Spin Polarizabilities Research Articles

Analyzing the effects of neutron polarizabilities in elastic Compton scattering off 3He

Motivated by the fact that a polarized 3He nucleus is expected to behave approximately as a polarized neutron, we examine manifestations of neutron electromagnetic polarizabilities in elastic Compton scattering from the Helium-3 nucleus. We calculate both unpolarized and double-polarization observables using chiral perturbation theory to next-to-leading order ( O ( e 2 Q ) ) at energies, ω ≲ m π , where m π is the pion mass. Our results show that the unpolarized differential cross-section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.

Moments of the spin structure functions [formula omitted] and [formula omitted] for [formula omitted

The spin structure functions g 1 for the proton and the deuteron have been measured over a wide kinematic range in x and Q 2 using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH 3 and ND 3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q 2 < 5 GeV 2 and W < 3 GeV . The first moments of g 1 for the proton and deuteron are presented – both have a negative slope at low Q 2 , as predicted by the extended Gerasimov–Drell–Hearn sum rule. The first extraction of the generalized forward spin polarizability of the proton γ 0 p is also reported. This quantity shows strong Q 2 dependence at low Q 2 . Our analysis of the Q 2 evolution of the first moment of g 1 shows agreement in leading order with Heavy Baryon Chiral Perturbation Theory. However, a significant discrepancy is observed between the γ 0 p data and Chiral Perturbation calculations for γ 0 p , even at the lowest Q 2 .

Experimental study of isovector spin sum rules

We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05l{Q}^{2}l2.92\text{ }\text{ }{\mathrm{GeV}}^{2}$. The integral is fit to extract the twist-4 element ${f}_{2}^{p\ensuremath{-}n}$ which appears to be relatively large and negative. Systematic studies of this higher twist analysis establish its legitimacy at ${Q}^{2}$ around $1\text{ }\text{ }{\mathrm{GeV}}^{2}$. We also performed an isospin decomposition of the generalized forward spin polarizability ${\ensuremath{\gamma}}_{0}$. Although its isovector part provides a reliable test of the calculation techniques of chiral perturbation theory, our data disagree with the calculations.

Highlights and perspectives of the JLab spin physics program

Nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent precision spin-structure data from Jefferson Lab have significantly advanced our knowledge of nucleon structure in the valence quark (high-x) region and improved our understanding of higher-twist effects, spin sum rules and quark-hadron duality. First, results of spin sum rules and polarizabilities in the low to intermediate Q 2 region are presented. Comparison with theoretical calculations, in particular with Chiral Perturbation Theory (ChPT) calculations, are discussed. Surprising disagreements of ChPT calculations with experimental results on the generalized spin polarizability, δ LT, were found. Then, precision measurements of the spin asymmetry, A 1, in the high-x region are presented. They provide crucial input for global fits to world data to extract polarized parton distribution functions. The up and down quark spin distributions in the nucleon were extracted. The results for Δd/d disagree with the leading-order pQCD prediction assuming hadron helicity conservation. Results of precision measurements of the g 2 structure function to study higher-twist effects are presented. The data indicate a significant higher-twist (twist-3 or higher) effect. The second moment of the spin structure functions and the twist-3 matrix element d 2 results were extracted. The high Q 2 result was compared with a Lattice QCD calculation. Results on the resonance spin-structure functions in the intermediate Q 2 range are presented, which, in combination with DIS data, enable a detailed study of quark-hadron duality in spin-structure functions. Finally, an experiment to study neutron transversity and transverse spin asymmetries is discussed. A future plan with the 12 GeV energy upgrade at JLab is briefly outlined.

Gerasimov-Drell-Hearn sum rule and the discrepancy between the new CLAS and SAPHIR data

Contribution of the K^+\Lambda channel to the Gerasimov-Drell-Hearn (GDH) sum rule has been calculated by using the models that fit the recent SAPHIR or CLAS differential cross section data. It is shown that the two data sets yield quite different contributions. Contribution of this channel to the forward spin polarizability of the proton has been also calculated. It is also shown that the inclusion of the recent CLAS C_x and C_z data in the fitting data base does not significantly change the result of the present calculation. Results of the fit, however, reveal the role of the S_{11}(1650), P_{11}(1710), P_{13}(1720), and P_{13}(1900) resonances for the description of the C_x and C_z data. A brief discussion on the importance of these resonances is given. Measurements of the polarized total cross section \sigma_{TT'} by the CLAS, LEPS, and MAMI collaborations are expected to verify this finding.

Near-threshold deuteron photodisintegration: An indirect determination of the Gerasimov-Drell-Hearn sum rule and forward spin polarizability (γ0) for the deuteron at low energies

It is shown that a measurement of the analyzing power obtained with linearly polarized \ensuremath{\gamma}-rays and an unpolarized target can provide an indirect determination of two physical quantities. These are the Gerasimov-Drell-Hearn (GDH) sum rule integrand for the deuteron and the sum rule integrand for the forward spin polarizability (${\ensuremath{\gamma}}_{0}$) near photodisintegration threshold. An analysis of data for the $d(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},n)p$ reaction and other experiments is presented. A fit to the world data analyzed in this manner gives a GDH integral value of $\ensuremath{-}603\ifmmode\pm\else\textpm\fi{}43\ensuremath{\mu}$b between the photodisintegration threshold and 6 MeV. This result is the first confirmation of the large contribution of the ${}^{1}{S}_{0}(M1)$ transition predicted for the deuteron near photodisintegration threshold. In addition, a sum rule value of 3.75\ifmmode\pm\else\textpm\fi{}0.18 fm${}^{4}$ for ${\ensuremath{\gamma}}_{0}$ is obtained between photodisintegration threshold and 6 MeV. This is a first indirect confirmation of the leading-order effective field theory prediction for the forward spin-polarizability of the deuteron.

Interfacial Spin Polarization and Magnetic Structure of Co/MgO/Co Magnetic Tunnel Junction: Ab Initio Calculation

Using ab initio method based on the density functional theory, the equilibrium bcc-Co(001)/rocksalt-MgO(001)/bcc-Co(001) magnetic tunnel junction structure was investigated. Spin polarization and magnetic moment were calculated for each atomic slab in the equilibrium structure by spin dependent density of states analysis. Interfacial Co atoms showed significantly larger spin polarization of -88.3%, compared to the value of inner Co slabs, -82.3%, and bulk bcc Co, -82.1%. Interestingly, Mg and O atoms also showed induced spin polarizability ranged from -45.0% to -66.0%, except for O atoms in the centered slab of barrier layer, which showed relatively small polarization, -14.9%. Magnetic moments for the electrode Co atoms were calculated to be approximately 1.74 microB with no significant variation across the electrode.

KAON CONTRIBUTIONS TO THE GERASIMOV–DRELL–HEARN INTEGRALS ON THE PROTON

Using KAON-MAID, an operator for kaon photo- and electro-production on the nucleon, we calculate contributions of kaon–hyperon final states to the Gerasimov–Drell–Hearn (GDH) integrals on the proton. We also calculate the corresponding contributions to the forward spin polarizability γ0 of the proton. By extending the operator to the finite Q2 region we then calculate kaon contributions to the generalized GDH integrals, as well as to the longitudinal-transverse polarizability δ0. Our results show relatively small but still sizable contributions.

THEORETICAL STUDY ON SPIN POLARIZATION IN SMALL ALUMINUM CLUSTERS

Geometric optimizations of neutral Al n (n = 2–11) clusters at B3LYP/6-31+G(d) level of theory demonstrate that small aluminum clusters are spin-polarized in ground state. Specifically, Al n (n = 3, 5, 7, 9, and 11) clusters are spin doublets, Al n (n = 2, 4, 6, and 8) are triplets, whereas Al 10 is a singlet. The spin polarizability decreases as the size of the cluster increases. The electronic spin polarization is mainly attributed to the atomic 3p electrons of aluminum atoms each of which has a nonzero orbital and spin angular momenta, respectively. Among all the clusters, Al 2 is the most spin-polarized; its evident triplet stability and electronic structural properties are partially ascribed to its nuclear spins, based on the calculations of indirect nuclear spin–spin coupling constants at B3LYP/6-311+G(3df) level of theory. As the size of the cluster increases, the influence of nuclear spins on electronic spin polarization declines due to the multiple couplings.

Properties of the πη, $ \eta{^\prime}$ ,σ, f0(980) and a0(980) mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings $F_{M\gamma\gamma}$ of mesons $(M)$ and their couplings $g_{MNN}$ to the nucleon as entering into the $t$-channel parts of the difference of the electromagnetic polarizabilities $(\alpha-\beta)$ and the backward angle spin polarizabilities $\gamma_\pi$ are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are $\alpha_n=13.4\pm 1.0$, $\beta_n=1.8\mp 1.0$ ($10^{-4}$ fm$^3$), and $\gamma^{(n)}_\pi=57.6\pm 1.8$ ($10^{-4}$ fm$^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.

Proton spin polarizabilities from polarized Compton scattering

Polarized Compton scattering off the proton is studied within the framework of subtracted dispersion relations for photon energies up to 300 MeV. As a guideline for forthcoming experiments, we focus the attention on the role of the proton's spin polarizabilities and investigate the most favorable conditions to extract them with a minimum of model dependence. We conclude that a complete separation of the four spin polarizabilities is possible, at photon energies between threshold and the $\ensuremath{\Delta}(1232)$ region, provided one can achieve polarization measurements with an accuracy of a few percent.

Investigating Neutron Polarizabilities through Compton Scattering onHe3

We examine manifestations of neutron electromagnetic polarizabilities in coherent Compton scattering from the helium-3 nucleus. We calculate gamma3He elastic scattering observables using chiral perturbation theory to next-to-leading order [O(e2Q)]. We find that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.

Frequency dependence of induced spin polarization and spin current in quantum wells

Dynamic response of two-dimensional electron systems with spin-orbit interaction is studied theoretically on the basis of quantum kinetic equation, taking into account elastic scattering of electrons. The spin polarization and spin current induced by the applied electric field are calculated for the whole class of electron systems described by $\mathbf{p}$-linear spin-orbit Hamiltonians. The absence of nonequilibrium intrinsic static spin currents is confirmed for these systems with arbitrary (nonparabolic) electron energy spectrum. Relations between the spin polarization, spin current, and electric current are established. The general results are applied to the quantum wells grown in [001] and [110] crystallographic directions, with both Rashba and Dresselhaus types of spin-orbit coupling. It is shown that the existence of the fixed (momentum-independent) precession axes in [001]-grown wells with equal Rashba and Dresselhaus spin velocities or in symmetric [110]-grown wells leads to vanishing spin polarizability at arbitrary frequency $\ensuremath{\omega}$ of the applied electric field. This property is explained by the absence of Dyakonov-Perel-Kachorovskii spin relaxation for the spins polarized along these precession axes. As a result, a considerable frequency dispersion of spin polarization at very low $\ensuremath{\omega}$ in the vicinity of the fixed precession axes is predicted. Possible effects of extrinsic spin-orbit coupling on the obtained results are discussed.

SPIN POLARIZABILITY OF THE NUCLEON IN THE EFFECTIVE FIELD THEORY OF HEAVY BARYON

We have constructed a heavy baryon effective field theory with photon as an external field in accordance with the symmetry requirements similar to the heavy quark effective field theory. By treating the heavy baryon and antibaryon equally on the same footing in the effective field theory, we have calculated the spin polarizabilities γi, i = 1,…,4 of the nucleon at third order and at fourth-order of the spin-dependent Compton scattering. At leading order (LO), our results agree with the corresponding results of the heavy baryon chiral perturbation theory, at the next-to-leading order (NLO) the results show a large correction to the ones in the heavy baryon chiral perturbation theory due to baryon–antibaryon coupling terms. The low-energy theorem is satisfied both at LO and at NLO. The contributions arising from the heavy baryon–antibaryon vertex were found to be significant and the results of the polarizabilities obtained from our theory is much closer to the experimental data.

Electromagnetic and spin polarizabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarizabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarizabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of finite volume chiral perturbation theory. We derive results relevant for lattice simulations of QCD, partially-quenched QCD and quenched QCD. Our results for the polarizabilities show a strong dependence on the lattice volume and quark masses, typically differing from the infinite volume limit by $\ensuremath{\sim}10%$ for current lattice volumes and quark masses.

NEW PREDICTIONS OF GENERALIZED SPIN POLARIZABILITIES IN HEAVY BARYON CHIRAL PERTURBATION THEORY

We review the recent progress of the theoretical understanding of the spin structure of the nucleon based on Heavy Baryon Chiral Perturbation Theory (HBChPT). At low Q2 the spin structure of the nucleon is encoded into the generalized spin polarizabilities (spin GP's) extracted from the virtual Compton scattering (VCS) amplitudes. The spin GP's of the nucleon have been calculated up to next-to-leading order in HBChPT. Furthermore, the forward spin generalized polarizabilities, which are related to the nucleon polarized structure functions g1 and g2 through the sum rules based on dispersion relations, also have been calculated in HBChPT up to next-to-leading order. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are also presented.

Predictions for polarized-beam and/or vector-polarized-target observables in elastic Compton scattering on the deuteron

Motivated by ongoing developments at High-Intensity Gamma Source (HI\ensuremath{\gamma}S) at Triangle Universities Nuclear Laboratory (TUNL) that include increased photon flux and the ability to circularly polarize photons, we calculate several beam-polarization and/or target-spin-dependent observables for elastic Compton scattering on the deuteron. This is done at energies of the order of the pion mass within the framework of heavy-baryon chiral perturbation theory. Our calculation is complete to $\mathcal{O}({Q}^{3})$ and at this order there are no free parameters. Consequently, the results reported here are predictions of the theory. We discuss paths that may lead to the extraction of neutron polarizabilities. We find that the photon/beam polarization asymmetry is not a good observable for the purpose of extracting ${\ensuremath{\alpha}}_{n}$ and ${\ensuremath{\beta}}_{n}$. However, one of the double polarization asymmetries, ${\ensuremath{\Sigma}}_{x}$, shows appreciable sensitivity to ${\ensuremath{\gamma}}_{1n}$ and could be instrumental in pinning down the neutron spin polarizabilities.

New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering (VCS) at ${\cal O}(p^4)$ in heavy baryon chiral perturbation theory. At this order, no unknown low energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the VCS amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double polarization experiments which allow to access these spin-flip GPs of the nucleon.

Measurement of the Generalized Forward Spin Polarizabilities of the Neutron

The generalized forward spin polarizabilities gamma(0) and delta(LT) of the neutron have been extracted for the first time in a Q2 range from 0.1 to 0.9 GeV2. Since gamma(0) is sensitive to nucleon resonances and delta(LT) is insensitive to the Delta resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on delta(LT) show significant disagreement with chiral perturbation theory calculations, while the data for gamma(0) at low Q2 are in good agreement with a next-to-leading-order relativistic baryon chiral perturbation theory calculation. The data show good agreement with the phenomenological MAID model.

THE GERASIMOV-DRELL-HEARN SUM RULE AND THE SPIN STRUCTURE OF THE NUCLEON

▪ Abstract The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal principles as causality, unitarity, and gauge invariance, these sum rules provide a unique testing ground to study the internal degrees of freedom that hold the system together. The present article reviews these sum rules for the spin-dependent cross sections of the nucleon by presenting an overview of recent experiments and theoretical approaches. The generalization from real to virtual photons provides a microscope of variable resolution: At small virtuality of the photon, the data sample information about the long-range phenomena, which are described by effective degrees of freedom (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at the larger virtualities. Through a rich body of new data and several theoretical developments, a unified picture of virtual Compton scattering emerges, which ranges from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep-inelastic lepton scattering.