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Fermi-Dirac Correlations in Λ Pairs in Hadronic Z Decays
R. Barate, D. Decamp, P. Ghez, C. Goy, J.P. Lees, F. Martin, E. Merle, M.N.
Minard, B. Pietrzyk, R. Alemany, et al.
To cite this version:
R. Barate, D. Decamp, P. Ghez, C. Goy, J.P. Lees, et al.. Fermi-Dirac Correlations in Λ Pairs in Hadronic Z Decays. Physics Letters B, Elsevier, 2000, 475, pp.395-406. �in2p3-00004624�
Fermi-Dirac Correlations in
Pairs in Hadronic Z Decays
The ALEPH Collaboration
)
CERN EP/99-172
8 December, 1999
Abstract
Two-particle correlationsofand
pairshave beenstudiedinmultihadronic
Zdecays recordedwiththeALEPH detectorat LEPintheyears from1992 to1995.
Thecorrelations were measuredas afunction of thefour-momentumdierence Q of
the pair. A depletion of events is observed in the region Q < 2 GeV which could
arisefrom theeects of Fermi-Dirac statistics. Inaddition thespincontent of the
pairsystemhasbeendetermined. ForQ>2GeV thefractionof pairswithspinone
isconsistent with thevalueof 0.75 expected fora statistical spinmixture,whilstfor
Q< 2 GeV thisfraction is found to be lower. For
pairs, where no Fermi-Dirac
correlationsareexpected,thespinonefractionismeasuredto beconsistentwith0.75
over theentireanalysedQrange.
(Submitted to Physics Letters B)
)Seenextpagesforthelistofauthors
R.Barate,D. Decamp,P.Ghez,C.Goy,J.-P.Lees,F.Martin, E.Merle,M.-N.Minard,B.Pietrzyk
Laboratoire de Physique des Particules (LAPP), IN 2
P 3
-CNRS, F-74019 Annecy-le-Vieux Cedex,
France
R. Alemany, S. Bravo,M.P.Casado, M.Chmeissani, J.M.Crespo, E. Fernandez, M.Fernandez-Bosman,
Ll.Garrido, 15
E. Grauges,A. Juste, M.Martinez, G. Merino, R. Miquel, Ll.M. Mir,A. Pacheco, I.Riu,
H.Ruiz
Institut de F
isica d'Altes Energies, Universitat Autonoma de Barcelona, E-08193 Bellaterra
(Barcelona),Spain 7
A. Colaleo, D. Creanza, M. de Palma, G. Iaselli, G. Maggi, M. Maggi, S. Nuzzo, A. Ranieri, G. Raso,
F.Ruggieri,G.Selvaggi,L.Silvestris,P.Tempesta,A.Tricomi, 3
G.Zito
Dipartimentodi Fisica,INFN SezionediBari,I-70126Bari,Italy
X.Huang,J.Lin,Q.Ouyang,T.Wang,Y.Xie,R. Xu,S. Xue,J.Zhang,L.Zhang,W.Zhao
InstituteofHigh-EnergyPhysics,Academia Sinica,Beijing,ThePeople'sRepublic ofChina 8
D. Abbaneo,G.Boix, 6
O.Buchmuller,M. Cattaneo,F.Cerutti, V.Ciulli,G.Dissertori, H. Drevermann,
R.W.Forty,M.Frank,T.C.Greening,A.W.Halley,J.B.Hansen,J.Harvey,P.Janot,B.Jost,I.Lehraus,
O. Leroy, P. Mato, A. Minten, A. Moutoussi, F. Ranjard, L. Rolandi, D. Schlatter, M. Schmitt, 20
O.Schneider, 2
P.Spagnolo,W. Tejessy,F.Teubert, E.Tourneer,A.E.Wright
EuropeanLaboratoryforParticlePhysics(CERN),CH-1211Geneva23,Switzerland
Z. Ajaltouni, F. Badaud, G. Chazelle, O. Deschamps, A. Falvard, C. Ferdi, P. Gay, C. Guicheney,
P.Henrard,J.Jousset,B.Michel,S. Monteil,J-C.Montret,D.Pallin,P.Perret,F.Podlyski
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,B.S.Nilsson,B.Rensch,A. Waananen
NielsBohrInstitute,DK-2100Copenhagen, Denmark 9
G.Daskalakis,A.Kyriakis,C.Markou,E.Simopoulou,I.Siotis,A. Vayaki
NuclearResearchCenterDemokritos(NRCD), GR-15310Attiki,Greece
A.Blondel,G.Bonneaud,J.-C.Brient,A. Rouge,M.Rumpf,M.Swynghedauw,M.Verderi,H.Videau
Laboratoire de Physique Nucleaire et des Hautes Energies, Ecole Polytechnique, IN 2
P 3
-CNRS,
F-91128PalaiseauCedex, France
E.Focardi,G.Parrini,K.Zachariadou
Dipartimentodi Fisica,UniversitadiFirenze, INFNSezionedi Firenze,I-50125Firenze, Italy
M.Corden,C.Georgiopoulos
Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL 32306-
4052,USA 13;14
A. Antonelli, G. Bencivenni, G. Bologna, 4
F. Bossi, P. Campana, G. Capon, V. Chiarella, P. Laurelli,
G.Mannocchi, 1;5
F.Murtas,G.P.Murtas,L.Passalacqua,M.Pepe-Altarelli
Laboratori Nazionalidell'INFN(LNF-INFN),I-00044Frascati,Italy
L.Curtis,J.G.Lynch,P.Negus,V.O'Shea,C.Raine,P.Teixeira-Dias,A.S.Thompson
DepartmentofPhysicsandAstronomy,UniversityofGlasgow,GlasgowG128QQ,UnitedKingdom 10
R. Cavanaugh,S. Dhamotharan,C.Geweniger, P. Hanke,G. Hansper,V. Hepp,E.E.Kluge, A.Putzer,
J.Sommer,K.Tittel,S. Werner, 19
M.Wunsch 19
InstitutfurHochenergiephysik,UniversitatHeidelberg,D-69120Heidelberg,Germany 16
R.Beuselinck,D.M.Binnie,W.Cameron,P.J.Dornan, 1
M.Girone,S.Goodsir,E.B.Martin,N.Marinelli,
A.Sciaba,J.K.Sedgbeer,E.Thomson,M.D. Williams
DepartmentofPhysics,Imperial College,LondonSW7 2BZ,UnitedKingdom 10
V.M.Ghete,P. Girtler,E.Kneringer,D. Kuhn,G.Rudolph
InstitutfurExperimentalphysik,UniversitatInnsbruck,A-6020Innsbruck,Austria 18
C.K. Bowdery, P.G. Buck, A.J. Finch, F. Foster, G. Hughes, R.W.L. Jones, N.A. Robertson,
M.I.Williams
DepartmentofPhysics,UniversityofLancaster,LancasterLA14YB,United Kingdom 10
I.Giehl,K.Jakobs,K.Kleinknecht,G.Quast,B.Renk,E.Rohne,H.-G.Sander,H.Wachsmuth,C.Zeitnitz
InstitutfurPhysik,UniversitatMainz,D-55099Mainz,Germany 16
J.J.Aubert,A. Bonissent,J.Carr,P.Coyle,P.Payre,D. Rousseau
CentredePhysiquedesParticules,FacultedesSciencesdeLuminy,IN 2
P 3
-CNRS,F-13288Marseille,
France
M.Aleppo,M.Antonelli,F.Ragusa
Dipartimentodi Fisica,UniversitadiMilano eINFN SezionediMilano,I-20133Milano,Italy
V.Buscher,H.Dietl,G.Ganis,K.Huttmann,G.Lutjens,C.Mannert,W.Manner,H.-G. Moser,S.Schael,
R.Settles, H.Seywerd,H.Stenzel,W. Wiedenmann,G.Wolf
Max-Planck-InstitutfurPhysik,Werner-Heisenberg-Institut,D-80805Munchen,Germany 16
P. Azzurri, J. Boucrot,O. Callot, S. Chen, A. Cordier, M. Davier, L.Duot, J.-F.Grivaz, Ph. Heusse,
A. Jacholkowska, 1
F. Le Diberder, J. Lefrancois, A.-M. Lutz, M.-H. Schune, J.-J.Veillet , I. Videau, 1
D. Zerwas
Laboratoiredel'AccelerateurLineaire,UniversitedeParis-Sud,IN 2
P 3
-CNRS,F-91898OrsayCedex,
France
G.Bagliesi,T.Boccali,C.Bozzi, 12
G.Calderini,R.Dell'Orso,I.Ferrante,L.Foa,A. Giassi,A.Gregorio,
F.Ligabue,P.S.Marrocchesi,A. Messineo,F.Palla,G.Rizzo,G.Sanguinetti,G.Sguazzoni,R.Tenchini,
A.Venturi,P.G.Verdini
Dipartimento di Fisica dell'Universita, INFN Sezione di Pisa, e Scuola Normale Superiore, I-56010
Pisa,Italy
G.A.Blair,G.Cowan,M.G.Green, T.Medcalf,J.A.Strong
DepartmentofPhysics,RoyalHolloway&BedfordNewCollege,UniversityofLondon,SurreyTW20
OEX,United Kingdom 10
D.R.Botterill,R.W.Clit,T.R.Edgecock,P.R. Norton,J.C.Thompson,I.R.Tomalin
ParticlePhysicsDept.,RutherfordAppletonLaboratory,Chilton,Didcot,OxonOX11OQX,United
Kingdom 10
B.Bloch-Devaux, P. Colas, S. Emery, W. Kozanecki, E. Lancon, M.-C.Lemaire, E. Locci, P. Perez,
J.Rander,J.-F.Renardy,A.Roussarie,J.-P.Schuller,J.Schwindling,A. Trabelsi, 21
B.Vallage
CEA, DAPNIA/Service de Physique des Particules, CE-Saclay, F-91191 Gif-sur-Yvette Cedex,
France 17
S.N. Black, J.H. Dann, R.P. Johnson, H.Y. Kim, N. Konstantinidis, A.M. Litke, M.A. McNeil,
G.Taylor
InstituteforParticlePhysics,UniversityofCaliforniaat SantaCruz,SantaCruz,CA95064,USA 22
C.N.Booth,S. Cartwright,F.Combley,M.Lehto, L.F.Thompson
10
FachbereichPhysik,UniversitatSiegen,D-57068Siegen,Germany 16
G.Giannini,B.Gobbo
Dipartimentodi Fisica,UniversitadiTrieste eINFN SezionediTrieste,I-34127Trieste,Italy
J.Rothberg,S. Wasserbaech
ExperimentalElementaryParticlePhysics,UniversityofWashington,WA98195Seattle,U.S.A.
S.R. Armstrong, P. Elmer, D.P.S. Ferguson, Y. Gao, S. Gonzalez, O.J. Hayes, H. Hu, S. Jin,
J. Kile, P.A. McNamara III, J. Nielsen, W. Orejudos, Y.B. Pan, Y. Saadi, I.J. Scott, J. Walsh,
J.H.vonWimmersperg-Toeller, SauLanWu,X.Wu, G.Zobernig
DepartmentofPhysics,UniversityofWisconsin, Madison,WI53706,USA 11
1
AlsoatCERN, 1211Geneva23, Switzerland.
2
NowatUniversitedeLausanne,1015Lausanne,Switzerland.
3
AlsoatCentroSicilianodiFisicaNucleareeStrutturadellaMateria,INFN,SezionediCatania,95129
Catania,Italy.
4
AlsoIstitutodiFisicaGenerale,UniversitadiTorino,10125Torino,Italy.
5
AlsoIstitutodiCosmo-GeosicadelC.N.R.,Torino,Italy.
6
SupportedbytheCommissionoftheEuropeanCommunities, contractERBFMBICT982894.
7
SupportedbyCICYT,Spain.
8
SupportedbytheNationalScienceFoundationofChina.
9
SupportedbytheDanishNaturalScience ResearchCouncil.
10
SupportedbytheUKParticlePhysicsand AstronomyResearchCouncil.
11
SupportedbytheUSDepartmentof Energy,grantDE-FG0295-ER40896.
12
NowatINFNSezione deFerrara,44100Ferrara,Italy.
13
SupportedbytheUSDepartmentof Energy,contractDE-FG05-92ER40742.
14
SupportedbytheUSDepartmentof Energy,contractDE-FC05-85ER250000.
15
Permanentaddress: UniversitatdeBarcelona,08208Barcelona,Spain.
16
SupportedbytheBundesministeriumfurBildung,Wissenschaft,ForschungundTechnologie,Germany.
17
SupportedbytheDirectiondesSciencesdelaMatiere,C.E.A.
18
SupportedbyFondszurForderungderwissenschaftlichenForschung,Austria.
19
NowatSAPAG,69185Walldorf,Germany.
20
NowatHarvardUniversity,Cambridge,MA02138,U.S.A.
21
NowatDepartementdePhysique,FacultedesSciencesdeTunis,1060LeBelvedere,Tunisia.
22
Studies of Bose-Einstein (BE) correlations of identical bosons and of Fermi-Dirac (FD)
correlationsofidenticalfermionsproducedinhighenergycollisionsprovidemeasurementsof
thedistributionofthe particlesourcesinspaceandtime. Thesecorrelationsoriginatefrom
the symmetrization or antisymmetrization of the two-particle wave functions of identical
particles and lead to an enhancement or a suppression of particle pairs produced close to
each other in phase space. This eect is sensitive tothe size of the source from which the
identicalparticlesofsimilarmomentaareemitted. Adescriptionofthetheorycanbefound
e.g., inreferences [1], [2]and [3].
Thispaperreportsonastudyof Fermi-Diraccorrelationsusingthe combinedsampleof
and
pairs (represented by () throughout this paper) reconstructed by ALEPH
in multihadronic Z decays at LEP 1. Section 2 summarizes the theory of Fermi-Dirac
correlations and the techniques used to study these correlations. Section 3 describes the
ALEPH detector and the selection of neutral decays. The results are presented in
Section4 and are followed by the conclusionsin Section5.
2 Theory
The strength of two-particle BE or FD correlation eects can be expressed in terms of a
two-particlecorrelation function C(p
1
;p
2
) dened as
C(p
1
;p
2
)=P(p
1
;p
2 )=P
0 (p
1
;p
2
); (1)
wherep
1 andp
2
arethefour-momentaofthe particles,P(p
1
;p
2
)isthemeasureddierential
cross section for the pairs and P
0 (p
1
;p
2
) is that of a reference sample, which is free of BE
or FD correlations but otherwise identical in all aspects to the data sample. The main
experimental diÆculty is to dene an appropriate reference sample P
0 (p
1
;p
2
) in order to
determinethat partof P(p
1
;p
2
)whichcan beattributed totheBE orFDcorrelations. An
example for such a reference sample is given by the JETSET Monte Carlo [4] for which
productionofhadronsissimulatedwithouttakingintoaccountBEorFDcorrelationeects.
The correlation function C is usually measured as a function of the Lorentz invariant
Q with Q 2
= (p
1 p
2 )
2
. For Q 2
= 0 the eects of BE and FD correlations reach their
extremevalues. VariousparametrisationsforC(Q)areproposedintheliterature. Herethe
GGLPparametrisation[5]
C(Q)=N[1+exp ( R 2
Q 2
)] (2a)
isused, together with analternative parametrisation[6]
C(Q)=N[1+exp ( R Q)] (2b)
density distribution in the rest frame of the emitted pair. The free parameters are the
normalisation N, the suppression parameter (jj 1) and the radius R , which can
be identied with the space-time extent of the source. In two-boson systems a value of
= 1 corresponds to a completely incoherent emission; jj is expected to be dierent
from unity if sources of dierent radii (for example, due to dierent resonance lifetimes)
contributetotheemissionofthe pairs[7]orif theparticleshavenon-zero spinasexplained
below. This parameter also accomodates for experimental backgrounds such as particle
misidentication.
Thetotalwavefunctiondescribingthenalstateoftwoidenticalparticlesmustbeeither
symmetric(s)or antisymmetric(a)under the exchange of the two particles, dependingon
thespinstatisticsofthe particles. Inthelimitofplanewaves(i.e., neglectingcontributions
frompossible nal state interactions) this leads to[8]
j
s;a j
2
=1cos [(p
1 p
2 )(r
1 r
2
)]; (3)
wheres (a) corresponds tothe + ( ) sign and r
1;2
are the four-vector positionsof the two
particles. In the case of identical spinless bosons,
s
completely describes the nal state,
whereas in the case of identical fermions both
s and
a
can contribute.
Since P
s;a (p
1
;p
2
) is proportional to the integral R
dr
1 dr
2 g(r
1
;r
2
;p
1
;p
2 )j
s;a j
2
, where
g(r
1
;r
2
;p
1
;p
2
) describes the source intensity and the integral is taken over the relative
space-time distances r
1 r
2
of the particleemission points,it follows that the correlation
functionC
s;a (p
1
;p
2
) forthe symmetric (antisymmetric) nal state should show anincrease
(decrease) forQ!0.
Foridenticalbosonswithspinoridenticalfermions,e.g.,two's,onehasalsotoconsider
their spin. For the () system the total spin may be S = 0 or S = 1 with spin wave
functions s
0
and s i
1
, where i = 1;0;1 are the eigenvalues of the third component of the
totalspin;s
0
isantisymmetricwhereas the s i
1
are symmetricunder theexchangeof thetwo
's. Asthe totalwavefunctionforthe()system isantisymmetric,s
0
must becombined
with
s
fromEq. 3 and the s i
1 with
a
to yieldantisymmetric wave functions:
0
=
s s
0
and i
1
=
a s
i
1
. In generalboth
0
and the i
1
can contribute toP(p
1
;p
2
),depending on
the source. However for a statistical spin mixture ensemble, where each of the four spin
states s
0
and s i
1
is emitted with the same probability, the contributions from the i
1 will
dominate by a factor of 3 and thus the correlation function C(Q) is expected to decrease
to0:5 as Q tends tozero.
A dierent way of investigatingthe () correlations is provided by the measurement
ofthe spin compositionof the() system, thatis todeterminethe fractions ofthe S=0
and S = 1 states. The method used in this paper was proposed in Ref. [9] and is based
on the measurement of the distribution dN=dy
in the di-hyperon centre-of-mass system.
In this system the momenta of the decay protons (antiprotons) of the () system are
transformed into their parent hyperon rest frames and y
is then the cosine of the angle
distributionsfor the S =0and S=1 states of asystem of identical hyperons are
dN=dy
j
S=0
= (N=2)(1 2
y
) (4a)
and
dN=dy
j
S=1
= (N=2)(1+( 2
=3)y
) (4b)
where
=
= 0:6420:013 is the decay asymmetry parameter [11]. In general
both spin states willcontribute. If the parameter " is dened as the fraction of the S =1
contribution, then " can be measured asa function of Q by tting the expression
dN=dy
=(1 ")dN=dy
j
S=0
+"dN=dy
j
S=1
(4c)
tothemeasureddistributionforagivenrangeofQ. Inthecaseofastatisticalspinmixture,
" is equal to 0.75 which results in a constant distribution for dN=dy
. The advantage of
this methodis that areference sample is not needed. In Ref. [9] the relation in Eq. 4 was
derivedforthedi-hyperonthresholdand alsoshown toholdapproximatelyforlowvaluesof
Q,where the relativemomentum of the two 's isnon-relativistic. Itwas recently pointed
out, however, that the validity range for Eq. 4can beextended toany Qvalue [12].
The correlation function C(Q) and the spin composition "(Q) yield dierent
measurements which are sensitive to the same physicaleect. If a source only emitteddi-
hyperons inatotal spinstateS =1orS=0,then"(Q)would beoneorzero,respectively,
independent of Q, whereas the correlation function C(Q) is still expected to show a Q
dependence.
Thequantity"(Q)canalsobeusedtoestimatethe sizeR ofthesource[12]. IfC(Q)
S=0
andC(Q)
S=1
are respectivelythe contributions ofthe S =0and the S =1statestoC(Q),
then for a statistical spin mixture ensemble C(Q)
S=0
and C(Q)
S=1
can be parametrised
with the formulaof Eq. 2a as
C(Q)
S=0
= 0:25N(1+exp ( R 2
Q 2
))
and
C(Q)
S=1
= 0:75N(1 exp ( R 2
Q 2
))
with jj1. With"(Q)=C(Q)
S=1
=(C(Q)
S=0
+C(Q)
S=1
) one nds
"(Q)=0:75(1 exp ( R 2
Q 2
))/(1 0:5exp ( R 2
Q 2
)); (5)
where the suppression parameter = 2 results from the requirement C(Q)
S=0 +
C(Q)
S=1
=C(Q), with C(Q) dened in Eq. 2a. In the ideal case C(Q)
S=1
is expected to
decrease to zero as Q tends to zero which implies =1. But due to the eects described
beforein connection withEq. 2, can deviate from one.
The ALEPH detector is described in detail elsewhere [13]. This analysis relies mainly on
the information from three concentric tracking detectors, a 1.8 m radius time projection
chamber (TPC) surrounding a small conventional drift chamber (ITC) and a two layer
siliconvertex detector (VDET).The TPC provides up to21 space pointspertrack and in
additionup to338samples ofthe particle's specic ionisation. TheITC measures8 points
per track and the VDET provides two high precision space points on the track near the
primary vertex. The tracking detectors are located inan axialmagnetic eld of 1.5Tand
have a combined track transverse momentum resolution of p
?
=p
?
= 0:0006p
?
0:005
(withp
?
inGeV=c).
The analysis was performed on data collected on and around the Z peak. The event
sample consists of a total of 3.9 million hadronic events corresponding to an integrated
luminosity of 142 pb 1
. A sample of 6.5 million Monte Carlo events with full detector
simulation [13], based on the JETSET 7.4 [4] generator, was used to provide a reference
sample and to calculate the selection eÆciencies as described in Section 4. This Monte
Carlosample does not includeBE orFD correlations.
Hadronic events were required to contain at least ve well reconstructed tracks. Each
such track must haveat least four TPC hits and apolarangle inthe range jcosj<0:95.
The pointof closest approachof the reconstructed tracks tothe beamaxis must bewithin
10 cmof the nominal interaction point along the beam direction and within 2 cm of it in
the plane transverse to the beam. The total energy of all tracks satisfyingthe above cuts
isrequired tobeat least 10% of the centre-of-mass energy.
Forthe selectionof the neutralV 0
decays (see alsoRef.[14])allcombinationsof tracks
with opposite charge and with momenta higher than 150 MeV are examined. Both tracks
mustoriginatefromacommonsecondary vertex with acceptable 2
. Forthe nalselection
and for the assignment of the dierent hypotheses K 0
, and
, the most importantcuts
are given below:
a) A 2
testofenergy-momentumconservationforagivenhypothesis,assumingthatthe
decayingparticleisproducedatthe primaryvertex andthatitdecaysatasecondary
vertex [15].
b) Cuts on the impact parameter D of the secondary tracks from the V 0
decay with
respect to the primary vertex. If D
r
is the component of D in the direction
perpendicular to the beam axis and D
z
is the component of D in the direction of
the beam axis then two cuts for each secondary V 0
track are applied: (D
r
=
r )
2
> 4
and (D
z
=
z )
2
>4,where
r
and
z
are the uncertainties on D
r
and D
z .
c) For V 0
candidates with tracks having a good dE=dx measurement, the ionisation is
requiredtobewithinthreestandarddeviationsofthatexpectedforagivenhypothesis.
