Recent HERMES results are presented on the flavor decomposition of the sea quark helicity distributions in the nucleon from semi-inclusive deep inelastic scattering. For the first time, a five component decomposition of quark helicity distributions using flavor tagging has been performed. The helicity distributions of the up and down quarks confirm the results obtained from inclusive deep inelastic scattering, however, there is no evidence for either a negative strange quark polarization or for a flavor asymmetry in the light sea polarization.Predstavljamo nedavne ishode mjerenja HERMES za okusno razdvajanje raspodjela heliciteta kvarkovskog mora u nukleonu zasnovane na polu-inkluzivnom dubokoneelastičnom raspršenju. Načinili smo prvo razdvajanje kvarkovskih raspodjela heliciteta na pet sastavnica primjenom označavanja okusa. Raspodjele heliciteta u i d kvarkova potvrđuju ishode mjerenja inkluzivnih duboko-neelastičnih raspršenja, međutim, ne nalazimo znakove niti za negativnu polarizaciju stranih kvarkova niti za asimetriju okusa u polarizaciji lakog mora

Lorenzon (on behalf of the HERMES collaboration), Wolfgang

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ISSN1330–0016CODEN FIZBE7FLAVOR SEPARATED QUARK POLARIZATIONS AT HERMESWOLFGANG LORENZONon behalf of the HERMES collaborationRandall Laboratory of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USAReceived 4 September 2003; Accepted 26 April 2004Online 22 October 2004Recent HERMES results are presented on the flavor decomposition of the sea quarkhelicity distributions in the nucleon from semi-inclusive deep inelastic scattering.For the first time, a five component decomposition of quark helicity distributionsusing flavor tagging has been performed. The helicity distributions of the up anddown quarks confirm the results obtained from inclusive deep inelastic scattering,however, there is no evidence for either a negative strange quark polarization or fora flavor asymmetry in the light sea polarization.PACS numbers: 13.60.-r, 13.88.+e, 14.20.Dh, 14.65.-q UDC 539.12Keywords: polarized lepton–nucleon interactions, polarized quark and anti-quarkdistributions1. IntroductionUnderstanding how the spin of the nucleon is constructed from its elementaryconstituents has proven to be a significant challenge both theoretically and exper-imentally. In a simple constituent quark model, the spin of the nucleon can bedecomposed as12=12∆Σ + ∆G + Lq + LG , (1)where ∆Σ and ∆G are the intrinsic spins carried by the quarks and gluons, and Lqand LG the orbital angular momenta of the quarks and gluons.To obtain some feeling for the expected magnitudes of these various contribu-tions to the nucleon polarization, one may turn to phenomenological models. Inthe constituent quark model, the nucleon is composed entirely of valence quarks.By imposing appropriate symmetry conditions on the nucleon wave function, oneobtains the values ∆u = +4/3 and ∆d = −1/3 (which adds up the net quark polar-ization ∆Σ of 1). If one considers instead of constituent quarks the current quarksFIZIKA B 13 (2004) 1, 315–320 315lorenzon: flavor separated quark polarizations at hermesseen by dynamical QCD processes, relativistic effects have to be taken into accountbecause of the light quark masses. Calculations performed in e.g. the relativisticbag model then suggest that ∆Σ ≃ 0.60 − 0.75 [1]. The remainder of the nucleonspin is accounted for by the angular momentum of the moving quarks. To includesea quarks in the picture one may turn, for example, to meson cloud models wherethe nucleon is described as a bare, valence object which has a probability to emitpseudo-scalar mesons. It is through the emission of such mesons that the quarksea is generated. One calculation performed in this way [2] indicates that the seaquarks should carry a negative polarization, but that the anti-quarks in the sea areunpolarized: all anti-quarks in this picture are members of a spin-0 meson, andtherefore carry no polarization. An alternative picture of the nucleon comes fromthe chiral-quark soliton model, where the nucleon appears as a chiral soliton in apion mean field. A recent calculation of this type [3], performed in the large Nclimit, suggests that the ū and d̄ quarks do carry a significant polarization, but ofopposite sign: ∆ū ≃ −∆d̄, and that ∆ū − ∆d̄ > d̄ − ū. Yet another picture of thenucleon comes from the statistical model, where the nucleon appears as a gas ofmassless partons. A calculation carried out in this model [4] suggests that the ū andd̄ quarks also carry a significant non-zero polarization, but that ∆ū −∆d̄ ∼ d̄ − ū.This brief sample of phenomenological models makes it clear that spin structureexperiments are probing very basic properties of the nucleon: The measurement ofthese quantities has the power to distinguish between different pictures of how thenucleon is constructed.2. Inclusive measurementsThe longitudinal spin structure function g1(x,Q2) has been measured by a num-ber of experiments using the scattering of polarized leptons from polarized tar-gets [5]. In leading order QCD and the quark parton model, this structure functionis given by the charge weighted sum over the polarized quark spin distributions ∆qfor flavor q: g1(x) =12∑qe2q∆q(x). The notation ∆q(x) denotes the polarized coun-terpart of the familiar parton distribution functions (PDF): ∆q(x) ≡ q+(x)−q−(x).Here, x is the Bjorken scaling variable, and q+(q−) indicates quarks whose spinsare parallel (anti-parallel) to the spin of the nucleon. In the framework of next-to-leading order (NLO) QCD, the relationship between g1(x,Q2) and the polarizedPDF’s is more complex, and includes a contribution from the gluon spin distribu-tion ∆G.Numerous spin-dependent NLO fits exist in the literature. One example is theglobal fit performed by the SMC collaboration [6]. The results indicate (using theAB factorization scheme) that the quark spins account for only a relatively smallfraction of the total nucleon spin (of order 38%). Further, the strange sea wouldseem to have a slight negative polarization, of order −10%. The gluon polarization∆G, by comparison, is only poorly constrained by the inclusive data, but there issome indication that it is positive. Since inclusive deep inelastic scattering (DIS) issensitive only to the magnitude of the quark charge, DIS fails to distinguish quarks316 FIZIKA B 13 (2004) 1, 315–320lorenzon: flavor separated quark polarizations at hermesfrom anti-quarks, i.e. ∆q = ∆(q + q̄). Therefore, no direct information about thesea quark polarizations is available from these inclusive measurements.3. Quark polarizations from semi-inclusive measurementsTo proceed further in our knowledge of the polarized parton distributions, ex-perimenters have turned to semi-inclusive asymmetry measurements. In these mea-surements a hadron is detected in coincidence with the scattered lepton. Throughthe agency of the fragmentation functions Dqh, a probabilistic relationship existsbetween the flavor of the struck quark q and the flavor content of the hadrons hgenerated in the final state. Although fragmentation functions have been extractedfrom mostly high energy e+e− collider data [7], their applicability at lower energiesis supported by their agreement with fragmentation functions [8] for charged pionsextracted from HERMES measurements of hadron multiplicities.By measuring the double spin asymmetries Ah1 in the cross sections for leptopro-duction of various types of hadrons, one can extract a complete flavor decompositionof the quark and anti-quark helicity distributions. In LO QCD, the photon-nucleondouble spin asymmetry Ah1 is given by1Ah1(x, z) =∑q e2q∆q(x)Dhq(z)∑q e2qq(x)Dhq(z)(1 + R(x))(1 + γ2). (2)The sum at the moderate beam energies of the HERMES experiment is over quarkand anti-quark flavors q = (u, ū,d, d̄, s, s̄), and z ≡ Eh/ν with ν and Eh being theenergies of the virtual photon and the detected hadron. The factor involving γ2 =Q2/ν2 and R, the ratio of longitudinal to transverse virtual photon cross section,accounts for the longitudinal component included in most parameterizations ofthe unpolarized PDFs q(x). Semi-inclusive asymmetries have been measured byHERMES in 1998–2000, where pions and kaons were identified from a deuteriumtarget, as shown in Fig. 1.Integrating Eq. (2) over z, the photon-nucleon asymmetry Ah1 can be rewrittenasAh1(x) =∑qP hq (x)∆q(x)q(x)(1 + R(x))(1 + γ2), (3)where P hq (x) are the spin-independent puritiesP h(x) ≡e2qq(x)max∫minDhq(z) dz∑q′ e2q′q′(x)max∫minDhq′(z) dz. (4)1For simplicity, we suppress here the weak logarithmic dependence of all functions on −Q2,the squared four-momentum of the exchanged virtual photon.FIZIKA B 13 (2004) 1, 315–320 317lorenzon: flavor separated quark polarizations at hermesFig. 1 . Virtual photoabsorption asymmetries Ah1 for semi-inclusive DIS on thedeuterium target as a function of Bjorken x, for identified charged pions and kaons.The error bars are statistical, and the bands represent the systematic uncertainties.Each purity function describes the conditional probability that the virtual photonhit a quark of flavor q when a hadron of type h was detected. In analogy withEq. (4), the purities were extracted from a Monte Carlo simulation, using a modelof the DIS process, the fragmentation process, and the detector.Fig. 2. Quark helicitydistributions at 〈Q2〉 =2.5 GeV2, as a functionof Bjorken x, comparedto two LO QCD fits topreviously published in-clusive data [9,10]. Theerror bars are statisticaland the error bands repre-sent the systematic uncer-tainties, which include thecontributions from the un-certainties of the unpolar-ized quark densities, thefragmentation model, andthe asymmetries.318 FIZIKA B 13 (2004) 1, 315–320lorenzon: flavor separated quark polarizations at hermesWith asymmetry data available for a variety of hadrons from both proton and“neutron” targets, the above system of equations (Eq. 3) becomes sufficiently con-strained to be solved to extract the ∆q(x) for several flavors of q. In combinationwith identified pions from hydrogen in 1996–1997 and with inclusive data, theyresult in the first five-flavor extraction of quark polarizations from semi-inclusivedata, as shown in Fig. 2. Sea quarks of all three flavors are treated independently,with the only assumption being ∆s(x)/s(x) ≡ ∆s̄(x)/s̄(x).The extracted distributions ∆u(x) and ∆d(x) are consistent with previous(semi-)inclusive results, but have much improved precision. The sea distributions,extracted separately for the first time, are consistent with zero and with each other.There is no indication of a negative polarization of the strange sea that appears inthe analysis of only inclusive data, in which SU(3) flavor symmetry in the analysisof hyperon beta decay is assumed. In addition, there is, as shown in Fig. 3, noevidence for as large a positive flavor asymmetry ∆ū(x)−∆d̄(x) in the light quarksea as was predicted by the theoretical calculations [3,4] discussed in Section 1. Infact, it appears that the simplest model, the meson cloud model, describes the databest.Fig. 3. The light quark sea flavor asymmetry ∆ū−∆d̄ in the helicity distributions,as a function of Bjorken x, at 〈Q2〉 = 2.5 GeV2, compared to three theoreticalpredictions [4,9,11]. The error bars are statistical and the error bands represent thesystematic uncertainties.In conclusion, a purity based extraction from new semi-inclusive DIS data hasproduced for the first time a five-flavor separation of helicity distributions. Thereis no evidence for either a negative strange quark polarization or for a flavor asym-metry in the light sea polarization.FIZIKA B 13 (2004) 1, 315–320 319lorenzon: flavor separated quark polarizations at hermesAcknowledgementsI wish to thank my colleagues in the HERMES collaboration. I acknowledge EdKinney for critical reading of the manuscript. The author’s research is supported inpart by the U.S. National Science Foundation, Intermediate Energy Nuclear ScienceDivision under grant No. PHY-0072297 and PHY-0244842.References[1] R. L. Jaffe and A. Manohar, Nucl. Phys. B 337 (1990) 509.[2] T. P. Cheng and L.-F. Li, Phys. Lett. B 366 (1996) 356; with correction in Phys. Lett.B 381 (1996) 487.[3] K. Goeke, P. V. Pobylitsa, M. V. Polyakov and D. Urbano, Nucl. Phys. A 680 (2000)308.[4] C. Bourrely, J. Soffer and F. Buccella, Eur. Phys. J. C 23 (2002) 487.[5] E142, P. Anthony et al., Phys. Rev. D 54 (1996) 6620; E154, K. Abe et al., Phys.Rev. Lett. 79 (1997) 26; HERMES, K. Ackerstaff et al., Phys. Lett. B 404 (1997) 383;E143, K. Abe et al., Phys. Rev. D. 58 (1998) 112003; HERMES, A. Airapetian et al.,Phys. Lett. B 442 (1998) 484; SMC, B. Adeva et al., Phys. Rev. D 58, (1998) 112001;E155, P. Anthony et al., Phys. Lett. B 493 (2000) 19.[6] SMC, B. Adeva et al., Phys. Rev. D 58 (1998) 112002.[7] B. Kniehl, G. Kramer and B. Pötter, Nucl. Phys. B 582 (2000) 514; S. Kretzer, Phys.Rev. D 62 (2000) 054001.[8] S. Kretzer, E. Leader and E. Christova, Eur. Phys. J. C 22 (2001) 269.[9] M. Glück, E. Reya, M. Stratmann and W. Vogelsang, Phys. Rev D 63 (2001) 094005.[10] J. Blümlein and H. Böttcher, Nucl. Phys. B 636 (2002) 225.[11] B. Dressler, K. Goeke, M. Polyakov and C. Weiss, Eur. Phys. J. C 14 (2000) 147.OKUSNO RAZDVOJENE KVARKOVSKE POLARIZACIJE U HERMESUPredstavljamo nedavne ishode mjerenja HERMES za okusno razdvajanje raspodjelaheliciteta kvarkovskog mora u nukleonu zasnovane na polu-inkluzivnom duboko-neelastičnom raspršenju. Načinili smo prvo razdvajanje kvarkovskih raspodjela he-liciteta na pet sastavnica primjenom označavanja okusa. Raspodjele heliciteta u id kvarkova potvrd–uju ishode mjerenja inkluzivnih duboko-neelastičnih raspršenja,med–utim, ne nalazimo znakove niti za negativnu polarizaciju stranih kvarkova nitiza asimetriju okusa u polarizaciji lakog mora.320 FIZIKA B 13 (2004) 1, 315–320

Okusno razdvojene kvarkovske polarizacije u HERMESU

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