Spin Structure Function Research Articles

Resonance contributions to nucleon spin structure in holographic QCD

We study polarized inelastic electron-nucleon scattering at low momentum transfer in the Witten-Sakai-Sugimoto model of holographic QCD, focusing on resonance production contributions to the nucleon spin structure functions. Our analysis includes both spin 3/2 and spin 1/2 low-lying nucleon resonances with positive and negative parity. We determine, in turn, the helicity amplitudes for nucleon-resonance transitions and the resonance contributions to the neutron and proton generalized spin polarizabilities. Extrapolating the model parameters to realistic QCD data, our analysis, triggered by recent experimental results from Jefferson Lab, agrees with the observation that the ∆(1232) resonance gives the dominant contribution to the forward spin polarizabilities at low momentum transfer. The contribution is negative and tends to zero as the momentum transfer increases. As expected, the contribution of the ∆(1232) to the longitudinal-transverse polarizabilities is instead negligible. The latter, for both nucleons, turn out to be negative functions with zero asymptote. The holographic results, at least for the proton where enough data are available, are in qualitative agreement with the resonance contributions to the spin polarizabilities extracted from experimental data on the helicity amplitudes.

Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in alpha , which is O(alpha ^5) in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (Bchi PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (mu H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the Bchi PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius R_textrm{Z}, if one uses the well-known experimental 1S hfs in H or the 2S hfs in mu H. We, respectively, obtain R_textrm{Z}(textrm{H}) = 1.010(9) fm, R_textrm{Z}(mu textrm{H}) = 1.040(33) fm. The total proton-structure effect to the hfs at O(alpha ^5) is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1S hfs in mu text {H} is 182.640(18),textrm{meV}.

Detailed study of quark-hadron duality in spin structure functions of the proton and neutron

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross section. The overlap region between these two pictures, where both yield similar predictions, is referred to as quark-hadron duality and has been extensively studied in reactions involving unpolarized hadrons. Some limited information on this phenomenon also exists for polarized protons, deuterons, and $^{3}\mathrm{He}$ nuclei, but not yet for neutrons.Purpose: In this paper, we present comprehensive and detailed results on the correspondence between the extrapolated deep inelastic structure function ${g}_{1}$ of both the proton and the neutron with the same quantity measured in the nucleon resonance region. Thanks to the fine binning and high precision of our data, and using a well-controlled perturbative QCD (pQCD) fit for the partonic prediction, we can make quantitative statements about the kinematic range of applicability of both local duality and global duality.Method: We use the most updated QCD global analysis results at high $x$ from the Jefferson Lab Angular Momentum Collaboration to extrapolate the spin structure function ${g}_{1}$ into the nucleon resonance region and then integrate over various intervals in the scaling variable $x$. We compare the results with the large data set collected in the quark-hadron transition region by the CLAS Collaboration, including, for the first time, deconvoluted neutron data, integrated over the same intervals. We present this comparison as a function of the momentum transfer ${Q}^{2}$.Results: We find that, depending on the integration interval and the minimum momentum transfer chosen, a clear transition to quark-hadron duality can be observed in both nucleon species. Furthermore, we show, for the first time, the approach to scaling behavior for ${g}_{1}$ measured in the resonance region at sufficiently high momentum transfer.Conclusions: Our results can be used to quantify the deviations from the applicability of pQCD for data taken at moderate energies and can help with extraction of quark distribution functions from such data.

Transverse proton gluon anisotropy points behind the Standard Model

The present work focuses on transverse gluon densities in the proton and derives exemplar distributions showing azimuthal anisotropies. Such anomalies relative to the Standard Model may be visible in scattering experiments involving protons. I describe baryons as mass eigenstates of a Hamiltonian structure on an intrinsic U(3) configuration space. This has yielded the neutral flavour baryon spectrum and given a rather accurate value for the neutron mass 939.9(5) MeV from first principles. Quark and gluon fields are shaped by the momentum form of the intrinsic wave function. This has led to parton distribution functions for the u and d valence quarks for the proton and to a proton spin structure function agreeing with experiments over four orders of magnitude in the parton momentum fraction.

Recent data analysis to revisit the spin structure function of the nucleon in Laplace space

Considering a fixed-flavor number scheme and based on Laplace transformation, we perform leading-order and next-to-leading-order QCD analyses that include world data on polarized structure functions ${g}_{1}$ and ${g}_{2}$. During our analysis, taking the DGLAP evolution equations, we employ the Jacobi polynomials expansion technique. In our recent analysis we utilize the recent available data and consequently include more data than what we did in our previous analysis. We obtain good agreements between our results for the polarized parton densities and nucleon structure functions with all available experimental data and some common parametrization models.

Nucleon spin structure functions, considering target mass correction, and higher twist effects at the NNLO accuracy and their transverse momentum dependence

Using recent and updated world data on polarized structure functions ${g}_{1}$ and ${g}_{2}$ we perform an analysis based on quantum chromodynamics (QCD) as a theory of strong interactions at next-next-to-leading-order accuracy. We include also target mass corrections and higher twist effects to get more precise results in our fitting procedure. To confirm the validity of our fitting results several sum rules are examined and we do a comparison for them with results from other models. In our analysis we employ the Jacobi polynomials approach to obtain analytical solutions of the Dokshitzer-Gribov-LipatovAltarelli-Parisi evolution equations for parton distribution functions (PDFs). Using the extracted PDFs from our data analysis as input, we also compute the $x$- and ${\mathbf{p}}_{T}$-dependence of some transverse momentum dependence PDFs in polarized case, based on covariant parton model. These functions are naively even time-reversal at twist-two approximation. The results for transverse momentum dependences indicate proper and acceptable behavior with respect to what are presented in other literatures.

Isospin asymmetry and quantum statistical interpretation of nucleons

In this paper, a statistical model introducing analytical expressions of [Formula: see text] dependent quantum statistical parton distributions is presented to explore proton and neutron structures. A merely theoretical maximum entropy method is applied to obtain thermodynamical variables determining parton distributions accurately. This study provides considering proton and neutron isospin asymmetry in order to improve the consistency of the framework achievements with the experimental results. The presented approach is extended to evaluate modified neutron structure in an [Formula: see text]-[Formula: see text] state. Also, the uniqueness of gluon distribution in proton and neutron is surveyed for both cases of lonely nucleon and [Formula: see text]-[Formula: see text] system. Eventually, the predicted unpolarized structure functions and the spin structure functions, only based on the maximum entropy method, are compared to CERN, HERMES, SLAC and the other data sets. Finally, the correlation of the obtained distributions with the experimental observations confirms the proposed statistical model.

Gluon EMC effects in nuclear matter

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 distributions (a ‘gluon EMC effect’) for the ratios of both the unpolarized and polarized gluon distributions in nuclear matter to those of a free nucleon.

Neutron spin structure from e-3He scattering with double spectator tagging at the electron-ion collider

The spin structure function of the neutron is traditionally determined by measuring the spin asymmetry of inclusive electron deep inelastic scattering (DIS) off polarized 3He nuclei. In such experiments, nuclear corrections are significant and must be treated carefully in the interpretation of experimental data. Here we study the feasibility of suppressing model dependencies by tagging both spectator protons in the process of DIS off neutrons in 3He at the forthcoming Electron-Ion Collider (EIC). This allows for a reconstruction of the momentum of the struck neutron to ensure it was nearly at rest in the initial state, thereby reducing sensitivity to nuclear corrections and suppressing contributions from electron DIS off protons in 3He. Using realistic accelerator and detector configurations, we demonstrate that the EIC can probe the neutron spin structure from xB of 0.003 to 0.651. We find that the double spectator tagging method results in reduced uncertainties by a factor of 2 on the extracted neutron spin asymmetries over all kinematics and by a factor of 10 in the low-xB region, thereby providing valuable insight into the spin and flavor structure of nucleons.

Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function gT(x)=g1(x)+g2(x), the less-studied but known transverse gluon polarization density ΔGT(x), and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.

Event Rates for the Scattering of Weakly Interacting Massive Particles from 23Na and 40Ar

Detection rates for the elastic and inelastic scattering of weakly interacting massive particles (WIMPs) off 23Na are calculated within the framework of Deformed Shell Model (DSM) based on Hartree-Fock states. At first, the spectroscopic properties of the detector nucleus, like energy spectra and magnetic moments, are evaluated and compared with experimental data. Following the good agreement of these results, DSM wave functions are used for obtaining elastic and inelastic spin structure functions, nuclear structure coefficients and so forth for the WIMP-23Na scattering. Then, the event rates are also computed with a given set of supersymmetric parameters. In the same manner, using DSM wavefunctions, nuclear structure coefficients and event rates for elastic scattering of WIMPs from 40Ar are also obtained. These results for event rates and also for annual modulation will be useful for the ongoing and future WIMP detection experiments involving detector materials with 23Na and 40Ar nuclei.

On quarks and the origin of QCD: Partons and baryons from intrinsic states

We create quarks from baryons in stead of constituting baryons from quarks. The quantum fields of QCD are generated via the exterior derivative (momentum form) of baryon wave functions on an intrinsic configuration space, the Lie group U(3). Local gauge transformations correspond to coordinate translations in the intrinsic space. A proton spin structure function and a proton magnetic moment are derived. We show how the spectrum of unflavoured baryons, the N and Delta resonances, can be understood from a mass Hamiltonian on the intrinsic space and note how our model resolves the problem of colour confinement. We calculate an approximate value for the relative neutron-to-proton mass shift and give an exact value for the neutron mass. We predict neutral charge singlets that may be interpreted as neutral pentaquarks at LHCb.

Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tagging

Background: DIS on the polarized deuteron with detection of a proton in the nuclear breakup region (spectator tagging) represents a unique method for extracting the neutron spin structure functions and studying nuclear modifications. The tagged proton momentum controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. Such measurements could be performed with the future electron-ion collider (EIC) and forward proton detectors if deuteron beam polarization could be achieved. Purpose: Develop theoretical framework for polarized deuteron DIS with spectator tagging. Formulate procedures for neutron spin structure extraction. Methods: A covariant spin density matrix formalism is used to describe general deuteron polarization in collider experiments (vector/tensor, pure/mixed). Light-front (LF) quantum mechanics is employed to factorize nuclear and nucleonic structure in the DIS process. A 4-dimensional representation of LF spin structure is used to construct the polarized deuteron LF wave function and efficiently evaluate the spin sums. Free neutron structure is extracted using the impulse approximation and analyticity in the tagged proton momentum (pole extrapolation). Results: General expressions of the polarized tagged DIS observables in collider experiments. Analytic and numerical study of the polarized deuteron LF spectral function and nucleon momentum distributions. Practical procedures for neutron spin structure extraction from the tagged deuteron spin asymmetries. Conclusions: Spectator tagging provides new tools for precise neutron spin structure measurements. D-wave depolarization and nuclear binding effects can be eliminated through the tagged proton momentum dependence. The methods can be extended to tensor-polarized observables, spin-orbit effects, and diffractive processes.

Measurement of the 3He spin-structure functions and of neutron (3He) spin-dependent sum rules at 0.035 ≤ Q2 ≤ 0.24 GeV2

The spin-structure functions g1 and g2, and the spin-dependent partial cross-section σTT have been extracted from the polarized cross-sections differences, Δσ∥(ν,Q2) and Δσ⊥(ν,Q2) measured for the He3→(e→,e′)X reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons with energies from 1.147 to 4.404 GeV were scattered at angles of 6∘ and 9∘ from a longitudinally or transversely polarized 3He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments Γ1‾(Q2), Γ2(Q2) and ITT(Q2) are evaluated with high precision for the neutron in the Q2 range from 0.035 to 0.24GeV2. The comparison of the data and the chiral effective field theory predictions reveals the importance of proper treatment of the Δ degree of freedom for spin observables.

Gluon transversity in polarized proton-deuteron Drell-Yan process

Nucleon spin structure functions have been investigated mainly by longitudinally-polarized ones for finding the origin of the nucleon spin. Other types of spin structure functions are transversely-polarized ones. In particular, quark transversity distributions in the nucleons have very different properties from the longitudinally-polarized quark distribution functions, especially in scaling violation, because they are decoupled from the gluon transversity, due to the fact that they are helicity-flip (chiral-odd) distributions. Such studies are valuable for finding not only the origin of the nucleon spin but also a signature on physics beyond the standard model, because the electric dipole moment of the neutron is proportional to the transversity distributions. Now, there is experimental progress on the quark transversity distributions; however, there is no experimental information on gluon transversity. In fact, the gluon transversity does not exist for the spin-1/2 nucleon due to the helicity-conservation constraint. One needs a hadron with spin more than or equal to one, so that the helicity flip of two units is allowed. A stable spin-1 target is, for example, the deuteron for studying the gluon transversity. In this work, we propose a possibility for finding the gluon transversity at hadron-accelerator facilities, especially in the proton-deuteron Drell-Yan process with the linearly-polarized deuteron, by showing theoretical formalism and numerical results. We show the dependencies of the Drell-Yan cross section on the dimuon-mass squared $M_{\mu\mu}^{\,2}$, the dimuon transverse-momentum $q_T$, the dimuon rapidity $y$ in the center-of-momentum frame, and the magnitude of the gluon transversity $\Delta_T g$.

Optimized determination of the polarized Bjorken sum rule

We determine the polarized Bjorken sum rule in two different ways: phenomenologically, by means of integration of the spin structure function within the truncated moment approach and theoretically, with use of the renormalization group for the optimization of the perturbation series. Presented approaches are universal and can be applied to any of the DIS sum rules.

Impact of recent COMPASS data on polarized parton distributions and structure functions

We perform a new extraction of polarized parton distribution functions (PPDFs) from the spin structure function experimental data in the fixed-flavor number scheme (FFNS). In this analysis, we include recent proton and deuteron spin structure functions obtained by the \texttt{COMPASS} collaboration. We examine the impact of the \texttt{new COMPASS} proton and deuteron data on the polarized parton densities and compare with results from our previous study (KATAO PPDFs), which used the Jacobi polynomial approach. We find the extracted PPDFs of the proton, neutron, and deuteron structure functions are in very good agreement with the experimental data. The results for extracted PPDFs are also compared with available theoretical models from the literature.

Updating spin-dependent Regge intercepts

We use new high statistics data from CLAS and COMPASS on the nucleon's spin structure function at low Bjorken x and low virtuality, Q^2 < 0.5 GeV^2, together with earlier measurements from the SLAC E-143, HERMES and GDH experiments to estimate the effective intercept(s) for spin dependent Regge theory. We find alpha_{a_1} = 0.31 \pm 0.04 for the intercept describing the high-energy behaviour of spin dependent photoabsorption together with a new estimate for the high-energy part of the Gerasimov-Drell-Hearn sum-rule, -15 \pm 2 mu b from photon-proton centre-of-mass energy greater than 2.5 GeV. Our value of alpha_[a_1} suggests QCD physics beyond a simple straight-line a_1 trajectory.

Analysis of the neutron spin structure function g1n by using the Laplace transform technique

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

Measurement of the Q^{2} Dependence of the Deuteron Spin Structure Function g_{1} and its Moments at Low Q^{2} with CLAS.

We measured the g_{1} spin structure function of the deuteron at low Q^{2}, where QCD can be approximated with chiral perturbation theory (χPT). The data cover the resonance region, up to an invariant mass of W≈1.9 GeV. The generalized Gerasimov-Drell-Hearn sum, the moment Γ_{1}^{d} and the spin polarizability γ_{0}^{d} are precisely determined down to a minimum Q^{2} of 0.02 GeV^{2} for the first time, about 2.5 times lower than that of previous data. We compare them to several χPT calculations and models. These results are the first in a program of benchmark measurements of polarization observables in the χPT domain.