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Measurement of the hadronic photon structure function F _2
γ(x, Q
2) in two-photon collisions at LEP
A. Heister, S. Schael, R. Barate, R. Bruneliere, I. de Bonis, D. Decamp, C.
Goy, S. Jezequel, J.P. Lees, F. Martin, et al.
To cite this version:
A. Heister, S. Schael, R. Barate, R. Bruneliere, I. de Bonis, et al.. Measurement of the hadronic photon structure functionF_2γ(x, Q2) in two-photon collisions at LEP. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2003, 30, pp.145-158. �in2p3-00013957�
CERN-EP 2003-033
June, 112003
Measurement of the Hadronic Photon
Structure Function F
2
(x; Q
2
)
in Two-Photon Collisions at LEP
The ALEPH Collaboration )
Abstract
ThehadronicphotonstructurefunctionF
2 (x;Q
2
)ismeasuredfromdatatakenwith
theALEPHdetectoratLEP.Atcentre-of-massenergiesbetween p
s=189GeVand
207GeVanintegratedluminosityof548:4pb 1
isanalyzedintworangesofQ 2
with
hQ 2
i=17:3GeV 2
and67:2GeV 2
. Detectoreects andacceptancearecorrected for
with a Tikhonov unfolding procedure. The results are compared to theoretical
predictionsandmeasurements fromother experiments.
Submitted to TheEuropean Physical Journal C
)See next pages for the listof authors
A.Heister,S.Schael
PhysikalischesInstitutdasRWTH-Aachen, D-52056Aachen,Germany
R.Barate,R. Bruneliere,I.DeBonis,D. Decamp,C.Goy,S.Jezequel,J.-P.Lees,F.Martin,E.Merle,
M.-N.Minard,B.Pietrzyk,B.Trocme
Laboratoire de Physique des Particules (LAPP), IN 2
P 3
-CNRS, F-74019 Annecy-le-Vieux Cedex,
France
S.Bravo,M.P.Casado,M.Chmeissani,J.M.Crespo,E.Fernandez,M.Fernandez-Bosman,Ll.Garrido, 15
M.Martinez,A.Pacheco,H. Ruiz
Institut de F
isica d'Altes Energies, Universitat Autonoma de Barcelona, E-08193 Bellaterra
(Barcelona),Spain 7
A.Colaleo,D.Creanza,N.DeFilippis,M.dePalma,G.Iaselli,G.Maggi,M.Maggi,S.Nuzzo,A.Ranieri,
G.Raso, 24
F.Ruggieri,G.Selvaggi,L.Silvestris,P.Tempesta,A.Tricomi, 3
G.Zito
DipartimentodiFisica,INFNSezionediBari,I-70126Bari,Italy
X.Huang,J.Lin,Q.Ouyang,T.Wang,Y.Xie,R. Xu,S. Xue,J.Zhang,L.Zhang,W.Zhao
InstituteofHighEnergyPhysics,AcademiaSinica,Beijing,ThePeople'sRepublicof China 8
D. Abbaneo,T.Barklow, 26
O.Buchmuller, 26
M.Cattaneo,B.Clerbaux, 23
H.Drevermann,R.W.Forty,
M.Frank,F.Gianotti,J.B.Hansen,J.Harvey,D.E.Hutchcroft, 30
,P.Janot,B.Jost,M.Kado, 2
P.Mato,
A.Moutoussi,F.Ranjard,L.Rolandi,D.Schlatter,G.Sguazzoni,F.Teubert,A. Valassi,I.Videau
EuropeanLaboratoryforParticlePhysics(CERN),CH-1211Geneva23,Switzerland
F. Badaud,S. Dessagne, A. Falvard, 20
D. Fayolle,P. Gay, J.Jousset, B.Michel, S. Monteil, D. Pallin,
J.M.Pascolo,P.Perret
Laboratoire de Physique Corpusculaire, Universite Blaise Pascal, IN 2
P 3
-CNRS, Clermont-Ferrand,
F-63177Aubiere,France
J.D.Hansen,J.R.Hansen,P.H. Hansen,A.C.Kraan,B.S.Nilsson
NielsBohrInstitute,2100Copenhagen,DK-Denmark 9
A.Kyriakis,C.Markou,E.Simopoulou,A.Vayaki,K.Zachariadou
NuclearResearchCenterDemokritos(NRCD),GR-15310Attiki,Greece
A.Blondel, 12
J.-C.Brient, F.Machefert,A.Rouge,H. Videau
LaoratoireLeprince-Ringuet,EcolePolytechnique,IN 2
P 3
-CNRS,F-91128PalaiseauCedex, France
V.Ciulli,E.Focardi,G.Parrini
DipartimentodiFisica,UniversitadiFirenze,INFN SezionediFirenze,I-50125Firenze,Italy
A. Antonelli, M. Antonelli, G. Bencivenni, F. Bossi, G. Capon, F. Cerutti, V. Chiarella, P. Laurelli,
G.Mannocchi, 5
G.P. Murtas,L.Passalacqua
LaboratoriNazionalidell'INFN(LNF-INFN), I-00044Frascati,Italy
J.Kennedy,J.G.Lynch,P.Negus,V.O'Shea,A.S.Thompson
DepartmentofPhysicsandAstronomy,UniversityofGlasgow,GlasgowG128QQ,UnitedKingdom 10
S.Wasserbaech
UtahValleyStateCollege,Orem,UT84058,U.S.A.
R.Cavanaugh, S.Dhamotharan, C.Geweniger,P.Hanke,V.Hepp,E.E.Kluge,A.Putzer,H.Stenzel,
K.Tittel,M.Wunsch 19
Kirchho-InstitutfurPhysik,UniversitatHeidelberg,D-69120Heidelberg,Germany 16
R. Beuselinck, W. Cameron, G. Davies, P.J. Dornan, M. Girone, 1
R.D. Hill, N. Marinelli,J. Nowell,
S.A.Rutherford,J.K.Sedgbeer,J.C.Thompson, 14
R.White
DepartmentofPhysics,ImperialCollege,LondonSW72BZ,United Kingdom 10
V.M.Ghete,P. Girtler,E.Kneringer,D. Kuhn,G.Rudolph
InstitutfurExperimentalphysik,UniversitatInnsbruck,A-6020Innsbruck,Austria 18
E. Bouhova-Thacker, C.K. Bowdery, D.P. Clarke, G. Ellis, A.J. Finch, F. Foster, G. Hughes,
R.W.L.Jones,M.R.Pearson,N.A.Robertson,M.Smizanska
DepartmentofPhysics,Universityof Lancaster,LancasterLA14YB, UnitedKingdom 10
O.vanderAa,C.Delaere, 28
G.Leibenguth, 31
V.Lemaitre 29
Institut de Physique Nucleaire, Departement de Physique, Universite Catholique de Louvain, 1348
Louvain-la-Neuve,Belgium
U. Blumenschein, F. Holldorfer, K. Jakobs, F. Kayser, K. Kleinknecht, A.-S. Muller, B. Renk, H.-
G.Sander,S.Schmeling,H. Wachsmuth,C.Zeitnitz,T.Ziegler
InstitutfurPhysik,UniversitatMainz,D-55099Mainz,Germany 16
A.Bonissent,P.Coyle,C.Curtil,A.Ealet,D.Fouchez,P. Payre,A.Tilquin
CentredePhysiquedesParticulesdeMarseille,UnivMediterranee,IN 2
P 3
-CNRS,F-13288Marseille,
France
F.Ragusa
DipartimentodiFisica,UniversitadiMilanoeINFNSezione diMilano,I-20133Milano,Italy.
A. David, H. Dietl, G. Ganis, 27
K. Huttmann, G. Lutjens, W. Manner, H.-G.Moser, R. Settles,
M.Villegas,G.Wolf
Max-Planck-InstitutfurPhysik,Werner-Heisenberg-Institut,D-80805Munchen, Germany 16
J. Boucrot, O. Callot, M. Davier, L. Duot, J.-F.Grivaz, Ph. Heusse, A. Jacholkowska, 6
L. Serin,
J.-J.Veillet
Laboratoiredel'AccelerateurLineaire,UniversitedeParis-Sud,IN 2
P 3
-CNRS,F-91898OrsayCedex,
France
P.Azzurri,G.Bagliesi,T.Boccali,L.Foa,A.Giammanco,A.Giassi,F.Ligabue,A.Messineo,F.Palla,
G.Sanguinetti,A.Sciaba,P.SpagnoloR. TenchiniA. VenturiP.G.Verdini
Dipartimento di Fisicadell'Universita,INFN Sezione diPisa, e ScuolaNormaleSuperiore, I-56010
Pisa,Italy
O.Awunor,G.A.Blair,G.Cowan,A.Garcia-Bellido,M.G.Green,L.T.Jones,T.Medcalf,A.Misiejuk,
J.A.Strong,P.Teixeira-Dias
DepartmentofPhysics,RoyalHolloway&BedfordNewCollege,UniversityofLondon,Egham,Surrey
TW20OEX,UnitedKingdom 10
R.W.Clit,T.R. Edgecock,P.R.Norton,I.R.Tomalin,J.J.Ward
ParticlePhysicsDept.,RutherfordAppletonLaboratory,Chilton,Didcot,OxonOX11OQX,United
Kingdom 10
B.Bloch-Devaux, D. Boumediene, P. Colas, B.Fabbro,E. Lancon,M.-C.Lemaire, E. Locci, P. Perez,
J.Rander,B.Tuchming,B.Vallage
CEA, DAPNIA/Service de Physique des Particules, CE-Saclay, F-91191 Gif-sur-Yvette Cedex,
France 17
A.M.Litke,G.Taylor
22
DepartmentofPhysics,Universityof SheÆeld,SheÆeldS37RH,UnitedKingdom
A.Bohrer,S. Brandt,C.Grupen,J.Hess,A. Ngac,G.Prange
FachbereichPhysik,UniversitatSiegen,D-57068Siegen,Germany 16
C.Borean,G.Giannini
DipartimentodiFisica,UniversitadiTriesteeINFN SezionediTrieste,I-34127Trieste,Italy
H.He,J.Putz,J.Rothberg
ExperimentalElementaryParticlePhysics,Universityof Washington,Seattle,WA 98195U.S.A.
S.R. Armstrong, K. Berkelman, K. Cranmer, D.P.S. Ferguson, Y. Gao, 13
S. Gonzalez, O.J. Hayes,
H. Hu, S. Jin, J. Kile, P.A. McNamara III, J. Nielsen, Y.B. Pan, J.H. vonWimmersperg-Toeller,
W.Wiedenmann, J.Wu, SauLanWu, X.Wu, G.Zobernig
DepartmentofPhysics,Universityof Wisconsin,Madison,WI53706,USA 11
G.Dissertori
InstituteforParticlePhysics,ETHHonggerberg,8093Zurich,Switzerland.
1
AlsoatCERN,1211Geneva23,Switzerland.
2
NowatFermilab,POBox500,MS352,Batavia,IL60510,USA
3
AlsoatDipartimentodiFisicadiCataniaandINFNSezionediCatania,95129Catania,Italy.
4
NowatUniversityofFlorida,DepartmentofPhysics,Gainesville,Florida32611-8440,USA
5
AlsoIstitutodiCosmo-GeosicadelC.N.R., Torino,Italy.
6
Alsoat Grouped'AstroparticulesdeMontpellier, UniversitedeMontpellierII, 34095,Montpellier,
France.
7
Supported byCICYT,Spain.
8
Supported bytheNationalScienceFoundationof China.
9
Supported bytheDanishNaturalScienceResearchCouncil.
10
Supported bytheUKParticlePhysicsandAstronomyResearchCouncil.
11
Supported bytheUS DepartmentofEnergy,grantDE-FG0295-ER40896.
12
NowatDepartementdePhysiqueCorpusculaire,UniversitedeGeneve,1211Geneve4,Switzerland.
13
AlsoatDepartmentofPhysics,TsinghuaUniversity,Beijing,ThePeople'sRepublicofChina.
14
Supported bytheLeverhulmeTrust.
15
Permanentaddress: UniversitatdeBarcelona,08208Barcelona,Spain.
16
Supported byBundesministeriumfurBildungundForschung,Germany.
17
Supported bytheDirectiondesSciences delaMatiere,C.E.A.
18
Supported bytheAustrianMinistryforScienceandTransport.
19
NowatSAPAG,69185Walldorf,Germany
20
Now atGrouped' Astroparticulesde Montpellier, UniversitedeMontpellierII,34095Montpellier,
France.
21
NowatBNPParibas,60325FrankfurtamMainz,Germany
22
Supported bytheUS DepartmentofEnergy,grantDE-FG03-92ER40689.
23
NowatInstitutInter-universitairedeshautesEnergies(IIHE),CP230,UniversiteLibredeBruxelles,
1050Bruxelles,Belgique
24
AlsoatDipartimentodiFisicaeTecnologieRelative,UniversitadiPalermo,Palermo,Italy.
25
Deceased.
26
NowatSLAC,Stanford,CA94309,U.S.A
27
Now atINFN SezionediRomaII,DipartimentodiFisica,UniversitadiRomaTorVergata, 00133
Roma,Italy.
28
ResearchFellowoftheBelgiumFNRS
29
ResearchAssociateof theBelgiumFNRS
30
NowatLiverpoolUniversity,LiverpoolL69 7ZE,UnitedKingdom
The hadronic structure function F
2
plays an important role in the description of the
hadronic natureofthe photon. It isafunction ofthe Bjorken variable xwhich inleading
order gives the fractional momentum of the resolved parton in the target photon, and
also a function of the virtualities Q 2
and P 2
of the two interacting photons. In this
measurementtwo-photon eventsare used whereone ofthe scattered electrons isdetected
(`tagged') in the luminosity calorimeters and the second one remains undetected, since
the scattering angleis toosmalland theelectron escapesalong the beam pipe. Forthese
single-tag events the virtuality P 2
of the photon radiated from the undetected electron
is small. This photon is considered as a quasi-real target photon that is probed by the
highlyvirtual photonfrom the tagged electron. In this case the dierentialcross section
forhadronproductionsimpliesand onlydepends onthe structure functionsF
2
and F
L .
It is given by [1]
d 3
dxdydQ 2
= 4
2
Q 4
x
1 y+ y
2
2
"
F
2 (x;Q
2
)
y 2
2(1 y y
2
2 )
F
L (x;Q
2
)
#
(x;y) (1)
where
Q 2
= q 2
=2E
beam E
tag
(1 cos
tag
) (2)
isthenegativesquaredfour-momentumofthevirtualphoton,E
tag
and
tag
aretheenergy
and scattering angle of the tagged beam electron, and is the ne structure constant.
The Bjorken variable xis given by
x= Q
2
2pq
= Q
2
Q 2
+W 2
; (3)
with the four-momenta q and p of the interacting photons and the total invariant mass
W of the hadronic nal state (P 2
= p
2
Q
2
). The inelasticity y is given by
y= qp
kp
=1 E
tag
2E
beam
(1+cos
tag
) (4)
where k is the four-momentum of the incident beam electron that is tagged. The ux
function (x;y) of the photons radiatedfromthe untagged beam electron is given in [1].
For typical experimental conditions y 1, thus the dierential cross section is not
sensitive to the longitudinal structure function F
L (x;Q
2
), and therefore eqn. (1) allows
F
2
tobe measured.
FromQuantumChromodynamics(QCD)itisexpectedthatthestructurefunctionF
2
separates into two components as rst described by Witten [2]. While the \point-like"
partis calculableinperturbativeQCD andshows arise withincreasing Q 2
,the \hadron-
like"partbecomesmoreimportantforlowxandisnotcalculablewithintheframeworkof
perturbative QCD,since thephoton uctuatesintoastate similartolightvector mesons
wherethe contributionof thegluondensity isimportant. VariousparametrizationsofF
2
Q 2
evolution,inclusionof heavy quarkavours, compositionofhadron-likeandpoint-like
contributionsand inclusionofhigherorderQCDcorrections. Earliercalculationssuered
from the limited experimental data available at the time. A very detailed review of the
current status is given in [13,14].
In thispaperthe selectionofthe datasampleisdescribed afterabriefintroductionof
the experimentalsetup. The Tikhonov unfoldingtechnique isthen explainedfollowed by
adiscussion ofthe systematicuncertainties. Results aregiven inthe lastsectiontogether
with a comparisonto other experiments and theoretical predictions.
2 The ALEPH Detector
A detailed description of the ALEPH detector and its performance can be found in
Refs. [15,16]. The centralpart of the ALEPH detector isdedicated tothe reconstruction
ofthetrajectoriesofchargedparticles. Thetrajectoryofachargedparticleemergingfrom
the interaction pointis measured by a two-layer silicon strip vertex detector (VDET), a
cylindrical drift chamber (ITC) and a large time projection chamber (TPC). The three
trackingdetectorsareplacedina1:5Taxialmagneticeldprovidedbyasuperconducting
solenoidal coil. Together they measure charged particle transverse momenta with a
resolution of Æp
t
=p
t
= 610 4
p
t
0:005 (p
t
in GeV/c). Photons are identied in the
electromagneticcalorimeter(ECAL), situatedbetweenthe TPCand thecoil. The ECAL
isalead/proportional-tubesamplingcalorimetersegmentedin0:9 Æ
0:9 Æ
projectivetowers
read out in three sections in depth. It has a total thickness of 22 radiation lengths and
yields a relativeenergy resolution of 0:18=
p
E +0:009 (E inGeV), for isolated photons.
Electrons are identied by their transverse and longitudinalshower prolesinthe ECAL
and their specic ionization in the TPC. The iron return yoke is instrumented with 23
layers of streamer tubes and formsthe hadron calorimeter (HCAL). The latter provides
arelativeenergyresolutionfor hadronsof 0:85=
p
E (E inGeV).Muons are distinguished
from hadrons by their characteristic pattern in HCAL and by the muon chambers,
composed of two double-layers of streamer tubes outside HCAL. The two luminosity
calorimeters, a silicon-tungsten detector (SiCAL) [17] and a lead/proportional wire
sampling calorimeter (LCAL), measure the energy of the scattered beam electrons and
cover the angular ranges of 24mrad <
tag
< 58mrad and 45mrad <
tag
< 160mrad.
The energy resolution is
E
=E =0:34=
p
E for SiCAL and
E
=E =0:0340:15=
p
E for
LCAL(E inGeV). Anenergy-owalgorithmcombinestheinformationfromthe tracking
detectorsandthecalorimeters[16]. Foreachevent,thealgorithmprovidesasetofcharged
and neutral reconstructed particles, called `energy-ow objects' inthe following.
Studies onthe trigger eÆciency have been performed indicatinga value of 100% over
thekinematicregionusedforthisanalysis[18]. Aconservativeestimatefortheuncertainty
onthis has been taken as 5% and 10% for the twoupper bins inthe Bjorken variable x.
The data used in this analysis were taken in the years 1998, 1999 and 2000 at dierent
centre-of-mass energies between p
s = 189GeV and p
s = 207GeV . Single tag events
are required to contain a single electron detected inthe luminosity calorimeters with an
energy of at least 70% of the beam energy. Although the silicon calorimeter covers a
range from 24mrad up to 58mrad, electrons are only detected for > 34mrad since
a tungsten shielding against backscattered synchrotron photons was introduced into its
acceptanceregionin1996. Inordertorejectdouble-tageventswherebothbeamelectrons
are detected, eventswith afurtherenergy-owobjectinthe luminositycalorimeterswith
morethan40%ofthebeamenergyareexcluded. Single-tageventscannotbedistinguished
from no-tag events with a \fake" tag produced by an o-momentum electron. This
backgroundcanbesuppressed bycuts inthe (;)plane fortaggedelectrons withenergy
less than 80% of E
beam
since o-momentum electrons are preferably emitted in the LEP
plane. Here isthe azimuthal angle and the angle between the scattered electron and
the beam direction. The cuts are shown in Fig. 1, from a comparison with Monte Carlo
simulationand the analysis ofangulardistributionsthe residualbackground isestimated
to be smaller than 1% [19]. In order to eliminate beam gas events, the reconstructed
interaction vertex is required tobe within 5cmin the z directionand 1cm inthe radial
directionof the nominal interaction point.
The data are analyzed separately for the centre-of-mass energies p
s = 189GeV,
p
s=196GeV, p
s=200GeV and p
s=205 207GeV becauseof dierentbackground
conditions and the dierent boosts of the hadronic system. The integrated luminosity
is listed in Table 1 which also shows the number of selected events and the cuts which
dene two bins in Q 2
. The boundary between the lower and the upper Q 2
range varies
with centre-of-mass energy andis chosen such that migrationbetween the two Q 2
-bins is
minimized.
The visiblehadronicnalstateisrequiredtoconsistofatleastthreechargedparticles
with aninvariantmass of atleast 3:5GeV=c 2
in thelowerQ 2
regionand 3GeV=c 2
inthe
upperQ 2
region. Eventswith particlesidentied aselectrons ormuonswith anenergyof
more than 2:5GeV in the nal state are rejected because they are more likely produced
in background processes than in the decay chain of hadronic nal state particles in
processes. It has been checked that these cuts do not aect the signal eÆciency, e.g.
events from open charm production are not rejected. The background from ! +
aswellas e +
e annihilationevents issimulatedand subtracted. The contamination from
!l
l isabout 4%inthe lowQ 2
region and7% inthe highQ 2
region. Thebackground
from annihilation events is between 0.4% and 1.5%. A detailed list of all investigated
background processescan be found inTable 2.
3.1 Unfolding Procedure
Inorder todeterminethe structurefunctionF
2
itisnecessary tomeasure thedierential
cross sectiond=dx. BothQ 2
and theinvariantmass ofthe hadronic system are aected
