Spin structure studies with polarized leptons

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Nuclear Physics A666&667 (2000) 267c-277c www.elsevier.nl/locate/npe

Spin Structure Studies with Polarized Leptons Edward R. Kinney ~ ~University of Colorado, CB 446, Boulder, Colorado 80309, USA and Deutsches Elektronen-Synchrotron DESY, Notkestrage 85, D-22603 Hamburg, FRG Precise measurements of the inclusive spin structure function gl of the nucleon are reviewed, focussing on recent measurements at SLAC, CERN and DESY. New semiinclusive measurements of the spin structure at CERN and DESY are discussed as well the planned measurements of the gluon contribution to the nucleon. New measurements of observables from transversly polarized nucleons are also briefly mentioned. 1. I N T R O D U C T I O N The study of the spin structure of the nucleon using deep inelastic scattering of polarized electrons and muons on polarized nucleon targets has been carried out for nearly 20 years, starting with the ground breaking experiments at SLAC[1,2] followed by the surprising results of the EMC experiment[3] ten years later. Since then there has been an intense world wide effort to verify the EMC measurement of g~, measure gP and furthermore measure both of these inclusive structure functions with high precision over as broad a kinematic range as possible. This second generation of experiments at SLAC[4-7], CERN[8] and DESY[9,10] has largely succeeded, and now experimental programs to proceed further are underway. At the same time, theoretical analysis of the inclusive structure functions has advanced substantially since the time of EMC. The primary results of the experimental programs will be discussed followed by discussion of future plans in the field. In particular, the experimental questions of most direct interest in the next five years are the determination of the gluon contribution to the nucleon spin, the contribution of the strange quark sea, and the determination of the transversity, the third twist-2 nucleon structure function which is required to completely specify the parton distribution at this order of QCD. The review will also be restricted to studies using polarized high energy lepton probes; the plans to study the nucleon spin at the Relativistic Heavy Ion Collider are reviewed elsewhere[Ill. 2. N E X T - T O - L E A D I N G MENTS

O R D E R A N A L Y S E S OF I N C L U S I V E M E A S U R E -

Since the publication of the results of the EMC experiment, programs at SLAC, CERN and DESY have repeated and extended the measurements of 9~ as well as made new measurements of g~. All of these modern experiments have results which agree well 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0375-9474(00)00035-X

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when appropriately evolved to the same Q~ and furthermore confirm the earlier result of EMC. In the limited space available here, it is impossible to discuss each of the different experimental programs, and so the focus will rather be on analyses of the world's data set by the E154 and Spin Muon Collaborations using perturbative QCD at Next-to-Leading order (NLO), as first performed by Ball, Forte, and Ridolfi[12]. Since these are several years old, they lack the latest data sets, in particular those of HERMES[10] and SLAC E155[13]. A new analysis by the SLAC E155 group is expected in the near future and preliminary results have been reported.[7]

2.1. E154 Analysis The E154 collaboration[14] have analyzed gf and g~ using the formalism of next-toleading order (NLO) perturbative QCD in which the inclusive structure function is a convolution of x and Q2 dependent polarized quark distribution functions. The evolution of these distributions is governed by the standard DGLAP equations[15]. As such analysis is renormalization scheme dependent, both of the two most common choices are calculated, namely the modified minimal subtraction (MS) and Adler-Bardeen (AB) schemes. In addition to using the data from E154, and the g~, gld, and g~ measurements from the earlier EMC,[3] E142,[4] E143,[16] Spin Muon Collaboration[17] (SMC), and HERMES[9] (g[~ only) experiments are used to determine the parameters in the ansatz chosen to describe the polarized quark distributions A f, where A f = Auy, Adv, A~), AG are the polarized valence, sea, and gluon distributions respectively. In addition it is assumed in the construction of A~) that the polarized light sea is isospin-symmetric (A~ = A~/). The strange sea is allowed to be arbitrary in overall size to that of the light sea, but is assumed to have the same z dependence and a maximal value equal to that determined for the light sea. It does not appear that in this parameterization it is possible for light and strange seas to have different sign contributions or that the strange sea could have a larger contribution than the light sea. The non-singlet distributions are not fixed by the data SU(3)jt .... coupling constants F and D derived from hyperon ~-decay. The separation of 9~ into sea+gluon and valence quark contributions which can be derived from the fit is shown in Fig. 1. The striking feature predicted by the analysis is that the contribution of the sea and gluons becomes strongly negative at low z; as their model assmnes an isospin symmetric sea, this essentially predicts that g~ should also become negative at low x, which has yet to be explored. 2.2. SMC Analysis The SMC has also recently performed an analyses[18] of the world's data set on gl also using a framework of perturbative QCD up to NLO. In this analysis, the final completely analyzed SMC data set was used, including improved low x data. While overall the method of determining the polarized parton distributions is similar to that of E154, in detail, there are significant differences. The ansatz chosen for the initial polarized parton distributions, A f is in fact somewhat different. However, instead of fitting two valence distributions, a sea distribution and a gluon distribution, only three distributions are used, the singlet distribution AE, the non-singlet distribution AqNs and the gluon distribution Ag. Also, in contrast to the E154 analysis, the normalization of the non-singlet distributions is constrained by the hyperon/3-decay data and SU(3)f~ .... symmetry. Extensive studies both of the numerical algorithms to handle the evolution as well as the

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systematic uncertainties resulting from the neglect of higher order QCD corrections and undertainties in the input parameterization were performed. The results of the analysis using the AB renormalization scheme are presented in Fig. 2. As in the case of E154, the polarized gluon distribution is positive at high x, but no strong decrease to a negative contribution is apparent at low x. Both groups find that the gluon distribution is poorly constrained by the inclusive data set, but in fact the singlet and non-singlet distributions are relatively well determined, essentially via their different Q2 evolution. It should be particularly noted that theoretical uncertainties are dominant in all cases at the higher values of x typically explored by experiment. There is general agreement that in order to progress further with purely inclusive data, it is critical that new measurements be performed with high accuracy to much lower x. Design studies are underway at HERA in order to learn how one could store polarized protons in the p-ring in addition to the polarized electron ring that already exisits. Recently the physics case and technical progress were reviewed at a workshop at DESY[19]. New inclusive experiments[20] are also proposed to determine g~ at high z using the high performance capabilities of the CEBAF accelerator at Thomas Jefferson National Accelerator Facility. From the results of the SMC analysis, it would also seem important that the machinery of NNLO evolution also be developed. Furthermore, the uncertainty in the results of these analyses which arises from the choice of parameterization remains difficult to quantify.

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3. S E M I - I N C L U S I V E S C A T T E R I N G A N D F L A V O R D E C O M P O S I T I O N While the structure function 91 is now relatively well determined from inclusive scattering, at least over an intermediate range of x, our understanding of the nucleon's spin structure, especially with respect to understanding the failure of the Ellis-Jaffe sums, has not advanced significantly although our phenomenological understanding is significantly more sophisticated. To move beyond the inclusive studies, SMC[21] began a program of measurements of so-called semi-inclusive scattering, where a hadron is detected in coincidence with the scattered positron, and after kinematic constraints are applied to ensure that the hadron has a high probability of containing the initial struck quark (current fragmentation), asymmetries are formed which can be analyzed using the standard formalism of factorizable fragmentation. Such an analysis can yield the contributions of the different quark flavors to the overal quark component of the nucleon spin, a so-called flavor

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decomposition. This program has been continued and extended by the HERMES experiment. Recently the HERMES collaboration has published a flavor decompostion using the data sets from their longitudinally polarized 1H target combined with those data from their 3He target run. Using only the asymmetries from undifferentiated charged hadrons, a flavor decomposition of AN into up, down, and sea contributions was obtained.[22] Figure 3 shows the results of a pure decomposition where no attempt is made to separate valence up or down distributions directly from the sea. In contrast to the earlier work of SMC, where a flavor symmetric assumption was chosen for the sea distributions, Aft = A d = Ag, here the polarization of the sea if assumed independent of flavor, that is A f i / u = A d / d = A g / s . The HERMES data set is in fact insensitive to this choice. A flavor decomposition into valence and sea terms was also performed and the results are compared to those of SMC in Fig. 4. The experiments are in excellent agreement and it can be seen that HERMES has significantly increased the precision of these flavor determinations.

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At present the experiment is collecting data using a longitudinally polarized deuterium target, which will provide a better determination of the down quark distribution; one sees that the up distribution is already well determined. Directly determining the polarization of the sea and in particular the strange sea remains a challenge; at present it appears consistent with zero but with large uncertainty. In 1997 it was decided to upgrade the PID of the detector by the replacement of the existing threshold (~.erenkov detector with a dual radiator ring imaging (~erenkov (RICH),[24] allowing identification of pions, kaons, and protons over nearly the full momentum acceptance of the spectrometer, 1-20 GeV/c. The primary physics motivation for this project was the desire to perform the first direct measurement of the contribution of the strange quark sea to the nucleon spin. The RICH upgrade has been operating successfully throughout the polarized deuterium run of 19981999 and so one may expect first results sometime in late 2000.

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OF T H E G L U O N P O L A R I Z A T I O N

Almost all partonic analyses of the nucleon spin point to a large positive contribution from the gluonic field in order to account for the ~'deficit" of contribution from the quark spins. A number of new programs at RICH, DESY, and CERN will attempt to measure the gluon polarization directly. Here, I will only discuss the experiments using polarized lepton beams. 4.1. H E R M E S

M e a s u r e m e n t s of G l u o n P o l a r i z a t i o n

In the next five years, the HERMES experiment will attempt to determine the gluon polarization in the nucleon over a range of intermediate x via a number of channels. The "cleanest" extraction will likely result from the determination of the semi-inclusive open charm asymmetry[25], principally through detection of D mesons. The existence of little, if any, intrinsic charm in the nucleon makes the detection of charmed hadrons an efficient tag for the photon-gluon fusion (PGF) process, which is sensitive to the gluon polarization. The D o meson in particular can be detected at HERMES via it Krr decay mode. In addition to open charm, the spectrometer has also been augmented to increase the acceptance and identification of hidden charm J/k0 mesons via their decay into muons. This has been accomplished with the installation of an iron wall downstream of the spectrometer which is instrumented with scintillation counters, and by the addition of hodoscope planes outside the standard acceptance of the spectrometer in order to detect muons which pass through the steel of the magnet yoke and field clamps. Since it is necessary to select inelastic (low z) J/kO's for determining the gluon polarization, downstream quadrupole magnets have been instrumented to detect low energy, small angle electron scattering, in order to determine the virtual photon kinematics of a fraction of the J / ~ mesons. By summer 2000 it is expected that the gluon polarization can be measured with an statistical uncertainty of 0.4. After the luminosity upgrade of HERA[26] is completed, it expected that another 2-year run will decrease this uncertainty by nearly a factor of 2. Recently, HERMES has reported[27] the observation of an unexpected negative asymmetry in the photoproduction of pairs of oppositely charged hadrons with relatively large components of momentum transverse to that of the incident photon, from a longitudinally polarized proton target. The asymmetry from these so-cMled "high pr" pairs has been proposed by Fontannaz, Schiff and Pire[28] to be a tag for the PGF process, allowing a determination of the gluon polarization independently of the charmed channels. The fundamental PGF process has a negative asymmetry, so the HERMES observation implies that the gluon polarization is positive at x ~ 0.2. A more detailed report is contained in these proceedings[29]. This method of extracting the gluon polarization has been studied in detail first for use in the COMPASS experiment[30] by Bravar, yon Harrach and Kotzinian[31]. This is a rapidly evolving topic, however it is fair to state that at present the theoretical treatment needs to be developed further before one can extract meaningful quantitative information about the gluon polarization from the HERMES observation. On the other hand, data taken with the polarized deuterium target in the period up to the May 2000 shutdown should add significant information both in terms of statistics and in terms of the understanding of the reaction mechanism and extraction, as the fraction of QCD

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Compton to PGF is different for the deuteron. This data set will be doubled again with the addition of a two year HERA run with longitudinally polarized deuterium after the HERA luminosity upgrade is completed. 4.2. T h e C O M P A S S E x p e r i m e n t at C E R N In 1996 the COMPASS collaboration at CERN proposed to make a direct measurement of the gluon polarization in the nucleon, using 100-200 GeV polarized muons incident on polarized proton and deuteron targets[30]. The primary method proposed was the measurement of the cross section asymmetry for open charm production in deep inelastic scattering, as just discussed for HERMES. In order to make the measurements feasible with the full intensity muon beam available, it was proposed to build a new, high-performance spectrometer with excellent particle identification and calorimetry. Installation is ongoing at present and first data are expected to be collected in late 2000. In the case of the measurement of the open charm asymmetry, the D o was identified as the best candidate, with projections based on its identification via the KTr decay (BR=4%). By tagging events with D *+ the accuracy of the measurement can be increased further. Since the first proposal by the collaboration, Bravar, von Harrach and Kotzinian[31] have performed an extensive analysis of the possibilities of using the measurement of the cross section asymmetry in production of pairs of oppositely charged hadrons with high transverse momentum, Pr. These studies suggest that an uncertainty of 5% can be achieved in the determination of AG/G over an intermediate range of x-gluon (= r]). While the primary focus of the muon program at COMPASS is the measurement of AG/G, the experiment will also be able to substantially improve the accuracy of low-x measurements of gf, gl~, and the different flavor components Aq. 5. N E W T R A N S V E R S E

MEASUREMENTS

In the above, I have restricted the discussion to spin structure as determined from longitudinally polarized targets. Previous measurements with transversely polarized targets have been restricted essentially to measurements of the second spin structure function g2. The primary motivation of SLAC E155X[32] was to perform a precise enough measurement of g2(x) to allow the determination of any deviation from the twist-2 part of g2(x) which arises from gl(x), the so-called Wandzura-Wilczek[33] term gWW. Such a deviation could be clearly interpreted as arising from higher twist, and is of great interest. First results from E155X are in fact presented elsewhere in these proceedings[34]. After the completion of the HERA luminosity upgrade, a major focus of the HERMES experiment will be running with transversely polarized targets in order to determine the transversity. Since this distribution is less well known, a brief introduction is included here. In fact, the complete description of the parton distributions of the nucleon at twist-2 requires three distributions: the unpolarized distributions contained in FI(Z), the helicity distributions contained in gl(x) and the transversity distributions whose structure function will here be denoted as hi(x). This distribution was first proposed and investigated by Ralston and Soper[35] in their study of the transverse asymmetry in polarized Drell-Yan reactions; it was further developed by groups led by Jaffe[36] and by Mulders[37]. Physically, one may think of the transversity as the distribution of quarks polarized parallel to the nucleon spin minus the distribution of quarks polarized antiparallel to the nucleon

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spin (in exact mimicry of the longitudinal case of gl) except that now the polarization of the nucleon is transverse to its momentum, rather than parallel. In a non-relativistic quark model, this is just a simple rotation, and in fact such models predict hi = gl. Any violation of this equation would be interpreted as arising from relativistic effects. Beyond its intrinsic interest as a fundamental parton distribution, the transversity also offers one an exciting new possibility of solving some of the difficulties in the interpretation of gl and AE. It is well known that the polarized gluon distribution mixes with the singlet polarized quark distributions Aq(x) in AS via the axial anomoly and thus Aq(x) is dependent on the renormalization scheme and the unknown gluon polarization, Ag(x). This is not the case for hi which therefore evolves with a completely different Q2 dependence. Furthermore, in contrast to gl, the antiquarks contribute to hi with opposite sign to that of quarks, hence the sea distributions largely cancel, and hi becomes predominantly sensitive to the valence quark distributions. The integral of hi gives the tensor charge of the nucleon, rather than the total quark spin, and this tensor charge may be reliably calculated on the lattice in the not too distant future. While it's integral may not be related directly to the quark spin contribution to the nucleon, in combination with gl it should help to consistently identify the valence, sea and gluon components of gl. Recently HERMES has observed[38] an single spin asymmetry in the azimuthal distribution of positive pions detected in coincidence with the deep inelastic scattering of a longitudinally polarized electron from a longitudinally polarized proton target; a detailed presentation is contained within these proceedings.J39] While the theoretical interpretation of this result is under vigorous development, it appears clear that the measurements of transversity are feasible. It should be mentioned that COMPASS also plans precise measurements of transverse charged pion asymmetries; the different ranges of Q2 accessible in the two experiments should be extremely useful in untangling the components of different twist and Q dependence, and so they should complement each other. 6. I N I T I A T I V E S B E Y O N D

2005

Given the typical proposal cycle of accelerator facilities, initiatives beyond 2005 are mostly still in the stage where the generation of the physics case is most important, and the experimental apparatus is still pre-conceptual or under initial investigation. The TJNAF institutional plan[40] looks to a series of future upgrades of the accelerator, starting with the increase to 6 GeV, with the next jump being to 12 GeV in approximately 5 years, and in the more distant future, an upgrade to an energy somewhere between 20 and 30 GeV. A design of a new experimental hall (Hall D) is underway, which will perform studies focussed on exotic meson and baryon states. For a number of years, there has been a proposal[41] to build a high luminosity (1035 cm-2s -1) facility in Europe, known as ELFE, with electron energy of approximately 30 GeV. Very recently there is also discussion underway to build a polarized g~ collider (EPIC) similar to that proposed at HERA but at x/~ ~ 20 GeV and with luminosity of 1033 cm-2s -1. At present the focus of these programs is the measurement of so-called skewed or non-forward parton distributions via the detection of asymmetries with exclusive 3-body final states. In particular, the measurement of exclusive deeply virtual Compton scattering has been shown by Ji[42] to

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be related to the total angular momentum of the quark and glue, possibly giving a way to determine the orbital angular momentum of the quarks. These studies are still at an early stage and as of yet, no one has ever measured one of these new distributions. 7. S U M M A R Y

After early exploratory measurements have demonstrated that the spin structure of the nucleon was surprising and not understood, a series of modern experiments at SLAC, CERN and DESY have determined the inclusive spin structure functions well at moderate x. First SMC and then HERMES have extended the inclusive measurements via semiinclusive measurements yielding polarized quark distributions for the different flavors. HERMES, COMPASS and RHIC will attempt to perform precise, direct measurements of the gluon polarization and the flavor decomposition of the sea quark spin densities in the next five years, in particular the polarization of the strange sea. Given the effort to date, the understanding of the spin structure remains elusive, and there remains a healthy program of experiments around the world attempting to unravel this mystery. REFERENCES

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