Evidence for Quark-Hadron Duality in the Proton Spin Asymmetry $A_1$

a r X i v :h e p -e x /0209018v 2 4 F e

b 2003

Evidence for Quark-Hadron Duality in the Proton Spin Asymmetry A 1

A.Airapetian,32N.Akopov,32Z.Akopov,32M.Amarian,27,32V.V.Ammosov,25E.C.Aschenauer,7H.Avakian,11

R.Avakian,32A.Avetissian,32E.Avetissian,32P.Bailey,15V.Baturin,24C.Baumgarten,21M.Beckmann,6S.Belostotski,24S.Bernreuther,30N.Bianchi,11H.P.Blok,23,31H.B¨o ttcher,7A.Borissov,19O.Bouhali,23M.Bouwhuis,15J.Brack,5S.Brauksiepe,12A.Br¨u ll,18I.Brunn,9H.J.Bulten,23,31G.P.Capitani,11E.Cisbani,27

G.Ciullo,10G.R.Court,16P.F.Dalpiaz,10R.De Leo,3L.De Nardo,1E.De Sanctis,11E.Devitsin,20P.K.A.de Witt Huberts,23P.Di Nezza,11M.D¨u ren,14M.Ehrenfried,7G.Elbakian,32F.Ellinghaus,7U.Elschenbroich,12,13J.Ely,5R.Fabbri,10A.Fantoni,11A.Fechtchenko,8L.Felawka,29B.W.Filippone,4H.Fischer,12B.Fox,5J.Franz,12S.Frullani,27Y.G¨a rber,9V.Gapienko,25F.Garibaldi,27E.Garutti,23G.Gavrilov,24V.Gharibyan,32G.Graw,21O.Grebeniouk,24P.W.Green,1,29L.G.Greeniaus,1,29A.Gute,9

W.Haeberli,17K.Ha?di,2M.Hartig,29D.Hasch,9,11D.Heesbeen,23F.H.Heinsius,12M.Henoch,9

R.Hertenberger,21W.H.A.Hesselink,23,31G.Hofman,5Y.Holler,6R.J.Holt,2B.Hommez,13G.Iarygin,8A.Izotov,24H.E.Jackson,2A.Jgoun,24P.Jung,7R.Kaiser,7E.Kinney,5A.Kisselev,24P.Kitching,1K.K¨o nigsmann,12H.Kolster,18M.Kopytin,24V.Korotkov,7E.Kotik,1V.Kozlov,20B.Krauss,9V.G.Krivokhijine,8G.Kyle,https://www.360docs.net/doc/b148008.html,gamba,https://www.360docs.net/doc/b148008.html,ziev,23,31P.Lenisa,10P.Liebing,7T.Lindemann,6W.Lorenzon,19A.Maas,7N.C.R.Makins,15H.Marukyan,32F.Masoli,10F.Menden,12V.Mexner,23N.Meyners,6O.Mikloukho,https://www.360docs.net/doc/b148008.html,ler,1,29V.Muccifora,11A.Nagaitsev,8E.Nappi,3Y.Naryshkin,24A.Nass,9K.Negodaeva,7W.-D.Nowak,7K.Oganessyan,6,11G.Orlandi,27S.Podiatchev,9S.Potashov,20D.H.Potterveld,2M.Raithel,9V.Rappoport,24D.Reggiani,10P.Reimer,2A.Reischl,23A.R.Reolon,11K.Rith,9A.Rostomyan,32D.Ryckbosch,13Y.Sakemi,30I.Sanjiev,2,24F.Sato,30I.Savin,8C.Scarlett,19A.Sch¨a fer,26C.Schill,12F.Schmidt,9G.Schnell,7K.P.Sch¨u ler,6A.Schwind,7J.Seibert,12B.Seitz,1R.Shanidze,9T.-A.Shibata,30V.Shutov,8M.C.Simani,23,31K.Sinram,6M.Stancari,10E.Ste?ens,9J.J.M.Steijger,23J.Stewart,7U.St¨o sslein,5K.Suetsugu,30S.Taroian,32A.Terkulov,20S.Tessarin,10

E.Thomas,11B.Tipton,4M.Tytgat,13G.M.Urciuoli,27J.

F.J.van den Brand,23,31

G.van der Steenhoven,23R.van de Vyver,13M.C.Vetterli,28,29V.Vikhrov,24M.G.Vincter,1J.Visser,23J.Volmer,7C.Weiskopf,9J.Wendland,28,29J.Wilbert,9T.Wise,17S.Yen,29S.Yoneyama,30B.Zihlmann,23,31and

H.Zohrabian 32

(The HERMES Collaboration)

1

Department of Physics,University of Alberta,Edmonton,Alberta T6G 2J1,Canada 2Physics Division,Argonne National Laboratory,Argonne,Illinois 60439-4843,USA

3

Istituto Nazionale di Fisica Nucleare,Sezione di Bari,70124Bari,Italy

4

W.K.Kellogg Radiation Laboratory,California Institute of Technology,Pasadena,California 91125,USA

5

Nuclear Physics Laboratory,University of Colorado,Boulder,Colorado 80309-0446,USA

6

DESY,Deutsches Elektronen-Synchrotron,22603Hamburg,Germany 7

DESY Zeuthen,Deutsches Elektronen-Synchrotron,15738Zeuthen,Germany

8

Joint Institute for Nuclear Research,141980Dubna,Russia

9

Physikalisches Institut,Universit¨a t Erlangen-N¨u rnberg,91058Erlangen,Germany

10

Istituto Nazionale di Fisica Nucleare,Sezione di Ferrara and Dipartimento di Fisica,Universit`a di Ferrara,44100Ferrara,Italy

11

Istituto Nazionale di Fisica Nucleare,Laboratori Nazionali di Frascati,00044Frascati,Italy

12

Fakult¨a t f¨u r Physik,Universit¨a t Freiburg,79104Freiburg,Germany

13

Department of Subatomic and Radiation Physics,University of Gent,9000Gent,Belgium

14

Physikalisches Institut,Universit¨a t Gie?en,35392Gie?en,Germany 15

Department of Physics,University of Illinois,Urbana,Illinois 61801,USA 16

Physics Department,University of Liverpool,Liverpool L697ZE,United Kingdom 17

Department of Physics,University of Wisconsin-Madison,Madison,Wisconsin 53706,USA

18

Laboratory for Nuclear Science,Massachusetts Institute of Technology,Cambridge,Massachusetts 02139,USA

19

Randall Laboratory of Physics,University of Michigan,Ann Arbor,Michigan 48109-1120,USA

20

Lebedev Physical Institute,117924Moscow,Russia

21

Sektion Physik,Universit¨a t M¨u nchen,85748Garching,Germany

22

Department of Physics,New Mexico State University,Las Cruces,New Mexico 88003,USA

23

Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF),1009DB Amsterdam,The Netherlands

24

Petersburg Nuclear Physics Institute,St.Petersburg,Gatchina,188350Russia 25

Institute for High Energy Physics,Protvino,Moscow oblast,142284Russia

26

Institut f¨u r Theoretische Physik,Universit¨a t Regensburg,93040Regensburg,Germany

27

Istituto Nazionale di Fisica Nucleare,Sezione Roma 1,

Gruppo Sanit`a and Physics Laboratory,Istituto Superiore di Sanit`a ,00161Roma,Italy

2 28Department of Physics,Simon Fraser University,Burnaby,British Columbia V5A1S6,Canada

29TRIUMF,Vancouver,British Columbia V6T2A3,Canada

30Department of Physics,Tokyo Institute of Technology,Tokyo152,Japan

31Department of Physics and Astronomy,Vrije Universiteit,1081HV Amsterdam,The Netherlands

32Yerevan Physics Institute,375036,Yerevan,Armenia

(Dated:February7,2008)

Spin-dependent lepton-nucleon scattering data have been used to investigate the validity of the

concept of quark-hadron duality for the spin asymmetry A1.Longitudinally polarised positrons

were scattered o?a longitudinally polarised hydrogen target for values of Q2between1.2and12

GeV2and values of W2between1and4GeV2.The average double-spin asymmetry in the nucleon

resonance region is found to agree with that measured in deep-inelastic scattering at the same values

of the Bjorken scaling variable x.This?nding implies that the description of A1in terms of quark

degrees of freedom is valid also in the nucleon resonance region for values of Q2above1.6GeV2.

The interaction between baryons and between baryons and leptons can generally be described by two comple-mentary approaches:with quark-gluon degrees of free-dom at high energy,where the quarks are asymptoti-cally free,and in terms of hadronic degrees of freedom at low energy,where e?ects of con?nement are large.In some speci?c cases,where the description in terms of hadrons is expected to apply most naturally,the quark-gluon description can also be successfully used.Such cases are examples of so-called quark-hadron duality. Bloom and Gilman[1]?rst noted this relationship be-tween phenomena in the nucleon resonance region and in deep-inelastic scattering(DIS).Speci?cally,they ob-served that the cross section for electro-production of nu-cleon resonances,if averaged over a large enough range of invariant mass W of the initial photon-nucleon sys-tem,exhibited the same behavior as the cross section observed in the DIS region.In other words,the scal-ing limit curve measured as a function of the variable x′=x+M2/Q2in DIS processes at high Q2and high νapproximately approaches the smooth curves derived from measurements in the resonance region at lowerνand Q2(here x=Q2/2Mνis the Bjorken scaling vari-able,?Q2is the four-momentum transfer squared,M is the proton mass andνthe energy of the exchanged virtual photon in the target rest frame).

Duality in strong interaction physics was originally formulated for hadron-hadron scattering[2]:the high-energy behavior of amplitudes,described within Regge theory in terms of t-channel Regge pole exchanges,was related to the behavior of the amplitudes at low-energy, which are well described by a sum over a few s-channel resonances[3,4].In QCD the Bloom-Gilman duality can be interpreted in the language of the operator prod-uct expansion in which moments of structure functions are expanded in powers of1/Q[5,6].The leading terms are associated with non-interacting partons and exhibit scaling,while the terms proportional to1/Q involve in-teractions between quarks and gluons.While the?rst moments of the structure functions depend weakly on Q2, this is not true for the higher moments,since at large x the scaling violations of structure functions(i.e.the Q2-dependence for?xed values of x)are very large,so that a leading order description in terms of parton distributions is unable to reproduce DIS data.Therefore,additional terms,which e?ectively account for higher-order,higher-twist and target-mass corrections,should be included. It has been shown that in that way a good description of measured values of F2structure function over a wide range of Q2and x can be obtained[7].

Recently,a sample of inclusive unpolarised electron-nucleon scattering data on hydrogen and deuterium tar-gets has been analysed to investigate the validity of quark-hadron duality[8].For the proton,it was observed that starting from Q2≥1.5GeV2duality in the unpo-larised structure function F2holds for individual reso-nance contributions,as well as for the entire resonance region1≤W2≤4GeV2.It is worthwhile to mention that duality in the unpolarised structure function holds only when comparing the data in the resonance region with phenomenological?ts to DIS data,while it does not hold when comparing with QCD?ts at leading order only.

In contrast to the extensive study of duality for the unpolarised,i.e.spin-averaged,photo-absorption cross section,the validity of duality has not been investigated for the spin-dependent scattering processes,which are re-lated to the spin-dependent photo-absorption cross sec-tion.Observation of duality for the spin asymmetry A1 is of particular interest as it may lead to a complemen-tary means to study the spin structure of the nucleon at large x,which is di?cult to measure in the DIS region with high-statistics.Since the DIS spin asymmetry A1 has been found to be independent of Q2for all measured values of x,the comparison of this asymmetry in the reso-nance and in the DIS regions is straightforward and does not depend on the choice of the parameterization of DIS cross section data.

In this Letter the?rst experimental evidence for quark-hadron duality for the proton spin asymmetry A1is re-ported.The data were collected by the HERMES exper-iment in1997with a27.57GeV longitudinally polarised positron beam incident on a longitudinally polarised hy-drogen gas target internal to the HERA lepton storage ring at DESY.The positrons in the HERA ring are trans-

3

versely polarised by emission of synchrotron radiation [9].Longitudinal polarisation is obtained by using

spin rota-

tors

located

upstream

and downstream

of the HERMES experiment [10].The beam polarisation was measured continuously using Compton backscattering of circularly polarised laser light [11].The average beam polarisation for the analysed data was 0.55with a relative systematic uncertainty of 3.4%.

The HERMES polarised target [12]consists of po-larised atomic hydrogen gas con?ned in a storage cell,fed by an atomic-beam source of nuclear-polarised hy-drogen based on Stern-Gerlach separation [13].The nu-clear polarisation of the atoms and the atomic fraction are continuously measured with a Breit-Rabi polarime-ter [14]and a target gas analyser.The average target polarisation for the analysed data was 0.88with a rela-tive systematic uncertainty of 4.7%[15].

Scattered positrons were detected by the HERMES spectrometer,described in Ref.[16].For all detected positrons the angular resolution was better than 0.6mrad,the momentum resolution was better than 1.6%aside from bremsstrahlung tails,and the Q 2-resolution was better than 2.2%.

In addition to the constraints of the acceptance of the HERMES spectrometer,the kinematic requirements for the analysis in the nucleon resonance region were:1≤W 2≤4GeV 2,and 1.2≤Q 2≤12GeV 2.The corre-sponding x range was 0.34

The evaluation of the longitudinal asymmetry A is based on the ratio of the luminosity weighted (i.e.nor-malized)count rates using the following formula:

A =

N →

?L →

??N →

?L →

?

Q 2,which describes its behavior in the deep inelas-tic region [15].The experimental systematic uncertainty receives a total contribution of about 8%from the follow-ing sources.The resolution smearing e?ects give contri-butions up to 5.6%.They were evaluated by comparing simulated results from two very di?erent assumptions for

A 1,a power law (A r es 1=x 0.7),and a step function (A r es

1=-0.5for W 2<1.8GeV 2and A r es 1=1.0for 1.8≤W 2≤4.0GeV 2),which is suggested by the hypothesis of the pos-sible dominance of the P 33resonance at low W 2and the S 11at higher W 2.The modi?cation of the depolari-sation factor D due to smearing e?ects was also taken into account.Other contributions are the uncertainties from beam and target polarisation (5.3%)and from the spectrometer geometry (2.5%).Contributions from ra-diative corrections,calculated using the POLRAD code [24],gave a contribution of up to 3%to the systematic uncertainty.

Also shown in Fig.1is the asymmetry A D IS

1

as mea-sured in DIS [15,23,25,26].The data in the resonance region are in agreement with those measured in DIS.The

data indicate that A r es

1may exceed the exact spin-?avor SU(6)symmetry expectation of 5/9at x =1,being in bet-ter agreement with the original and long standing pre-diction of 1at x =1[27].This latter prediction is also

favored by the measured A D IS

1

at large x and by more recent expectations [28,29,30].The curve in Fig.1is

a power law ?t to the world DIS data at x >0.3:A D IS

1=x 0.7.This parameterisation of A 1is constrained to 1at x =1and does not depend on Q 2,as indicated by ex-

4

perimental data in this range

[26].The average ratio

of

the measured A r es

1to the DIS ?t is 1.11±0.16(stat.)±0.18(syst.).

0.20.40.60.811.21.400.10.20.30.40.50.60.70.80.9

1

x

A 1

FIG.1:Spin asymmetry A 1as a function of x measured in the resonance region (full circles).Error bars represent the statistical uncertainties;the systematic uncertainty for the data in the resonance region is about 16%.Open symbols are previous results obtained in the DIS region.The curve represents a power law ?t to DIS data at x >0.3.

Originally,duality was introduced by Bloom and Gilman [1]by considering the variable x ′=x +M 2/Q 2instead of the Bjorken variable x ,while more recently the Nachtmann variable ξ=2x/(1+

0.380.36 1.60.46±0.200.500.45 2.00.77±0.210.570.51 2.30.88±0.290.640.57 2.60.76±0.280.780.68 2.90.99±0.29

In summary,the ?rst experimental evidence of quark-hadron duality for the spin asymmetry A 1(x )of the pro-ton has been observed for Q 2between 1.6GeV 2and 2.9GeV 2.The spin asymmetries measured in the nucleon resonance region at W 2≤4GeV 2have been found to be in agreement with the spin asymmetries measured in the DIS region at larger W 2.Target-mass e?ects are found to be small in the HERMES kinematics.This experi-mental ?nding indicates that the description of the spin asymmetry in terms of quark degrees of freedom is on average valid also in the nucleon resonance region within the Q 2-range probed by the present experiment.

We gratefully acknowledge the DESY management for its support,the sta?s at DESY and the collaborating institutions for their signi?cant e?ort,and our funding agencies for ?nancial support.This work was supported by the FWO-Flanders,Belgium;the Natural Sciences and Engineering Research Council of Canada;the IN-TAS and ESOP network contributions from the Euro-pean Community;the German Bundesministerium f¨u r Bildung und Forschung;the Deutsche Forschungsgemein-schaft (DFG);the Deutscher Akademisches Austausch-dienst (DAAD);the Italian Istituto Nazionale di Fisica Nucleare (INFN);Monbusho International Scienti?c Re-search Program,JSPS,and Toray Science Foundation of Japan;the Dutch Foundation for Fundamenteel Onder-zoek der Materie (FOM);the U.K.Particle Physics and Astronomy Research Council;and the U.S.Department of Energy and the National Science Foundation.

5

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