral pion electroproduction in the resonance region up to the deep inelastic region at backward angles

We have made the first measurements of the virtual Compton scattering (VCS) process via the H$(e,e'p)\gamma$ exclusive reaction in the nucleon resonance region, at backward angles. Results are presented for the $W$-dependence at fixed $Q^2=1$ GeV$^2$, and for the $Q^2$-dependence at fixed $W$ near 1.5 GeV. The VCS data show resonant structures in the first and second resonance regions. The observed $Q^2$-dependence is smooth. The measured ratio of H$(e,e'p)\gamma$ to H$(e,e'p)\pi^0$ cross sections emphasizes the different sensitivity of these two reactions to the various nucleon resonances. Finally, when compared to Real Compton Scattering (RCS) at high energy and large angles, our VCS data at the highest $W$ (1.8-1.9 GeV) show a striking $Q^2$- independence, which may suggest a transition to a perturbative scattering mechanism at the quark level.

Spin structure functions ofHe3at finiteQ2

Using recently derived relations between spin-dependent nuclear and nucleon $g_1$ and $g_2$ structure functions at finite $Q^2$, we study nuclear effects in the $^3$He nucleus in the nucleon resonance and deep inelastic regions. We compare the finite-$Q^2$ results with the standard convolution formulas obtained in high-$Q^2$ kinematics, and quantify the nuclear effects on the neutron structure functions extracted from $^3$He data.

Deuteron spin structure functions in the resonance and deep inelastic scattering regions

We derive relations between spin-dependent nuclear and nucleon ${g}_{1}$ and ${g}_{2}$ structure functions within the nuclear impulse approximation, which are valid at all ${Q}^{2}$, and in both the resonance and deep inelastic regions. We apply the formalism to the specific case of the deuteron, which is often used as a source of neutron structure information, and compare the size of the nuclear corrections calculated using exact kinematics and using approximations applicable at large ${Q}^{2}$.

Measurement of the x- and Q2-dependence of the asymmetry A1 on the nucleon

We report results for the virtual photon asymmetry $A_1$ on the nucleon from new Jefferson Lab measurements. The experiment, which used the CEBAF Large Acceptance Spectrometer and longitudinally polarized proton ($^{15}$NH$_3$) and deuteron ($^{15}$ND$_3$) targets, collected data with a longitudinally polarized electron beam at energies between 1.6 GeV and 5.7 GeV. In the present paper, we concentrate on our results for $A_1(x,Q^2)$ and the related ratio $g_1/F_1(x,Q^2)$ in the resonance and the deep inelastic regions for our lowest and highest beam energies, covering a range in momentum transfer $Q^2$ from 0.05 to 5.0 GeV$^2$ and in final-state invariant mass $W$ up to about 3 GeV. Our data show detailed structure in the resonance region, which leads to a strong $Q^2$--dependence of $A_1(x,Q^2)$ for $W$ below 2 GeV. At higher $W$, a smooth approach to the scaling limit, established by earlier experiments, can be seen, but $A_1(x,Q^2)$ is not strictly $Q^2$--independent. We add significantly to the world data set at high $x$, up to $x = 0.6$. Our data exceed the SU(6)-symmetric quark model expectation for both the proton and the deuteron while being consistent with a negative $d$-quark polarization up to our highest $x$. This data setshould improve next-to-leading order (NLO) pQCD fits of the parton polarization distributions.

Single particle sum rules in the nuclear deep-inelastic region

We have modeled the parton distribution in nuclei using a suitably modified nuclear Fermi motion. The modifications concern the nucleon rest energy which changes the Bjoerken x in a nuclear medium. We also introduce final state interactions between the scattered nucleon and the rest of the nucleus. The energy-momentum sum rule is saturated. Good agreement with experimental data of the EMC effect for x>0.15 and nuclear lepton pair production data has been obtained.

A Study on the Structure of the Proton

The structure function of the proton has been investigated and has been found to possess the power law behaviour in conformity with the empirical fits to the experimental findings. We have estimated F 2 ( x , Q 2 ) / F 2 ( x , Q 0 2 ) with the anomalous dimension D A predicted from the statistical model as an input and the result is found to be in good agreement with the recent data available in the deep inelastic region.

Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region

We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47 and 0.60 and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. These measurements were performed using a 5.7 GeV longitudinally-polarized electron beam and a polarized $^3$He target. The results for $A_1^n$ and $g_1^n$ at $x=0.33$ are consistent with previous world data and, at the two higher $x$ points, have improved the precision of the world data by about an order of magnitude. The new $A_1^n$ data show a zero crossing around $x=0.47$ and the value at $x=0.60$ is significantly positive. These results agree with a next-to-leading order QCD analysis of previous world data. The trend of data at high $x$ agrees with constituent quark model predictions but disagrees with that from leading-order perturbative QCD (pQCD) assuming hadron helicity conservation. Results for $A_2^n$ and $g_2^n$ have a precision comparable to the best world data in this kinematic region. Combined with previous world data, the moment $d_2^n$ was evaluated and the new result has improved the precision of this quantity by about a factor of two. When combined with the world proton data, polarized quark distribution functions were extracted from the new $g_1^n/F_1^n$ values based on the quark parton model. While results for $\Delta u/u$ agree well with predictions from various models, results for $\Delta d/d$ disagree with the leading-order pQCD prediction when hadron helicity conservation is imposed.

Neutron spin structure in the valence quark region

I present in this talk the latest results of the neutron spin physics program at Jefferson Laboratory in Hall A using the highly polarized electron beam and a high pressure polarized 3He target. This program includes among others experiment E99-117 in which the neutron spin asymmetry was measured in the deep inelastic region with high precision. This asymmetry is observed, for the first time, to change sign from negative to positive values between 0.3 < x < 0.6. Furthermore we perform a flavor decomposition of the spin-dependent to spin-independent quark distributions ratios in the nucleon and find that relativistic quark models are in better agreement than pQCD fits using the hadron helicity conservation constraint as x ® 1.

Measurement of beam-spin asymmetries for π+ electroproduction above the baryon resonance region

We report the first evidence for a non-zero beam-spin azimuthal asymmetry in the electroproduction of positive pions in the deep-inelastic region. Data have been obtained using a polarized electron beam of 4.3 GeV with the CLAS detector at the Thomas Jefferson National Accelerator Facility (JLab). The amplitude of the $\sin\phi$ modulation increases with the momentum of the pion relative to the virtual photon, $z$, with an average amplitude of $0.038 \pm 0.005 \pm 0.003$ for $0.5 < z < 0.8$ range.