An idea of possible anomalous contribution of non-perturbative origin to the
nucleon spin was examined by analysing data on spin asymmetries in polarized
deep inelastic scattering of leptons on nucleons. The region of high Bjorken x
was explored. It was shown that experimental data available at present do not
evidence for this effect.Comment: Submitted to Mod.Phys.Lett. 

Adeva B.

Altarelli G.

Efremov A. V.

WOJCIECH WIŚLICKI

English

arXiv

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SEARCH FOR ANOMALY AT HIGH x IN POLARIZED DEEP INELASTIC SCATTERING DATA

An idea of possible anomalous contribution of non-perturbative origin to the nucleon spin was examined by analysing data on spin asymmetries in polarized deep inelastic scattering of leptons on nucleons. The region of high Bjorken x was explored. It was shown that experimental data available at present do not evidence for this effect

Wislicki, W

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SEARCH FOR ANOMALY AT HIGH X IN POLARIZEDDEEP INELASTIC SCATTERING DATAWOJCIECH WISLICKI*So ltan Institute for Nuclear StudiesHo_za 69, PL-00-681 WarsawAn idea of possible anomalous contribution of non-perturbative origin to the nucleonspin was examined by analysing data on spin asymmetries in polarized deep inelasticscattering of leptons on nucleons. The region of high Bjorken x was explored. It wasshown that experimental data available at present do not exhibit any evidence for thiseect.As one of possible explanations of the nucleon spin problem it was suggested 1;2that the overall quark spin in the nucleon may be diminished by the axial anomalyterm. If the anomaly is related to the gluon polarization then it is observable atsmall x only. However, as discussed in refs.3;4, there is no a priori argument thatthe anomaly must be the small-x eect only. For the region of high x the model ofthe nucleon as consisting of three massive constituent quarks is well justied. Thevalence quarks move in a non-perturbative colour background eld which could beidentied with the anomaly and possess a non-trivial spin structure. The problem ofeective spin dilution by a colour eld in the constituent-like picture of the nucleonis sometimes addressed in the context of non-perturbative models of hadrons andis worth of being investigated experimentally.In order to estimate the eect of a possible colour screening of the quarks spin inthe nucleon we analyse existing data on the inclusive and semi-inclusive asymmetriesmeasured in polarized deep inelastic scattering experiments. A direct way to do thiswould be a comparison of the quark spin distributions obtained from the C-evenspin observables, e.g. g1 or single-charge semi-inclusive asymmetries, where theanomaly contributes, with the anomaly free C-odd quantities, as g3 or the semi-inclusive asymmetries for dierence of charge 3. Any inconsistency between themwould eventually evidence for a large-x anomaly. However, the only data available*email: wislicki@fuw.edu.pl12 Search for Anomaly at High x : : :at present are C-even 5−14. Therefore the method we use here is to express C-even asymmetries by quark spin distributions, using the parametrization of gauge-invariant quark spins, modied by the anomaly term as proposed in refs. 3;4, andt them to all existing data.It was shown that in order to make the quark spin distributions gauge indepen-dent, and thus ensure conservation of chirality, one has to modify the quark helicitydistributions q(x;Q2)" and q(x;Q2)#~q(x;Q2)" = q(x;Q2)" +14(x;Q2)~q(x;Q2)# = q(x;Q2)# −14(x;Q2) (1)for both quarks and antiquarks and for each quark flavour. In the following allquark distributions will refer to the proton.In experiments on polarized deep inelastic scattering of leptons on nucleons onedetermines the cross section asymmetries 5A(x;Q2) =a(x;Q2)− p(x;Q2)a(x;Q2) + p(x;Q2): (2)The indices a and p refer to the sum of spins of the virtual photon and the nucleonfor two opposite polarizations of the target nucleon. For the proton and neutrontarget a = 1=2 and p = 3=2. In case of deuteron target these spins are equalto 0 and 2, respectively.a In the inclusive measurement the cross sections in (2)are the inclusive polarized deep inelastic cross sections and for the semi-inclusiveexperiments they refer to polarized cross sections for leptoproduction of hadrons inthe current fragmentation region.In the region of high x the non-strange sea, the strange sea and the ratio ofthe transverse to the longitudinal photoabsorption cross sections are negligible.Assuming anomaly (1) the inclusive asymmetries for the proton, the neutron andthe deuteron targets are given in the quark-parton model (QPM) asAp1(x;Q2) =29u(x;Q2) + 118d(x;Q2) + 13(x;Q2)29u(x;Q2) + 118d(x;Q2); (3)An1 (x;Q2) =118u(x;Q2) + 29d(x;Q2) + 13(x;Q2)118u(x;Q2) + 29d(x;Q2)(4)andAd1(x;Q2) =518 [u(x;Q2) + d(x;Q2)] + 23(x;Q2)518 [u(x;Q2) + d(x;Q2)]: (5)The QPM analysis of semi-inclusive asymmetries requires knowledge about frag-mentation functions of quarks into hadrons Dhq (z;Q2). Since not all of them areaThe deuteron cross section is considered to be the sum of the proton and the neutron crosssections, corrected for the D-state of the deuteron as in ref. 8Search for Anomaly at High x : : : 3measured one has to reduce the number of independent fragmentation functions byusing charge conjugation and isospin symmetry and some additional assumptionsfor favoured and unfavoured fragmentation functions 6;15D1  D+u = D+d = D−u = D−d = DK−s = DK+sD2  D−u = D−d = D+u = D+d = D+s = D+s = D−s = D−sD3  DK+u = DK−uD4  DK−u = DK−d = DK−d = DK−s = DK+u = DK+d = DK+d = DK+sD5  Dpu = Dpd = Dpu = DpdD6  Dpu = Dpd = Dps = Dps = Dpu = Dpd= Dps = Dps : (6)We assume that fragmentation functions do not depend on quark helicity and thatthe fragmentation of a parton factorize from its distribution. The factorization iswell conrmed for quarks at high Q2 and in the current fragmentation region whichis eectively selected by cuting on the Feynman variable, xF > 0, or on the fractionof the virtual photon energy taken by the nal state hadron, z = Eh=  0.Factorization was never studied for the anomaly and it remains an assumptionadditional to the QPM. Semi-inclusive data of EMC 5 and SMC 6;9 were takenwithout hadron identication and only the electric charge of a hadron was known.Therefore the semi-inclusive asymmetries have to be derived for the mixture ofpions, kaons and protons in the nal state. Spin asymmetries for the production ofpositive (negative) hadrons on the proton, neutron and deuteron at high x are thefollowing:A+(−)1 p (x;Q2) =49D+(−)u u(x;Q2) +19D+(−)d d(x;Q2) + 23D(x;Q2)49D+(−)u u(x;Q2) +19D+(−)d d(x;Q2); (7)A+(−)1n (x;Q2) =19D+(−)d u(x;Q2) + 49D+(−)u d(x;Q2) +23D(x;Q2)19D+(−)d u(x;Q2) + 49D+(−)u d(x;Q2)(8)andA+(−)1 d (x;Q2) =19 [4D+(−)u +D+(−)d ][u(x;Q2) + d(x;Q2)] + 43D(x;Q2)19 [4D+(−)u +D+(−)d ][u(x;Q2) + d(x;Q2)];(9)whereD+u  D1 +D3 +D5D+d  D2 +D4 +D5D−u  D2 +D4 +D6D−d  D1 +D4 +D6: (10)4 Search for Anomaly at High x : : :In eqs. (7-10) Di R 1z0dz Di(z;Q2); i = 1; : : : ; 6 (z0 = 0:2 in ref.9 and 0:1 in ref.5), and D is the fragmentation function of the anomaly.b It is expected to be thesame for the positive and negative hadrons and is dened ascD  D+ +DK+ +Dp= D− +DK− +Dp: (11)The fragmentation function of the anomaly D can be determined, as suggestedin ref. 3, by comparing the semi-inclusive asymmetry for all hadrons, includingpositive, negative and neutrald, on the deuteron, Asum1 d , to the inclusive asymmetryAd1(x;Q2) =gd1 (x;Q2)Fd1 (x;Q2), which are expected to be equal. To account for neutralparticles, for which fragmentation functions are poorly known, we use again theisospin symmetry and charge conjugation to relate them to measured functionsD1;:::;6. For neutral hadrons not heavier than the nucleon those relations are17:D0u = D0u = D0d = D0d =12(D1 +D2)D0s = D0s = D2Du = Du = Dd = Dd=16(D1 + 2D2)Ds = Ds =13(D2 +D3)D!u = D!u = D!d = D!d =32(D1 +D2)D!s = D!s = 3D2DKSu = DKSu = DKLu = DKLu = D4DKSd = DKSd= DKLd = DKLd=12(D3 +D4)DKSs = DKSs = DKLs = DKLs =12(D1 +D4)Dnu = Dnd = Dnu = Dnd = D5Dnu = Dnd = Dns = Dns = Dnu = Dnd = Dns = Dns = D6: (12)The asymmetry Asum1 d is equal toAsum1 d (x;Q2) =19A[u(x;Q2) + d(x;Q2)] + 43B(x;Q2)19A[u(x;Q2) + d(x;Q2)]; (13)where the coecients A and B depend on the fragmentation functions (12) and arebThe fragmentation function of the anomaly can be dierent than the fragmentation function ofa quark into the same hadron. The assumption of their equality, in our opinion unjustied, wasimplicitly done in ref. 16cIn ref. 3 the anomaly fragmentation function refers to any charged hadron and not to the speciccharge as in our casedTaking only positive and negative hadrons, as in ref. 3, is not sucient.Search for Anomaly at High x : : : 5equal toA =803D1 +853D2 + 9D3 +372D4 + 18D5 + 12D6B ’ 1:68D: (14)The asymmetry Asum1 d (13) can be rewritten in the formAsum1 d (x;Q2) =gd1(x;Q2)F d1 (x;Q2)+23(x;Q2)F d1 (x;Q2)5BA− 1; (15)henceD ’ 0:12A: (16)In our analysis we used the inclusive asymmetries on proton from EMC 5, SMC 7and E143 11, on deuteron from SMC 8 and E143 12 and on neutron from E142 10,HERMES 13 and E154 14 experiments. We used also single-charge semi-inclusiveasymmetries on proton from EMC 5 and on proton and deuteron from SMC 9.We considered only range of x > 0:15. If more than one data set is availablefor given asymmetry the data were combined in SMC bins. For each bin of xeqs. (3),(4),(5),(7) and (9) constitute a system of 7 linear equations for 3 spin dis-tributions u, d and . Asymmetries were assumed to be independent of Q2,consistent with ithe SMC and E143 observations for the inclusive case 7;8;12. Anypossible eects of scale mixing by anomaly were neglected. For quark distributionfunctions the GRV parametrization 18 at Q2 = 10 GeV2 was used and for fragmen-tation functions we used EMC data 15. Three unknown spin distributions, u(x),d(x) and (x), were evaluated from the system of seven equations by the leastsquares method, using the full correlation matrix between asymmetries 9e The dis-tributions of u(x), d(x) and (x) are given in tab. 1f. The values of integralsTable 1. The values of u, d and  obtained at < x > for x > 0:15. The rst error is statisticaland the second is systematicxL − xU < x > u(x) d(x) (x)0:15− 0:2 0:17 1:159 0:092 0:037 −0:636  0:084  0:030 0:051 0:058 0:0110:2− 0:3 0:24 0:919 0:067 0:027 −0:535  0:065  0:024 0:065 0:045 0:0090:3− 0:4 0:34 0:693 0:076 0:022 −0:185  0:073  0:020 −0:009 0:050 0:0040:4− 0:7 0:48 0:376 0:045 0:011 −0:156  0:047  0:007 0:021 0:031 0:004of u(x), d(x) and (x) are listed in tab. 2. Contributions from the unmeasuredregion x > 0:7 were estimated from the extrapolation of the function AxB(1− x)Cdetermined from the t to measured points at 0:15 < x < 0:7. We observe thateFor EMC data 5 the covariance matrix is not known. It was assumed that correlations arethe same as for SMC proton data and the influence of this assumption on values of polarizeddistributions was found to be negligible.fIn evaluation of systematic errors the correlations between systematic errors of asymmetries wereunknown. The correlation coecients were varied between 0% and 100% and it was found that themaximum change of the systematic error of the anomaly was 12%. This contribution was addedto the systematic error.6 Search for Anomaly at High x : : :the anomaly distribution (x) does not exhibit any signicant deviation from zero.The integralR 10:15dx(x) is consistent with null hypothesis within one standarddeviation.In addition to ongoing experiments at DESY (HERMES) and at SLAC (E155),which will provide new data on both inclusive and hadron asymmetries, substantialreduction of the statistical error in the region od high x is expected in the COMPASSexperiment, presently under construction at CERN 19. Particles scattered andproduced on the proton and deuteron polarized targets at angles up to 180 mradwill be detected by a dedicated spectrometer equiped with a magnet of wide apertureand thus enriching event statistics at high x. Adding to the present analysis theinclusive and semi-inclusive asymmetries measured with the precission foreseen athigh x in COMPASS one gets the statistical error of the anomaly term  equal to0:004.Table 2. Integrals of u, d and x 0:15− 0:7 0:7− 1 0.15-1Rdxu(x) 0:396  0:018  0:005 0:048 0:002 0:001 0:444 0:019 0:005Rdxd(x) −0:184 0:018 0:004 −0:024  0:002 0:001 −0:208  0:018  0:004Rdx (x) 0:013  0:012  0:002 0:002  0:002  (3  10−4) 0:015 0:013 0:0021. G.Altarelli and G.G.Ross, Phys. Lett. B214(1988)3812. A.V.Efremov and O.V.Teraev, JINR E2-88-287(1988)3. S.D.Bass, Phys. Lett. B367(1996)3354. S.D.Bass and A.W.Thomas, Phys. Lett. B312(1993)345,S.D.Bass, Z. Phys. C60(1993)3435. EMC, J.Ashman et al., Nucl. Phys. B328(1989)16. SMC, B.Adeva et al., Phys. Lett. B369(1996)937. SMC, B.Adeva et al., Phy. Lett. B402(1997)4148. SMC, D.Adams et al., Phys. Lett. B396(1997)3389. SMC, B.Adeva et al., hep-ex/9711008, CERN-PPE-97-147, Phys.Lett. B in print10. E142, P.L.Anthony et al., Phys. Rev. D54(1996)662011. E143, K.Abe et al., Phys. Rev. Lett. 74(1995)34612. E143, K.Abe et al., Phys. Rev. Lett. 75(1995)2513. HERMES, K.Ackersta et al., Phys. Lett. B404(1997)38314. E154, K.Abe et al., Phys. Rev. Lett. 79(1997)2615. EMC, M.Arneodo et al., Nucl. Phys. B321(1989)54116. S.Gullenstern et al., Phys. Lett. B312(1993)16617. B.Andersson, G.Gustafson and C.Peterson, Nucl. Phys. B135(1978)27318. M.Gluck, E.Reya and A.Vogt, Phys. Lett., B306(1993)39119. The COMPASS Collaboration, G.Baum et al., A Proposal for a Common Muon andProton Apparatus for Structure and Spectroscopy, CERN/SPSLC 96-14, SPSLC/P297

Search for Anomaly at High x in Polarized Deep Inelastic Scattering Data

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