Spin physics at HERMES

The primary goal of the HERMES experiment is the study of the spin structure of the nucleon. Results on the measured inclusive and semi-inclusive hadron asymmetries using a polarized positron beam on polarized ³He, hydrogen and deuterium targets are here presented. In the covered kinematic range, 0.023<x _Bj <0.6 and 1 GeV²<Q ²<10GeV² the polarized quark distribution were determined for all up (u+?u) and down (d+?) quarks, and separately for valence and sea quarks. The up quark polarization is positive, and the down quark polarization is negative. The polarization of the sea is consistent with zero in the measured range. A first indication of a positive gluon polarization is presented, based on the measured spin asymmetry in the photo-production of hadron pairs with high transverse momentum p _T . This asymmetry is negative, which is in contrast to the measured positive asymmetry for inclusive experiments.     

New target transverse spin dependent azimuthal asymmetries from COMPASS experiment

In general, eight target transverse spin-dependent azimuthal modulations are allowed in semi inclusive deep inelastic scattering of polarized leptons on a transversely polarized target. In the QCD parton model four of these asymmetries can be interpreted within the leading order approach. Two of them, namely Collins and Sivers effects were already measured by HERMES and COMPASS experiments. Other two leading twist and remaining four azimuthal asymmetries which can be interpreted as twist-three contributions have been measured for the first time in COMPASS using a 160 GeV/c longitudinally polarized (P _l }~ −0.8) muon beam and a transversely polarized ⁶LiD target. We present here the preliminary results from the 2002–2004 data. on behalf of the COMPASS collaboration     

Study of TMDs with polarized beam and/or targets

A Fourier analysis of single- and double-spin azimuthal asymmetries measured at HERMES in semi-inclusive deep-inelastic scattering of unpolarized or longitudinally polarized leptons off tranversely polarized protons is presented for pions and charged kaons. The extracted amplitudes can be interpreted as convolutions of transverse momentum-dependent distribution and fragmentation functions. In particular, the measured double-spin asymmetries are sensitive to the poorly known worm-gear quark distribution g _1T ^⊥      

Predictions for azimuthal asymmetries in pion and kaon production in SIDIS off a longitudinally polarized deuterium target at HERMES

Predictions are made for azimuthal asymmetries in pion and kaon production from SIDIS off a longitudinally polarized deuterium target for HERMES kinematics, based on information on the “Collins fragmentation function” from DELPHI data and on predictions for the transversity distribution function from non-perturbative calculations in the chiral quark-soliton model. There are no free parameters in the approach, which has already been successfully applied to explain the azimuthal asymmetries from SIDIS off polarized proton targets observed by HERMES and SMC. Received: 8 January 2002 / Revised version: 25 January 2002 / Published online: 26 April 2002     

The (spin) structure of the nucleon

A selection of new data obtained by the HERMES experiment at DESY is presented, which provides new insight into the QCD structure of the nucleon. Using polarized lepton beams and polarized targets, the spin-dependent structure function g ₁(x) has been determined for ¹ H, ² H and ³ He. By also observing one of the produced hadrons it has been possible to extract the polarization distribution of individual quark flavours in the nucleon as well. Further information on nucleon structure has been obtained by observing (almost) exclusive reactions, which can be interpreted in terms of the recently introduced generalized parton distributions (GPDs). As an example of such data measurements of both the beam-spin and beam-charge asymmetries resulting from deeply virtual Compton scattering (DVCS) are presented. By embedding the deep-inelastic scattering process in the nuclear environment additional information can be obtained on nucleon structure and some QCD effects. The potential of this technique is illustrated by showing new results on tagged structure functions and hadronization in nuclei.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 13.88. + e Polarization in interactions and scattering - 14.20.Dh Protons and neutrons - 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processesG. van der Steenhoven: For the HERMES Collaboration     

Spin physics and more with HERMES

A review of recent results obtained by the HERMES experiment is given. Inclusive measurements on polarized and unpolarized targets provide precise information on the polarized structure functions g₁^d and g₁^p and the isoscalar unpolarized structure function ratio F₂^A/F₂^d. The geometrical acceptance of the HERMES detector and the good particle identification capabilities allow the study of semi-inclusive reactions as well. Using polarized targets, the polarized quark distribution functions can be extracted as well as a first indication of the transversity distributions . On unpolarized heavy targets, hadron formation in a nuclear environment is studied. Finally, data on Deeply Virtual Compton Scattering, the hard exclusive electroproduction of real photons, are presented, which are closely linked to the novel framework of Generalised Parton Distributions. For this reaction HERMES has measured the asymmetry main beam charge as well as in-beam spin.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 13.60.Le Meson production - 24.85.+p Quarks, gluons, and QCD in nuclei and nuclear processes - 25.30.Mr Muon scattering (including the EMC effect)B. Seitz: For the HERMES Collaboration     

Charged hadron multiplicities at the HERMES experiment

The HERMES collaboration has measured charge-separated pion and kaon multiplicities in semi-inclusive deep inelastic scattering using a 27.6 GeV electron or positron beam scattering off a hydrogen or deuterium target. The results are presented as a function of the Bjorken variable x _B , the negative squared four-momentum transfer Q ², the hadron fractional energy z and it’s transverse momentum P _{h ⊥}. These data will be very useful to understand the quark-fragmentation process in deep-inelastic hadron electro-production and will serve as crucial input in the understanding of spin asymmetries in polarized semi-inclusive deep-inelastic scattering.     

Single-spin asymmetries in the Bethe-Heitler process e − + p → e − + γ + p induced by loop corrections

The single-spin beam and target asymmetries in the hard electroproduction process e ⁻ + p → e ⁻ + γ + p induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason for the appearance of such asymmetries is the nonzero imaginary part of the amplitude (on the level of radiative corrections) caused by diagrams with photon radiation from the outgoing electron. We calculate the single-spin beam and target asymmetries at a longitudinally polarized electron beam or at arbitrary polarizations of the target proton for the CLAS and HERMES experimental conditions. The text was submitted by the authors in English.     

Collins effect and single spin azimuthal asymmetriesin the HERMES and COMPASS experiments

Predictions are made for single spin azimuthal asymmetries due to the Collins effect in pion production from semi-inclusive deeply inelastic scattering off transversely and longitudinally polarized targets for the HERMES and COMPASS experiments. The x-dependence of the asymmetries is evaluated using the parton distribution functions from the chiral quark-soliton model. The overall normalization of the predicted asymmetries is determined by the information on the Collins fragmentation function extracted from previous HERMES data on azimuthal asymmetries from a longitudinally polarized target. The single spin asymmetries A _UT from the transversely polarized proton target are found to be about for positive and neutral pions both at HERMES and COMPASS. For a longitudinally polarized target we obtain for COMPASS and .Received: 18 September 2003, Published online: 26 November 2003     

Longitudinal and transverse target-spin asymmetries associated with DVCS on the proton at HERMES

Measurements of azimuthal cross-section asymmetries from deeply virtual Compton scattering on transversely and longitudinally polarized hydrogen and longitudinally polarized deuterium targets at HERMES are reported. By comparing the HERMES results on the transverse target-spin asymmetry with theoretical calculations based on a phenomenological model of generalized parton distributions, a model-dependent constraint on the total angular momentum carried by quarks in the nucleon is obtained.     

Flavor asymmetry of polarized antiquark distributions and semi-inclusive DIS

The –expansion of QCD suggests large flavor asymmetries of the polarized antiquark distributions in the nucleon. This is confirmed by model calculations in the large– limit (chiral quark–soliton model), which give sizable results for and . We compute the contributions of these flavor asymmetries to the spin asymmetries in hadron production in semi-inclusive deep–inelastic scattering. We show that the large flavor asymmetries predicted by the chiral quark–soliton model are consistent with the recent HERMES data for spin asymmetries in charged hadron production. Received: 30 November 1999 / Published online: 17 March 2000     

COMPASS results on transverse spin asymmetries in identified two-hadron production in SIDIS

COMPASS is a fixed target experiment at CERN where nucleon spin structure and hadron spectroscopy are investigated using a 160 GeV/c polarized μ⁺ beam. An important part of its physics program are the measurements of single spin asymmetries (SSA) in semi-inclusive deep inelastic scattering (SIDIS) on transversely polarized targets. Data on a deuteron target (⁶LiD) were taken in 2002–04. After taking the first data on a transversely polarized proton target (NH₃) in 2007, a full year of data taking followed in 2010 to increase precision. The SSA of identified hadron pairs consisting of charged pions and/or kaons from the 2010 data are shown for the first time and compared to model predictions and results from HERMES.     

Analyzing the nucleon spin in weak interaction processes at HERA energies

We investigate the possibility to measure the spin content carried by the different quark flavors in a nucleon by means of polarized deep inelastic scattering with W^± exchange at HERA. Such measurements require a polarized proton beam. The expected inclusive and semi-inclusive asymmetries are sizable and for realistic luminosites the expected statistical accuracies are good enough to extract new and relevant information on the valence quark and the strange sea distributions.     

Hadron formation in deep-inelastic positron scattering in a nuclear environment

The influence of the nuclear medium on the production of charged hadrons in semi-inclusive deep-inelastic scattering has been studied by the HERMES experiment at DESY using a 27.5 GeV positron beam. The differential multiplicity of charged hadrons and identified charged pions from nitrogen relative to that from deuterium has been measured as a function of the virtual photon energy and the fraction z of this energy transferred to the hadron. There are observed substantial reductions of the multiplicity ratio at low and at high z, both of which are well described by a gluon-bremsstrahlung model of hadronization. A significant difference of the -dependence of is found between positive and negative hadrons. This is interpreted in terms of a difference between the formation times of protons and pions, using a phenomenological model to describe the - and z-dependence of . Received: 20 February 2001 / Revised version: 3 May 2001 / Published online: 8 June 2001     

Spin structure function of deuteron g<Subscript>1</Subscript><Superscript>d</Superscript> from COMPASS

New results on the longitudinal inclusive spin asymmetry A ₁ ^d in the range 1 < Q ² < 100(GeV/c)^2 and 0.004 < x < 0.7 are presented. From these results we derive the spin-dependent structure function g ₁ ^d which we use to evaluate the scale-invariant flavor-singlet axial charge . The contribution of the measured region is evaluated by a QCD fit of the world data. The data were obtained by the COMPASS experiment at CERN using a 160GeV polarized muon beam scattered off a large double-cell polarized ⁶LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region x < 0.03.     

Spin density matrix elements in exclusive ρ0 electroproduction on?1H and 2H targets at 27.5?GeV beam?energy

Spin Density Matrix Elements (SDMEs) describing the angular distribution of exclusive ρ ⁰ electroproduction and decay are determined in the HERMES experiment with 27.6 GeV beam energy and unpolarized hydrogen and deuterium targets. Eight (fifteen) SDMEs that are related (unrelated) to the longitudinal polarization of the beam are extracted in the kinematic region 1<Q ²<7 GeV², 3.0<W<6.3 GeV, and −t<0.4 GeV². Within the given experimental uncertainties, a hierarchy of relative sizes of helicity amplitudes is observed. Kinematic dependences of all SDMEs on Q ² and t are presented, as well as the longitudinal-to-transverse ρ ⁰ electroproduction cross-section ratio as a function of Q ². A small but statistically significant deviation from the hypothesis of s-channel helicity conservation is observed. An indication is seen of a contribution of unnatural-parity-exchange amplitudes; these amplitudes are naturally generated with a quark-exchange mechanism.     

Valence and sea contributions to the nucleon spin

The first moments of the polarized valence parton distribution functions (PDFs) truncated to the wide Bjorken x region 0.004<x<0.7 are directly (without any fitting procedure) extracted in the next to leading order (NLO) QCD from both COMPASS and HERMES data on pion production in polarized semi-inclusive DIS (SIDIS) experiments. The COMPASS and HERMES data are combined in two ways and two scenarios for the fragmentation functions (FFs) are considered. Two procedures are proposed for an estimation of light sea quark contributions to the proton spin. Both lead to the conclusion that these contributions are compatible with zero within the errors.     

Inclusive hadron photoproduction from longitudinally polarized protons and deuterons

We report measurements of the asymmetry A₆ for inclusive hadron production on longitudinally polarized proton and deuteron targets by circularly polarized photons. The photons were produced via internal and external bremsstrahlung from an electron beam of 48.35 GeV. Asymmetries for both positive and negative signed hadrons, and a subset of identified pions, were measured in the momentum range 10<P<30 GeV at 2.75° and 5.5°. Small non-zero asymmetries are observed for the proton, while the deuteron results are consistent with zero. Recent calculations do not describe the data well.