SMC performed an investigation of the spin structure of the nucleon by
measuring deep inelastic scattering of polarised muons off polarised protons
and deuterons. A summary of the results for spin structure functions and sum
rules is given.Comment: 8 pages, LaTeX, Talk given at the Workshop on "Symmetry and Spin -
  PRAHA98", Prag, September 1998. Proceedings to be published by Czech. Journ.
  Phy

B. Adeva

D. Adams

Eva-Maria Kabuss

J. Ashman

J. D. Bjorken

J. Ellis

K. Abe

R. Ball

English

arXiv

Crossref

Results on the nucleon spin structure

SMC performed an investigation of the spin structure of the nucleon by measuring deep inelastic scattering of polarised muons off polarised protons and deuterons. A summary of the results for spin structure functions and sum rules is given.SMC performed an investigation of the spin structure of the nucleon by measuring deep inelastic scattering of polarised muons off polarised protons and deuterons. A summary of the results for spin structure functions and sum rules is given

Kabuss, Eva-Maria

CERN Document Server

arXiv:hep-ex/9901003v1  7 Jan 1999RESULTS ON THE NUCLEON SPIN STRUCTUREEva-Maria Kabuß ∗Inst. fu¨r Kernphysik, Mainz University, D-55099 Mainz, Germanyfor the Spin Muon CollaborationSMC performed an investigation of the spin structure of the nucleon bymeasuring deep inelastic scattering of polarised muons off polarised protonsand deuterons. Asymmetries and spin structure functions were obtained forx > 0.0008 and Q2 > 0.2 GeV2. Using a next-to-leading order QCD analysis ofall experimental results polarised parton distributions and their first momentswere determined. All data show a clear violation of the Ellis-Jaffe sum rule.The Bjorken sum rule is found to be valid and is tested to the 10% level.1. IntroductionTo investigate the spin structure of the nucleon SMC studies deep inelastic scat-tering of polarised muons off polarised protons and deuterons. From the measuredlongitudinal asymmetries the spin structure functions, g1, can be extracted byA‖ =dσ↑↓ − dσ↑↑dσ↑↓ + dσ↑↑≈ Dg1F1. (1)The depolarisation factor D gives the polarisation transfer from the lepton to thenucleon and increases with the energy transfer. F1 is the unpolarised structurefunction.In the quark parton modell (QPM) g1 is related to the quark helicity distribu-tions functions, ∆q = q↑ − q↓, byg1(x,Q2) =12∑qe2q(∆q(x,Q2) + ∆q¯(x,Q2)) (2)where Q2 is the negative square of the four momentum transfer, Bjorken x themomentum fraction carried by the struck quark and eq the quark charge. Thenotation q↑ (q↓) refers to parallel (antiparallel) orientation of the quark and thenucleon spins. The first moments aq(Q2) =1∫0(∆q(x,Q2) + ∆q¯(x,Q2))dx andΓ1(Q2) =1∫0g1(x,Q2)dx can be used to study the contribution of quark helicitiesto the nucleon spin and to test the Ellis-Jaffe [1] and Bjorken [2] sum rules.∗) supported by the BMBFCzechoslovak Journal of Physics, Vol. 0 (2013), Suppl. S0 1Eva-Maria KabußThe first measurement of the Ellis-Jaffe sum rule for the first moment of gp1by the EMC [3] showed a strong violation of the sum rule. Interpreted in theQPM this pointed to a very small contribution of quark helicities to the protonspin and a negative polarisation of the strange sea quarks. This led to a series ofnew experiments at CERN, SLAC and also at DESY studying the spin structureof the proton and the neutron in more detail. These new data also allow to testthe fundamental Bjorken sum rule Γp1 − Γn1 =∣∣∣ gAgV∣∣∣ /6. In addition, the structurefunction data are precise enough to perform next-to-leading order perturbativeQCD analyses and determine the polarised parton distributions.2. The experimentThe SMC experiment (NA37) was located at the M2 muon beam line of theCERN SPS and took data using polarised proton and deuteron targets from 1992to 1996.The 190 and 100 GeV muon beam with about 4·107µ per 2.2 s spill was naturallypolarised. The polarisation was determined by two independent measurements us-ing a dedicated second spectrometer downstream of the main experiment. The firstmethod measured the energy spectrum of the decay electrons from muon decay, thesecond one used the cross section asymmetry in polarised muon electron scattering[4]. The results were pµ = −0.795± 0.019 at 187.4 GeV and pµ = −0.81± 0.03 at99.4 GeV.The heart of the experiment was the polarised solid state target. It was polarisedusing dynamic nuclear polarisation in a 2.5 T longitudinal field of a superconductingmagnet. The target temperature was maintained at ≈ 50− 300 mK during normaloperation by a dilution refrigerator. From 1992 to 1995 SMC used butanol ordeuterated butanol as target material whereas for the 1996 data taking ammoniawas chosen improving the dilution factor f by 30% from about 0.13 for butanolto about 0.17 for ammonia. The target was divided into two cells of 65 cm lengthpolarised in opposite directions. To reduce systematic uncertainties due to changesin the detector response the target polarisation was reversed every 5 hours byrotating the magnetic field with the help of an additional 0.5 T dipole magnet.The average longitudinal polarisation was pT = ±0.90 for protons and ±50% fordeuterons. It was measured to an accuracy of 2-3% using 9 NMR coils embeddedin the target material. In addition to the continuous measurement of the protonpolarisation the polarisation of 14N was determined in dedicated measurements [5]and found to depend on the proton polarisation as predicted by the equilibriumspin temperature relation. Typical nitrogen polarisations were ±0.14 for protonpolarisations of ±0.89.The scattered muons and the produced forward going hadrons were detectedin an open forward spectrometer using about 150 wire chamber planes placed up-stream and downstream of a large gap dipol magnet. Due to the large number ofwire planes the measured asymmetries were hardly sensitive to occasional problems2 Czech. J. Phys. 0/S0 (2013)Nucleon spin structurewith single planes. There was no particle identification for hadrons, but electronhadron separation was obtained with the help of a lead/iron scintillator calorimeter.The measured counting rates for longitudinal beam and target polarisationswere used to determine the raw asymmetryAraw‖ (x,Q2) =N↑↓ −N↑↑N↑↓ +N↑↑, (3)which is related to the lepton nucleon (A‖) and photon nucleon asymmetries (A1,A2) byAraw‖ = pµpTfA‖ = pµpTfD(A1 + ηA2). (4)In a separate measurement using transversly polarised targets the transverse asym-metryAraw⊥ =N↑→ −N↑←N↑→ +N↑←= pµpTfd(A2 + η′A1) (5)was measured. D, d, η and η′ are known kinematic factors. A2 was found to besmall in the kinematic range of the SMC data [6,7] and thus the second term ineq. 4 can be neglected.3. Results for A1 and g1Inclusive asymmetries are determined using two methods. In the first one,called standard method, only scattered muons are used, in the second one, anyhadron in addition to the scattered muon signals a true deep inelastic scatteringand provides a discrimination between these events and background events likeradiative events or elastic electron muon scattering [8]. Thus, the effective dilutionfactor f ′ = f ·σ1γ/σtot is much larger for the hadron method than for the standardone (see fig. 1a ).In the SMC spectrometer mainly forward produced charged hadrons with mo-menta ph > 5 GeV were detected. Events with a high mass W of the final statecontain in general several hadrons with high momenta. HighW events are typicallyfound at small x, so that a good acceptance for deep inelastic events is obtained forx < 0.1, whereas in the high x region many hadrons are not detected due to the lowmomenta at lowW . In addition cuts are applied to reject electrons from conversionof Bremstrahlung photons. Monte Carlo studies show that more than 80% of thedeep inelastic events are found by requiring at least one additional hadron to thescattered muon. The results for Ap1 from both methods are compared in fig. 1bfor x > 0.0008 and Q2 > 0.2 GeV2. Good agreement is obtained between the tworesults with the statistical erros bars smaller for x < 0.1 for the hadron method.The optimal SMC data set for Ap1 and Ad1 is shown in fig. 2 in comparison to mea-surements from the EMC [3] at a similar Q2 and the lower Q2 data from E143 [9].Systematic uncertainties are shown as bands at the bottom. At low x, the maincontributions are due to the uncertainty of radiative corrections, the neglect of A2Czech. J. Phys. 0/S0 (2013) 3Eva-Maria Kabuß0.050.10.150.210-310-210-11f’xhadron-taggedinclusive-0.100.10.20.30.40.50.60.710-310-210-11A1protonx(a)hadron-taggedinclusiveFig. 1. Comparison a) of the effective dilution factor f ′, b) of the proton asymmetriesAp1 from the standard analysis method and the hadron method.and acceptance variations. At high x they stem from uncertainties of R and thebeam and target polarisation.-0.200.20.40.60.8110-310-210-11A1protonx(a)SMC  Q2 > 0.2 GeV2SMC  Q2 > 1.0 GeV2E143EMC-0.100.10.20.30.40.510-310-210-11A1deuteronx(b)SMC Q2 > 0.2 GeV2SMC Q2 > 1.0 GeV2E143Fig. 2. The optimal data set of SMC for A1 together with results from other experiments.Statistical errors are shown as error bars, while the shaded bands below indicate thesystematic uncertainty for the SMC measurement.In addition to the x dependence also the Q2 dependence of A1 was investigated.No Q2 dependence is observed in the kinematic range of the SMC data.An extension of the measured asymmetries down to x = 6 · 10−5 with Q2 >0.01 GeV2 is under study. In this kinematic region the inclusive events are domi-4 Czech. J. Phys. 0/S0 (2013)Nucleon spin structurenated by muon scattering off atomic electrons. In 1995/6 data were collected usinga dedicated ”low x” trigger in which both a minimal energy deposit in the hadronicpart of the calorimeter and the detection of a muon was demanded [10]. Fig. 3ashows the kinematic acceptance of this trigger compared to other experiments,while the preliminary results for Ap1 are shown in fig. 3b. The two SMC data setsare compatible in the overlap region. At low x no significant spin effects are visible.xbj10-410-310-210-11Q2 (GeV2 )10-210-111010 2EMC (p)SMC (p,d)SMC (p,d) low x data, DIS98E143 (p,d)Hermes (n)E142 (n)E154 (n)-0.2-0.100.10.20.30.410-410-310-210-11A1protonxpreliminarySMC, low Q2 dataSMC, optimal set of the dataFig. 3. a) Kinematic acceptance of the ”low x” trigger compared to other experiments,b) preliminary results on Ap1 compared to the SMC optimal data set. The error bars arestatistical errors, the bands indicate the systematic uncertainties.For Q > 0.2 GeV2 the spin structure functions, g1, are calculated from themeasured asymmetries with eq. 1 using F1 = F2/2x(1 + R), where F2(x,Q2) andR(x,Q2) are taken from unpolarised measurements (see fig. 4).4. QCD analysisTo determine the first moment, Γ1(Q20), the results for g1(x,Q2) at a fixedQ2 = Q20 are needed. Though the precision of the available data and theQ2 range donot allow a direct measurement of a possible Q2 dependence of A1 = g1/F1 differentQ2 behaviours of g1 and F1 are expected from perturbative QCD. Therefore, theQ2 dependence of g1 is estimated from a next-to-leading-order (NLO) perturbativeQCD analysis [11] of all available proton, neutron and deuteron data with Q2 >1 GeV2. In this analysis g1 is decomposed into polarised quark singlet ∆Σ, gluon∆g and nonsinglet distributions ∆qNS for the proton and the neutron. The NLOanalysis is done in the Adler-Bardeen and the MS scheme [12]. In the fit someparameters like the normalisation of the nonsinglet distributions were constrainedby using the neutron and hyperon β decay constants assuming SU(3) flavour. TheCzech. J. Phys. 0/S0 (2013) 5Eva-Maria Kabuß-0.200.20.40.60.8110-310-210-11g1protonx(a)SMC Q2 > 0.2 GeV2SMC Q2 > 1.0 GeV2-1-0.8-0.6-0.4-0.200.20.410-310-210-11g1deuteronx(b)SMC Q2 > 0.2 GeV2SMC Q2 > 1.0 GeV2Fig. 4. a) gp1 and b) gd1 vs. x at the measured Q2 for the optimal data set. The statisticaluncertainties are shown as error bars, and the bands indicate the size of the systematicuncertainties.results for the polarised parton distributions x∆Σ, x∆g and x∆qNS are shown infig. 5.In the QPM the quark contribution to the nucleon spin is given by the singletaxial charge a0 = au + ad + as whereas it is ambiguous in NLO pQCD due to theaxial anomaly. Thus, the first moment of ∆Σ, aΣ is equal to a0 in the MS scheme,while in the AB scheme the gluon contribution must be subtracted. The resultsaAB0 = 0.23± 0.07(sta)± 0.19(sys&th) and aMS0 = 0.19± 0.05(sta)± 0.04(sys&th)are similar in both schemes and correspond to about 1/3 of the naive Ellis-Jaffeexpectation of 0.58. The result for the gluon contribution ag(Q2) =1∫0∆g(x,Q2)dxaABg = 0.99+1.17−0.31 (sta)+0.42−0.22 (sys)+1.43−0.45 (th) (6)shows that very little can be said about this quantity on the basis of the presentdata.5. Sum rulesUsing the results of the QCD analysis g1(x,Q20 = 5 GeV2) is obtained fromg1(x,Q20) = g1(x,Q2)+[gfit1 (x,Q20)− gfit1 (x,Q2)]. The extrapolation of g1 to x = 0and x = 1 is done by integrating the fit results for x < 0.003 and x > 0.8 (seefig. 6a). The results at Q20 = 5 GeV2Γp1 = 0.121± 0.003 (sta) ± 0.005 (sys) ± 0.017 (th)Γd1 = 0.021± 0.004 (sta) ± 0.003 (sys) ± 0.016 (th)Γn1 =−0.075± 0.007 (sta) ± 0.005 (sys) ± 0.019 (th) (7)6 Czech. J. Phys. 0/S0 (2013)Nucleon spin structure-0.4-0.3-0.2-0.100.10.20.30.410 -2 10 -1 1x×DS (x)X-0.4-0.3-0.2-0.100.10.20.30.410 -2 10 -1 1x×D g(x)X-0.8-0.6-0.4-0.200.20.40.610-210-11x×D qp NS  (x)X-1.2-1-0.8-0.6-0.4-0.2010-210-11x×D qn NS  (x)XFig. 5. Polarised parton distributions determined at Q2 = 1 GeV2. The uncertaintiesare statistical (cross hatched band), experimental systematic (vertically hatched band),and theoretical (horizontally hatched band).show a violation of the Elle-Jaffe sum rules of about 3 σ.To test the Bjorken sum rule the fit has to be repeated releasing the constraintsfor the nonsinglet moments using gA/gV as a free parameter. A consistent value ofgA/gV with the nominal value used above is obtained. The resulting value for theBjorken sum rule at Q2 = 5 GeV2Γp1 − Γn1 = 0.174+0.024−0.012 (8)is in excellent agreement with the theoretical value of Γp1 −Γn1 = 0.181± 0.003. Analternative way to determine Γp1 − Γn1 restricts the QCD analysis to the nonsingletdistribution which is decoupled from the evolution of ∆Σ and ∆g. Here, data pointsfor gp1 and gn1 at the same kinematics are needed so that only the SLAC E143 andSMC can be used presently (see fig. 6b)). The resultΓp1 − Γn1 = 0.181+0.026−0.021 (9)Czech. J. Phys. 0/S0 (2013) 7Eva-Maria Kabuß-0.0200.020.040.060.0810 -4 10 -3 10 -2 10 -1 1x × g1p(x) SMC EMCE143X-0.01-0.00500.0050.010.0150.0210-610-510-410-310-200.020.040.060.080.110-410-310-210-11x × g1NS(x) SMC E143XFig. 6. a) xgp1 vs. x for the world data with the uncertainties of the fit due to experimentalsystematics and theoretical sources shown by the bands, b) xgNS1 vs. x from E143 andSMC with the QCD fit at Q2 = 5 GeV2 with the error band representing the systematicand theoretical uncertainty of the fit. All points are shown with their statistical errors.is constistent with the above result, but due to the smaller data set the experimen-tal errors are larger. The theoretical error, however, is smaller than for the firstmethod, so that with the forthcoming data from E155 and HERMES a significantimprovement is expected.References[1] J. Ellis and R. L. Jaffe, Phys. Rev. D9 (1974) 1444; Phys. Rev. D10 (1974) 1669.[2] J. D. Bjorken, Phys. Rev. 148 (1966) 1467; Phys. Rev. D1 (1970) 1376.[3] EMC, J. Ashman et al., Nucl. Phys. B328 (1989) 1.[4] SMC, B. Adeva et al., Nucl. Instr. Meth. A343 (1994) 363, B. Adeva et al., inpreparation.[5] SMC, B. Adeva et al., Nucl. Instr. Meth. A419 (1998) 60.[6] SMC, D. Adams et al., Phys. Lett. B296 (1997) 338.[7] SMC, D. Adams et al., Phys. Rev. D56 (1997) 5330.[8] SMC, B. Adeva et al., CERN-EP/98-85, submitted to Phys. Rev. D.[9] E143, K. Abe et al., Phys. Rev. Lett. 74 (1995) 346.[10] J. Kiryluk, Proc. of DIS98 (Brussels 1998), to be published.[11] SMC, B. Adeva et al., CERN-EP/98-86, submitted to Phys. Rev. D.[12] R. Ball, S. Forte and G. Ridolfi, Phys. Lett. B378 (1996) 255.8 Czech. J. Phys. 0/S0 (2013)

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Results on the nucleon spin structure

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