Quark helicity distributions in the nucleon for up, down, and strange quarks from semi-inclusive deep-inelastic scattering

A. Airapetian et al. (HERMES Collaboration)

Phys. Rev. D 71, 012003 – Published 24 January 2005

Abstract

Polarized deep-inelastic scattering data on longitudinally polarized hydrogen and deuterium targets have been used to determine double-spin asymmetries of cross sections. Inclusive and semi-inclusive asymmetries for the production of positive and negative pions from hydrogen were obtained in a reanalysis of previously published data. Inclusive and semi-inclusive asymmetries for the production of negative and positive pions and kaons were measured on a polarized deuterium target. The separate helicity densities for the up and down quarks and the anti-up, anti-down, and strange sea quarks were computed from these asymmetries in a “leading order” QCD analysis. The polarization of the up-quark is positive and that of the down-quark is negative. All extracted sea quark polarizations are consistent with zero, and the light quark sea helicity densities are flavor symmetric within the experimental uncertainties. First and second moments of the extracted quark helicity densities in the measured range are consistent with fits of inclusive data.

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Received 19 July 2004

DOI:https://doi.org/10.1103/PhysRevD.71.012003

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Vol. 71, Iss. 1 — 1 January 2005

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Images

Figure 1
Diagram of the deep-inelastic scattering process. The incoming lepton emits a virtual photon which is absorbed by one of the quarks in the nucleon. In the case depicted, the struck quark fragments into a pion in the final state. In semi-inclusive processes, the scattered lepton and part of the hadronic final state are detected in coincidence.
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Figure 2
Schematic diagram of the HERA accelerator layout until 2000 with the location of experiments. Also shown are the locations of the spin rotators and the two polarimeters.
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Figure 3
Diagram of the HERMES polarized target. Shown are the atomic beam source (ABS), the target gas analyzer (TGA), and the Breit-Rabi polarimeter (BRP). SFT, MFT, and WFT label the strong, medium, and weak field transitions in the ABS and the BRP.
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Figure 4
Side view of the HERMES spectrometer. The positron beam enters from the left. The spectrometer is split into two halves, one above the beam and one below, by a flux exclusion plate to protect the beams from the magnetic field. See the text for further details on the detectors.
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Figure 5
Typical PID detector responses. The distributions are based on a small set of the data collected in 2000, except for the threshold Čerenkov response, which was computed from a data set of similar size collected in 1997. The truncated mean is shown in the case of the TRD. The relative size of the lepton (dashed line) and hadron distributions (solid line) was scaled to the flux ratio in the respective data-taking periods to give a better idea of the level of contamination possible from each detector. The flux ratio of electrons to hadrons is typically $\sim 10 %$ for these data.
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Figure 6
Tracking system resolution for lepton and hadron tracks for the detector configuration used since 1998. In the left panel the relative momentum resolution is displayed, and the right panel shows the resolution in the horizontal scattering angle $θ_{x}$ , both as a function of the track momentum $p$ .
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Figure 7
Two-dimensional distribution of PID values for all particles in the acceptance. The quantities $P I D 3$ and $P I D 5$ are defined as $P I D 3 \equiv {P I D}_{c a l} + {P I D}_{p r e} + {P I D}_{r i c}$ and $P I D 5 \equiv {P I D}_{t r d}$ .
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Figure 8
The distribution of the total $P I D$ value. This logarithmic ratio of probabilities includes the particle fluxes and the responses of all PID detectors. The left-hand peak is the hadron peak, while the right-hand peak originates from leptons. The limits that were applied in the analysis are shown as vertical lines.
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Figure 9
Identification efficiency and hadron contamination of the DIS lepton sample as a function of $x$ . Because correlations between the responses of the PID detectors were neglected, the contaminations are uncertain by a factor of 2. The deuteron data have slightly worse efficiencies and contaminations because of the better hadron-lepton discrimination of the threshold Čerenkov counter compared to the RICH.
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Figure 10
Čerenkov angles associated with the three particle hypotheses as a function of the particle momentum. The characteristic angles of Čerenkov light emitted in the aerogel ( $n = 1.03$ ) are given by the solid lines. The characteristic angles for emission in the gas ( $n = 1.0014$ ) are shown as the dashed lines. The corresponding histogram entries are experimentally determined angles of a sample of SIDIS hadrons.
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Figure 11
The observed asymmetries $A_{∥}$ and $A_{∥}^{π^{+}}$ on the proton target compared with the corresponding Born asymmetries. The Born asymmetries are offset horizontally for better presentation. See the text for details.
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Figure 12
Uncertainty inflation caused by detector smearing and QED radiative effects. The left-hand panel shows the uncertainty inflation of the inclusive asymmetry for the proton and the right-hand panel that of the positive pion asymmetry. In both panels the open triangles present the uncertainty inflation caused by detector effects, the open squares present the inflation caused by QED radiative effects, and the filled circles show the total uncertainty inflation.
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Figure 13
The inclusive and semi-inclusive Born level asymmetries on the proton, corrected for instrumental smearing and QED radiative effects. The error bars give the statistical uncertainties, and the shaded bands indicate the systematic uncertainty. The open squares show the positive and negative hadron asymmetries measured by the SMC collaboration, limited to the HERMES $x$ range [50].
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Figure 14
The inclusive and semi-inclusive Born level asymmetries on the deuteron. One data point at $x = 0.45$ for the $K^{-}$ asymmetry including its large error bar is outside the displayed range; all data points are listed in Table 13. See Fig. 13 for details.
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Figure 15
The semi-inclusive Born asymmetries for positive and negative pion production on the proton as a function of $z$ . The error bars indicate the statistical uncertainties and the error band represents the systematic uncertainties. The solid line is the $z$ dependence from the Monte Carlo simulation of the asymmetries.
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Figure 16
Born level Monte Carlo asymmetries on the proton in the experimental acceptance and in $4 π$ . The left-hand plot compares the semi-inclusive asymmetries $A_{1, p}^{π^{+}}$ and the right-hand plot the semi-inclusive asymmetries $A_{1, p}^{π^{-}}$ . The asymmetries in the experimental acceptance also include the hadron momentum cut. For display purposes the full data points have been offset horizontally. The lower panels present the same data in the form of the difference in the asymmetries divided by the total experimental uncertainty $σ_{b o r n}$ in the corresponding measured Born asymmetry.
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Figure 17
Multiplicities of charged pions and kaons in the HERMES acceptance compared with Monte Carlo data as function of $z$ . Statistical uncertainties in the data are too small to be visible. The multiplicities shown were not corrected for radiative and instrumental effects.
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Figure 18
Purities for positive and negative pions and kaons on a proton and a free neutron target. Each column corresponds to scattering off a certain quark flavor. The shaded bands indicate the estimated systematic uncertainties due to the fragmentation parameters. The estimate is derived from a comparison of two parameter sets. See text for details.
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Figure 19
The quark polarizations in the $5 parameter \times 9$ $x$ -bins fit. The polarizations, shown as a function of $x$ , were computed from the HERMES inclusive and semi-inclusive asymmetries. The error bars are the statistical uncertainties. The band represents the total systematic uncertainty, where the light gray area is the systematic error due to the uncertainties in the fragmentation model, and the dark gray area is from the contribution of the Born asymmetries.
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Figure 20
The quark helicity distributions $x Δ q (x, Q_{0}^{2})$ evaluated at a common value of $Q_{0}^{2} = 2.5 {G e V}^{2}$ as a function of $x$ . The dashed line is the GRSV2000 parametrization (LO, valence scenario) [18] scaled with $1 / (1 + R)$ and the dash-dotted line is the Blümlein-Böttcher (BB) parametrization (LO, scenario 1) [67]. See Fig. 19 for explanations of the uncertainties shown.
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Figure 21
The flavor asymmetry in the helicity densities of the light sea evaluated at $Q_{0}^{2} = 2.5 {G e V}^{2}$ . The data are compared with predictions in the $χ Q S M$ [74] and a meson cloud model [81]. The solid line with the surrounding shaded band show the $χ Q S M$ prediction together with its $\pm 1 σ$ uncertainties while the dash-dotted line shows the prediction in the meson cloud model. The uncertainties in the data are presented as in Fig. 19.
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Figure 22
The semi-inclusive Born level asymmetry $A_{1, d}^{K^{+} + K^{-}}$ for the total charged kaon flux on a deuterium target, corrected for instrumental smearing and QED radiative effects. The uncertainties are presented analogously to Fig. 13.
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Figure 23
The average strange quark helicity density $x \cdot [Δ s (x) + Δ \bar{s} (x)] / 2$ from the isoscalar extraction method (full points). For comparison the open symbols denote the results from a five parameter fit (see text), which are offset horizontally for presentation. The band in the bottom part gives the total systematic uncertainty on the results from the isoscalar extraction. The dark shaded area corresponds to the uncertainty from the input asymmetries, and the open part relates to the uncertainty in $λ_{s}$ .
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Figure 24
Matrices $n_{u} (i, j) = n_{⇒⃖} (i, j) + n_{⇐⃖} (i, j)$ for DIS events and SIDIS $π^{+}$ events on the proton. The binning shown corresponds to the nine bins in $x$ that were used in the asymmetry and $Δ q$ analysis (Table 5). See the text for details.
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