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Masses, lifetimes and production rates of Ξ − and Ξ ¯ + at LEP 1
DELPHI Collaboration
J. Abdallah
ab, P. Abreu
y, W. Adam
be, P. Adzic
n, T. Albrecht
t, T. Alderweireld
b,c,d,
R. Alemany-Fernandez
l, T. Allmendinger
t, P.P. Allport
z, U. Amaldi
af, N. Amapane
ax, S. Amato
bb, E. Anashkin
am, A. Andreazza
ae, S. Andringa
y, N. Anjos
y, P. Antilogus
ab, W.-D. Apel
t, Y. Arnoud
q,
S. Ask
ac, B. Asman
aw, J.E. Augustin
ab, A. Augustinus
l, P. Baillon
l, A. Ballestrero
ay, P. Bambade
w, R. Barbier
ad, D. Bardin
s, G.J. Barker
t, A. Baroncelli
ap, M. Battaglia
l, M. Baubillier
ab, K.-H. Becks
bg, M. Begalli
h,i,j, A. Behrmann
bg, E. Ben-Haim
w, N. Benekos
ai, A. Benvenuti
g, C. Berat
q, M. Berggren
ab, L. Berntzon
aw, D. Bertrand
b,c,d, M. Besancon
aq, N. Besson
aq, D. Bloch
m,
M. Blom
ah, M. Bluj
bf, M. Bonesini
af, M. Boonekamp
aq, P.S.L. Booth
z,, G. Borisov
x, O. Botner
bc, B. Bouquet
w, T.J.V. Bowcock
z, I. Boyko
s, M. Bracko
at,au,av, R. Brenner
bc, E. Brodet
al, P. Bruckman
u, J.M. Brunet
k, B. Buschbeck
be, P. Buschmann
bg, M. Calvi
af, T. Camporesi
l, V. Canale
ao, F. Carena
l, N. Castro
y, F. Cavallo
g, M. Chapkin
as, Ph. Charpentier
l, P. Checchia
am,
R. Chierici
l, P. Chliapnikov
as, J. Chudoba
l, S.U. Chung
l, K. Cieslik
u, P. Collins
l, R. Contri
p, G. Cosme
w, F. Cossutti
az,ba, M.J. Costa
bd, D. Crennell
an, J. Cuevas
ak, J. D’Hondt
b,c,d, J. Dalmau
aw, T. da Silva
bb, W. Da Silva
ab, G. Della Ricca
az,ba, A. De Angelis
az,ba, W. De Boer
t, C. De Clercq
b,c,d,
B. De Lotto
az,ba, N. De Maria
ax, A. De Min
am, L. de Paula
bb, L. Di Ciaccio
ao, A. Di Simone
ap, K. Doroba
bf, J. Drees
bg,l, G. Eigen
f, T. Ekelof
bc, M. Ellert
bc, M. Elsing
l, M.C. Espirito Santo
y,
G. Fanourakis
n, D. Fassouliotis
n,e, M. Feindt
t, J. Fernandez
ar, A. Ferrer
bd, F. Ferro
p, U. Flagmeyer
bg, H. Foeth
l, E. Fokitis
ai, F. Fulda-Quenzer
w, J. Fuster
bd, M. Gandelman
bb, C. Garcia
bd, Ph. Gavillet
l, E. Gazis
ai, R. Gokieli
l,bf, B. Golob
at,au,av, G. Gomez-Ceballos
ar, P. Goncalves
y, E. Graziani
ap, G. Grosdidier
w, K. Grzelak
bf, J. Guy
an, C. Haag
t, A. Hallgren
bc, K. Hamacher
bg, K. Hamilton
al, S. Haug
aj, F. Hauler
t, V. Hedberg
ac, M. Hennecke
t, H. Herr
l,,
J. Hoffman
bf, S.-O. Holmgren
aw, P.J. Holt
l, M.A. Houlden
z, J.N. Jackson
z, G. Jarlskog
ac, P. Jarry
aq, D. Jeans
al, E.K. Johansson
aw, P.D. Johansson
aw, P. Jonsson
ad, C. Joram
l,
L. Jungermann
t, F. Kapusta
ab, S. Katsanevas
ad, E. Katsoufis
ai, G. Kernel
at,au,av, B.P. Kersevan
l,at,au,av, U. Kerzel
t, B.T. King
z, N.J. Kjaer
l, P. Kluit
ah, P. Kokkinias
n, C. Kourkoumelis
e, O. Kouznetsov
s, Z. Krumstein
s, M. Kucharczyk
u, J. Lamsa
a, G. Leder
be, F. Ledroit
q, L. Leinonen
aw, R. Leitner
ag, J. Lemonne
b,c,d, V. Lepeltier
w, T. Lesiak
u, W. Liebig
bg,
D. Liko
be, A. Lipniacka
aw, J.H. Lopes
bb, J.M. Lopez
ak, D. Loukas
n, P. Lutz
aq, L. Lyons
al, J. MacNaughton
be, A. Malek
bg, S. Maltezos
ai, F. Mandl
be, J. Marco
ar, R. Marco
ar, B. Marechal
bb,
M. Margoni
am, J.-C. Marin
l, C. Mariotti
l, A. Markou
n, C. Martinez-Rivero
ar, J. Masik
o, N. Mastroyiannopoulos
n, F. Matorras
ar, C. Matteuzzi
af, F. Mazzucato
am, M. Mazzucato
am, R. Mc Nulty
z, C. Meroni
ae, E. Migliore
ax, W. Mitaroff
be, U. Mjoernmark
ac, T. Moa
aw, M. Moch
t, K. Moenig
l,1, R. Monge
p, J. Montenegro
ah, D. Moraes
bb, S. Moreno
y, P. Morettini
p, U. Mueller
bg, K. Muenich
bg, M. Mulders
ah, L. Mundim
h,i,j, W. Murray
an, B. Muryn
v, G. Myatt
al, T. Myklebust
aj,
M. Nassiakou
n, F. Navarria
g, K. Nawrocki
bf, R. Nicolaidou
aq, M. Nikolenko
s,m, P. Niss
aw,
0370-2693©2006 Elsevier B.V.
doi:10.1016/j.physletb.2006.06.029
Open access under CC BY license.
A. Oblakowska-Mucha
v, V. Obraztsov
as, A. Olshevski
s, A. Onofre
y, R. Orava
r, K. Osterberg
r, A. Ouraou
aq, A. Oyanguren
bd, M. Paganoni
af, S. Paiano
g, J.P. Palacios
z, H. Palka
u,
Th.D. Papadopoulou
ai, L. Pape
l, C. Parkes
aa, F. Parodi
p, U. Parzefall
l, A. Passeri
ap, O. Passon
bg, L. Peralta
y, V. Perepelitsa
bd, A. Perrotta
g, A. Petrolini
p, J. Piedra
ar, L. Pieri
ap, F. Pierre
aq, M. Pimenta
y, E. Piotto
l, T. Podobnik
at,au,av, V. Poireau
l, M.E. Pol
h,i,j, G. Polok
u, V. Pozdniakov
s,
N. Pukhaeva
b,c,d,s, A. Pullia
af, J. Rames
o, A. Read
aj, P. Rebecchi
l, J. Rehn
t, D. Reid
ah, R. Reinhardt
bg, P. Renton
al, F. Richard
w, J. Ridky
o, M. Rivero
ar, D. Rodriguez
ar, A. Romero
ax, P. Ronchese
am, P. Roudeau
w, T. Rovelli
g, V. Ruhlmann-Kleider
aq, D. Ryabtchikov
as, A. Sadovsky
s,
L. Salmi
r, J. Salt
bd, C. Sander
t, A. Savoy-Navarro
ab, U. Schwickerath
l, R. Sekulin
an, M. Siebel
bg, A. Sisakian
s, G. Smadja
ad, O. Smirnova
ac, A. Sokolov
as, A. Sopczak
x, R. Sosnowski
bf, T. Spassov
l, M. Stanitzki
t, A. Stocchi
w, J. Strauss
be, B. Stugu
f, M. Szczekowski
bf, M. Szeptycka
bf,
T. Szumlak
v, T. Tabarelli
af, A.C. Taffard
z, F. Tegenfeldt
bc, J. Timmermans
ah,∗, L. Tkatchev
s, M. Tobin
z, S. Todorovova
o, B. Tome
y, A. Tonazzo
af, P. Tortosa
bd, P. Travnicek
o, D. Treille
l, G. Tristram
k, M. Trochimczuk
bf, C. Troncon
ae, M.-L. Turluer
aq, I.A. Tyapkin
s, P. Tyapkin
s,
S. Tzamarias
n, V. Uvarov
as, G. Valenti
g, P. Van Dam
ah, J. Van Eldik
l, N. van Remortel
r, I. Van Vulpen
l, G. Vegni
ae, F. Veloso
y, W. Venus
an, P. Verdier
ad, V. Verzi
ao, D. Vilanova
aq, L. Vitale
az,ba, V. Vrba
o, H. Wahlen
bg, C. Walck
aw, A.J. Washbrook
z, C. Weiser
t, D. Wicke
l,
J. Wickens
b,c,d, G. Wilkinson
al, M. Winter
m, M. Witek
u, O. Yushchenko
as, A. Zalewska
u, P. Zalewski
bf, D. Zavrtanik
at,au,av, V. Zhuravlov
s, N.I. Zimin
s, A. Zintchenko
s, M. Zupan
naDepartment of Physics and Astronomy, Iowa State University, Ames, IA 50011-3160, USA bPhysics Department, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
cIIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium
dFaculté des Sciences, Université de l’Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium ePhysics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece fDepartment of Physics, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway gDipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy
hCentro Brasileiro de Pesquisas Físicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil iDepartamento de Física, Pont. Universidade Católica, C.P. 38071, BR-22453 Rio de Janeiro, Brazil jInstituto de Física, Universidade Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil
kCollège de France, Laboratoire de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris cedex 05, France lCERN, CH-1211 Geneva 23, Switzerland
mInstitut de Recherches Subatomiques, IN2P3-CNRS/ULP-BP20, FR-67037 Strasbourg cedex, France nInstitute of Nuclear Physics, NCSR Demokritos, PO Box 60228, GR-15310 Athens, Greece
oFZU, Institute of Physics of the CAS High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic pDipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy qInstitut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, FR-38026 Grenoble cedex, France rHelsinki Institute of Physics and Department of Physical Sciences, PO Box 64, FIN-00014 University of Helsinki, Finland
sJoint Institute for Nuclear Research, Dubna, Head Post Office, PO Box 79, RU-101 000 Moscow, Russian Federation tInstitut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany
uInstitute of Nuclear Physics PAN, ul. Radzikowskiego 152, PL-31142 Krakow, Poland
vFaculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland wUniversité de Paris-Sud, Laboratoire de l’Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, FR-91405 Orsay cedex, France
xSchool of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK yLIP, IST, FCUL-Av. Elias Garcia, 14-1◦, PT-1000 Lisboa Codex, Portugal zDepartment of Physics, University of Liverpool, PO Box 147, Liverpool L69 3BX, UK aaDepartment of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, UK abLPNHE, IN2P3-CNRS, Université Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris cedex 05, France
acDepartment of Physics, University of Lund, Sölvegatan 14, SE-223 63 Lund, Sweden adUniversité Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne cedex, France aeDipartimento di Fisica, Università di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy afDipartimento di Fisica, Università di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 2, IT-20126 Milan, Italy
agIPNP of MFF, Charles University, Areal MFF, V Holesovickach 2, CZ-180 00, Praha 8, Czech Republic ahNIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands
aiNational Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece ajPhysics Department, University of Oslo, Blindern, NO-0316 Oslo, Norway
akDepartamento de la Fisica, Universidad Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spain alDepartment of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK amDipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy
anRutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK
aoDipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy apDipartimento di Fisica, Università di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy
aqDAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette cedex, France arInstituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain asInstitute for High Energy Physics, Serpukov, PO Box 35, Protvino, Moscow Region, Russian Federation
atJ. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
auLaboratory for Astroparticle Physics, University of Nova Gorica, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia avDepartment of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
awFysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden
axDipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy ayINFN, Sezione di Torino and Dipartimento di Fisica Teorica, Università di Torino, Via Giuria 1, IT-10125 Turin, Italy
azDipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy baIstituto di Fisica, Università di Udine, IT-33100 Udine, Italy
bbUniversidade Federal do Rio de Janeiro, C.P. 68528 Cidade Universidade, Ilha do Fundão, BR-21945-970 Rio de Janeiro, Brazil bcDepartment of Radiation Sciences, University of Uppsala, PO Box 535, SE-751 21 Uppsala, Sweden
bdIFIC, Valencia-CSIC, and DFAMN, Universidade de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain beInstitut für Hochenergiephysik, Österreich Akademie der Wissenschaft, Nikolsdorfergasse 18, AT-1050 Vienna, Austria
bfInstitute Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland bgFachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany
Received 23 May 2006; accepted 16 June 2006 Available online 23 June 2006
Editor: M. Doser
Abstract
Measurements of theΞ−andΞ¯+masses, mass differences, lifetimes and lifetime differences are presented. TheΞ¯+sample used is much larger than those used previously for such measurements. In addition, theΞ production rates inZ→bb¯andZ→qq¯ events are compared and the positionξ∗of the maximum of theξdistribution inZ→qq¯events is measured.
©2006 Elsevier B.V.
1. Introduction
This Letter presents measurements of the masses and mean lifetimes ofΞ− andΞ¯+and of their mass and lifetime differ- ences, together with a study ofΞ−2production inZ0hadronic decays.
Previous measurements of theΞ¯+mass and mean lifetime suffer from low statistics compared toΞ−measurements, since they came from bubble chamber or hyperon beam experiments with a large asymmetry in the production ofΞ−andΞ¯+. The Particle Data Group[1]lists only∼80 events used for measure- ment of theΞ¯+mass and 34 for its mean lifetime, compared to
∼2400 events for theΞ−mass and∼87 000 for its mean life- time. The present analysis uses about 2500Ξ−and 2300Ξ¯+, with small backgrounds. The symmetry in the production of particles and antiparticles inZ0decays makes direct measure- ments ofΞ−andΞ¯+mass and lifetime differences with high precision feasible. A non-zero value of either difference would signal violation of CPT invariance.
A comparison of theΞ production rates in Z0→bb¯ and Z0→qq¯events is also presented, together with a measurement
* Corresponding author.
E-mail address:[email protected](J. Timmermans).
1 Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany.
Deceased.
2 Antiparticles are implicitly included unless explicitly stated otherwise.
of the position ξ∗ of the maximum of the distribution inξ =
−lnxp, wherexpis the fractionalΞ momentum.
2. The DELPHI detector and event selection
The DELPHI detector is described elsewhere[2,3]. The de- tectors most important for this analysis are the Vertex Detector (VD), the Inner Detector (ID), the Time Projection Chamber (TPC), and the Outer Detector (OD). The VD consists of three concentric layers of silicon strip detectors, located at radii of 6, 9 and 11 cm. The data used here were taken in 1992–1995 in- clusive, when the polar angles covered for particles crossing all three VD layers were 43◦< θ <137◦, whereθis given with re- spect to thezaxis.3In 1994 and 1995, the first and third layers had double-sided readout and gave bothRφandzcoordinates.
The TPC is the main tracking device where charged-particle tracks are reconstructed in three dimensions for radii between 29 cm and 122 cm. The ID and OD are two drift chambers lo- cated at radii between 12 cm and 28 cm and between 198 cm and 206 cm respectively, and provide additional points for the track reconstruction.
3 In the standard DELPHI coordinate system, thezaxis is along the electron direction, thexaxis points towards the centre of LEP, and theyaxis points up- wards. The polar angle to thezaxis is calledθand the azimuthal angle around thezaxis is calledφ; the radial coordinate isR=
x2+y2. Open access under CC BY license.
A charged particle was accepted in the analysis if its track length was above 30 cm, its momentum above 100 MeV/c, and its relative momentum error below 100%.
An event was classified as hadronic if it had at least 7 charged particles with momentum above 200 MeV/ccarrying more than 15 GeV reconstructed energy in total and at least 3 GeV in each hemisphere defined with respect to thezaxis.
The analysis used 3.25 million reconstructed hadronic de- cays of the Z, consisting of 0.67 million from the 1992 run, 0.68 million from 1993, 1.29 million from 1994, and 0.61 mil- lion from 1995.
Simulated events were produced using the JETSET parton shower generator [4], and then processed with the DELPHI event simulation programDELSIM[3]which fully simulates all detector effects. For each of the years 1992 to 1994, about 1 million fully simulatedqq¯ events were analyzed in the same way as the real data, and about 0.6 million for 1995. The to- tal number of simulated events used was thus about 3.6 million, comparable to the number of real events. The number ofΞ− andΞ¯+decays generated in the simulation was about 89 000.
3. Analysis
TheΞ−hyperon was studied by a complete reconstruction of the decay chain Ξ−→Λπ−, where Λ→pπ−. A simi- lar analysis procedure was used previously for−reconstruc- tion[5].
All pairs of oppositely-charged particles were tried in a search for Λ candidates. For each such pair, a vertex fit was performed by the standard DELPHIV0search algorithm4[3].
A pair was accepted as aΛcandidate if theχ2-probability of the secondary vertex fit exceeded 0.1%, the measured flight dis- tance from the primary vertex of the Λ candidate in the xy plane exceeded twice its error, and the angle between the mo- mentum vector sum of the two tracks and the vector joining the primary and secondary vertices was less than 0.1 radians (the loss of signal due to this cut has been shown to be negligible).
The inclusiveΛreconstruction efficiency was around 19%[3], including the 63.9% branching ratio ofΛ→pπ−[1]. The in- variant mass of the Λ candidate was required to be between 1.105 and 1.125 GeV/c2.
One by one, the remaining tracks of charged particles that crossed the Λtrajectory in the xy plane were then combined with the Λ candidate to form aΞ− candidate. AllΞ− were assumed to originate from the beam interaction point, which was calculated event by event.
A constrained fit was performed if:
• the intersection between the Λ and the charged particle trajectory was more than 8 mm away from the main vertex in thexyplane;
4 AV0consists of two oppositely charged particles originating from a neutral particle decaying in flight.
• the Λ and charged particle trajectories were less than 7 mm apart in the zdirection at the point of crossing in the xyplane;
• and the charged particle had an impact parameter with re- spect to the main vertex in thexyplane of at least 0.5 mm.
The fit used was a general least squares fit with kinemati- cal and geometrical constraints applied to eachΞ−candidate.
The 16 measured variables in the fit were the five parameters of the helix parameterization of each of the three charged par- ticle tracks and thezcoordinate of the beam interaction point (thex andy coordinates were so precisely measured that they could be taken as fixed). The two unmeasured variables were the decay radii of theΞ−andΛ. TheΞ−decay point was then determined from thisΞ− decay radius and the π− trajectory while theΛdecay point was determined from the point on the proton trajectory at theΛdecay radius. The curvedΞ−track was not measured, but calculated in the fit.
Four constraints required the momenta of the Ξ− and Λ at their decay points to be in the same direction as the trajec- tory joining their production and decay positions, two required the other π− to meet the proton at the Λ decay radius, and the last (seventh) constrained theΛmass to its nominal value (1115.684±0.006)MeV/c2. For further details concerning the fitting procedure, see[6].
The pull distributions of the 16 fitted quantities were all ap- proximately normally distributed, with mean 0 within±0.1 and standard deviation 1 within±0.1, both for data and for the sim- ulated events.
The following cuts were used to select theΞ−andΞ¯+sam- ples:
• theχ2-probability of the fit had to exceed 1%;
• theΞ momentum,pΞ, had to fulfill 1.2< ξ <4.2 where ξ= −lnxp andxp=pΞ/pbeam; this corresponds to 0.015<
xp<0.3 or 0.7< pΞ<14 GeV/c;
• theΞ momentum had to point into the barrel region of the detector (|cosθ|<0.85);
• the decay radius of theΞ in thexy plane had to exceed 2 cm;
• the decay radius of theΞ in thexy plane had to be less than theΛdecay radius.
Fig. 1shows the right-sign (Λπ−andΛπ¯ +) mass distribu- tions and theΞ signals before and after the cuts were applied.
Apart from a difference in mass resolution, the agreement be- tween data and simulation was very good. The distributions of the variables used in the selection ofΞ candidates are shown in Fig. 2for wrong-sign (Λπ+andΛπ¯ −) as well as for right-sign (Λπ−andΛπ¯ +) combinations.
The fit gave a narrow mass peak fromΞ decays on a small background, as shown inFig. 3(a); 2478±68Ξ−and 2256± 63 Ξ¯+ decays were reconstructed, as shown in Figs. 3(b) and (c). The fitted curves consist of a linear term for the back- ground, and two Gaussian distributions with common mean for the signal. TheΞ mass resolution depends on momentum.
Therefore the signal is, in principle, the sum of an infinite num-
Fig. 1. The right-sign (Λπ−andΛπ¯ +) mass distribution with theΞ(Ξ−andΞ¯+added) signals in differentχ2probability bins for data and simulation. The data are represented by the points with error bars and the simulation by the histograms, which are normalized to the same number of entries: (a) shows theΞ signal without any other cuts applied for events with aχ2fit probability below 1%, (b) shows theΞsignal without any other cuts applied for events with aχ2fit probability above 1%, (c) shows theΞsignal after all cuts given in the text were applied for events with aχ2fit probability above 1%.
ber of Gaussians. But two give a reasonably good fit. The fitted widths of the two Gaussians were (2.0±0.1) MeV/c2 and (5.6±0.4)MeV/c2, with a relative fraction of 1.29±0.18.
The corresponding widths from fitting simulated data were (1.8±0.1) MeV/c2 and (5.5±0.5) MeV/c2, with a rela- tive fraction of 2.01±0.27. This parameterization of signal and background was used in the determination of theΞ−and Ξ¯+masses.
The only possible physical background is the decay±→ ΛK±. The number of − reconstructed in our Ξ− analysis is estimated to be at most five, and consequently to have no significant influence.
3.1. Measurement ofΞ−andΞ¯+masses and mass difference Table 1gives the fitted mass and mass difference values for the real data. As already described, the signal (seeFig. 3) was represented by two Gaussian distributions with common mean and the background by a linear term.
In order to correct for any bias due to the data processing or to the analysis and fit procedure, the mass values obtained
from the data were corrected by the difference between the val- ues obtained in the same way from the simulated events and the input value used in the simulation (1321.3 MeV/c2). As no ef- fect could be identified that might affect theΞ−andΞ¯+masses differently, the correction was calculated once for each year, us- ing the corresponding fully simulatedΞ±sample.Table 1also shows these corrections, and the corrected mass values. The statistical errors of the corrected values contain the statistical errors of the simulation.
TheΞ±mass value averaged over all years was(1321.45± 0.05) MeV/c2 with a χ2 probability for the combination of 33% before correction, and(1321.35±0.06)MeV/c2 with a χ2probability of 17% after correction. Thus the average cor- rection amounted to(−0.10±0.04)MeV/c2.
3.1.1. Mass scale calibration
The mass scale was calibrated by determining theΛandKs0 masses in the same way, and comparing the resulting values with the known values [1]. TheΛ andKs0 samples used for this purpose were spread over each whole year and their sizes
Fig. 2. All the variables used in theΞselection for candidates in the mass intervalMΞ±5 MeV/c2. The histograms are from the simulation and the points with error bars are the data. The years 1992 to 1995 have all been added, both for data and simulation. The simulation histograms are normalized to the data ones.
All variables are shown for right-sign (Λπ−andΛπ¯ +) and wrong-sign (Λπ+andΛπ¯ −) combinations after all cuts have been made: (a), (b)χ2probability, (c), (d)ξ= −ln(pΞ/pbeam), (e), (f) cosine of the polar angleθof theΞmomentum, (g), (h) flight distance of theΞin thexyplane, (i), (j) distance in thexy plane between theΛandΞdecay points.
were restricted to make it possible to use the same signal and background parameterizations as for theΞ.5
TheΛandKs0decays were reconstructed by considering all pairs of oppositely charged particles, and the vertex defined by each pair was determined by minimizing theχ2of the extrapo- lated tracks. Consequently, this was a purely geometrical vertex fit, as opposed to the mass-constrained fit described above for theΞ candidates. The measuredΛandKs0mass offsets from their nominal values are shown inTable 2.
5 The reconstructedΛsamples were typically twice as large as the recon- structedΞsamples while theKs0samples were typically 10 times larger.
The widths of theΛandKs0mass distributions are somewhat larger for data than for simulation. A study was made in which the reconstructed variables in simulation, one by one, were ar- tificially “smeared” and a corresponding extra measurement er- ror added, such that the width of the mass peak in simulation agreed with that in the data. The spreads of the shifts obtained by smearing different variables, amounting to 0.05 MeV/c2for K0and 0.04 MeV/c2forΛ, were included in the errors for the corrected offsets quoted inTable 2. However, the means of the mass values from the smearings agreed with the “unsmeared”
values.
Offsets of the correctedΛandKs0mass values from their known values can arise from an error in the correction for dE/dxlosses, an error in the assumed magnetic field, or, most likely, a combination of the two.
Fig. 3. 1992–1995 data: (a) theΞ− andΞ¯+ sample, (b) theΞ− sample, (c) theΞ¯+ sample, The points with error bars show the right-sign (Λπ−,Λπ¯ +) combinations. The wrong-sign (Λπ+,Λπ¯ −) combinations are shown as the shaded histograms. The curves show the fits to theΞmass distributions described in the text (solid line).
Table 1
Ξ−andΞ¯+mass fit results. Values are in MeV/c2. In the simulated (‘MC’) sample, the generatedΞ−mass was 1321.3 MeV/c; the corresponding mass shifts per year are used to correct the mass values found in the data. The errors are statistical only
Year 1992 1993 1994 1995
MΞ−in data 1321.60±0.17 1321.25±0.16 1321.45±0.10 1321.50±0.16
MΞ+in data 1321.70±0.18 1321.49±0.14 1321.46±0.12 1321.19±0.18
MΞ±in data 1321.65±0.13 1321.37±0.11 1321.45±0.08 1321.36±0.12
MΞ−−MΞ+in data −0.10±0.25 −0.23±0.22 −0.02±0.15 0.31±0.24
MΞ±−1321.3 in MC 0.14±0.07 −0.02±0.07 0.06±0.07 0.30±0.09
CorrectedMΞ− 1321.46±0.18 1321.27±0.17 1321.39±0.12 1321.20±0.19
CorrectedMΞ+ 1321.56±0.19 1321.51±0.16 1321.40±0.14 1320.89±0.20
CorrectedMΞ± 1321.51±0.15 1321.39±0.12 1321.39±0.10 1321.06±0.15
Table 2
Measured offsets from the nominalK0andΛmasses in MeV/c2, and the corresponding offsets inΞmass, together with the final, resultingΞ±mass values. The errors of the correctedK0andΛmasses include the spread from the simulation smearing, see text
Year 1992 1993 1994 1995
MK0offset in data −0.87±0.06 −1.09±0.05 −0.75±0.06 −0.80±0.06
MK0offset in MC 0.01±0.05 0.56±0.04 0.38±0.04 0.68±0.04
CorrectedMK0offset −0.88±0.09 −1.65±0.08 −1.13±0.09 −1.48±0.09
MΛoffset in data 0.14±0.05 −0.14±0.05 −0.09±0.06 −0.07±0.06
MΛoffset in MC 0.09±0.06 0.01±0.04 0.09±0.04 0.17±0.04
CorrectedMΛoffset 0.04±0.08 −0.15±0.07 −0.18±0.08 −0.24±0.08
CalculatedMΞoffset −0.13±0.09 −0.44±0.07 −0.36±0.06 −0.47±0.07
ResultingMΞ± 1321.64±0.17 1321.82±0.14 1321.75±0.12 1321.53±0.17
Table 3
Systematic error contributions to theΞmass measurement
Source MeV/c2
ΛandK0mass scale ±0.04
Fit parameterization ±0.03
Simulation smearing ±0.02
Total ±0.05
TheΞ mass offset can be expressed as a function of theKs0 andΛmass offsets, as
MΞ=( bΞ dΞ)
bK dK bΛ dΛ
−1 MK MΛ
,
wherebi are theΞ,Ks0 andΛmass shift coefficients due to magnetic field changes, and di are those due to dE/dx cor- rection changes. The values of these coefficients were found using Monte Carlo techniques:bΞ =0.0805±0.0004,bK= 0.2376±0.0010,bΛ=0.0438±0.0002, dΞ =0.20±0.02, dK=0.367±0.017 anddΛ=0.162±0.011.
Inserting the observedKs0andΛmass shifts and the mass offset coefficients into the above equation, taking all errors into account, gave the Ξ mass offsets presented in Table 2.
The last line of that table gives the final correctedΞ± mass values per year. The final average corrected mass value is (1321.71±0.06±0.04)MeV/c2with aχ2probability for the combination of 53%. The second error quoted is the unfolded contribution from the uncertainty in the calibration offsets.
3.1.2. Other systematic uncertainties
The effect of using different parameterizations for the shape of theΞ mass peak and for the background was studied, as well as that of using various fitting techniques (maximum likelihood and minimumχ2). These variations gave a spread in the final Ξ mass value of±0.03 MeV/c2.
Applying the same “smearing” technique to the simulatedΞ events as was described above for theΛandKs0analysis gave a spread in the finalΞ mass value of±0.02 MeV/c2. Again the average of the values from the smearing study agreed with the unsmeared value.
As a cross-check, theΞmass was measured as a function of the momentum of the pion from theΞ−decay. This is generally the one passing through the most material, and it is not affected by theΛmass constraint. Thus it is the one most sensitive to dE/dxcorrections. No systematic effect depending on the pion momentum was observed. TheΞ mass was also measured as a function of the polar angle of the Ξ momentum and of the observed distance in thexyplane from the beam axis. Again no systematic variation was found.
The total systematic error was thus ±0.05 MeV/c2, as shown inTable 3.
3.1.3. Results
The measured averageΞ masses are:
MΞ−=
1321.70±0.08(stat.)±0.05(syst.)
MeV/c2, MΞ+=
1321.73±0.08(stat.)±0.05(syst.)
MeV/c2,
MΞ−+Ξ+=
1321.71±0.06(stat.)±0.05(syst.)
MeV/c2, where the systematic errors quoted are common to all three val- ues.
The systematic errors cancel in the mass difference6, where the small statistical errors on the uncorrected values can there- fore be fully exploited. The mass difference measured in the data is
M=MΞ−−MΞ+=(−0.03±0.12)MeV/c2 which corresponds to a fractional mass difference of (MΞ−−MΞ+)/Maverage=(−2.5±8.7)×10−5.
This improves the precision on this CPT violation test quantity by a factor of 3 compared to the current PDG value of(11± 27)×10−5[1].
3.2. Measurement ofΞ−andΞ¯+lifetimes and lifetime difference
The measurement of the mean lifetimes of theΞ−andΞ¯+ and their lifetime differences uses theΞ− andΞ¯+candidates with aΛπ invariant mass within±5 MeV/c2of the nominal mass, where the signal to background ratio is about 6 : 1. This is the sample for which data and simulation were compared in detail inFig. 2.
The mean lifetimes were estimated using a maximum likeli- hood fit. The time distribution of the combinatorial background was estimated simultaneously in the fit by using the wrong-sign combinations. The observed proper time distributions and the fitted functions for the wrong-sign and right-sign distributions are shown inFigs. 4 and 5, respectively. As the mean lifetimes are much shorter forc- andb-baryons than for aΞ, allΞ may safely be assumed to originate from the interaction point.
The proper time was calculated as
(1) t=dΞMΞ/PΞ,
wheredΞis the fitted flight distance in thexy plane,PΞ is the fitted momentum of theΞ candidate in thexyplane, andMΞ is the nominalΞ mass.
For right-sign and wrong-sign candidates in the proper time interval 0.04 ns to 2.0 ns, the following likelihood function was formed:
L= (2)
Nrs
i=1
F (ti) ·
Nws
j=1
B(tj).
The first factor, the F (t ) product, represents the right-sign (Λπ−,Λπ¯ +) combinations. The second factor, theB(t )prod- uct, is an empirical parameterization of the wrong-sign (Λπ+,
¯
Λπ−) combinations. The same function B(t ) was also used to describe the background in the right-sign sample. Thus, by maximizing the joint likelihood function L, the background
6 It was checked that there was no difference between masses ofΛandΛ,¯ and that theK0mass did not depend on the charge of the highest momentum particle in the decay.
Fig. 4. The observed time distribution in the wrong-sign sample for 1992–1995 data. The two lower curves are theb-functions described in the text. Their sum, used to describe the combinatorial background, is also shown. Only events with times larger than 0.04 ns were used in the fit.
Fig. 5. The observed time distribution in the right-sign sample for 1992–1995 data. The lowest curve is the estimate of the contribution from combinatorial background events, obtained by fitting the wrong-sign combinations. The middle curve is the estimate of the contribution ofΞ−andΞ¯+decays. The upper curve represents the fit to the observed time distribution, i.e., the sum of the two lower distributions.
Table 4
Fit results and statistical errors forΞ−andΞ¯+lifetime fits. Values are in nanoseconds
Year 1992 1993 1994 1995
τΞ− 0.131±0.012 0.179±0.014 0.199±0.015 0.167±0.016
τΞ+ 0.165±0.015 0.146±0.013 0.205±0.015 0.169±0.020
τ=τΞ−−τΞ+ −0.034±0.020 +0.033±0.019 −0.006±0.021 −0.002±0.025
contribution in the right-sign sample was naturally constrained to the shape of the wrong-sign distribution.
The right-sign functionF (t )was given by
(3) F (t )= 1
σ0+1
σ0S(t)+B(t ) ,
where S(t) is a normalized probability density function for the observed signal, i.e. it is proportional to(t )e−t /τΞ, where (t ) is an empirical efficiency parameterization of the time- dependent forme(c1+c2t ) determined from the simulation. The relative normalization of the signalS(t)and backgroundB(t ) in the right-sign sample,σ0, was fixed by the observed num- ber of right-sign (Nrs) and wrong-sign (Nws) events in the fitted time interval 0.04 ns to 2.0 ns,σ0=NrsN−wsNws.
The background functionB(t )was given by
(4) B(t )= 1
b1+1
b1
b(t;σ1)
N1 +b(t;σ2) N2
,
where
(5) b(t;σi)= 1
(β)σi t
σi β−1
e−
t σi,
and N1 and N2 are normalization constants for the two - distributionsb(t;σi). The valueβ=3 provided a good descrip- tion of the wrong-sign distribution. The parametersb1,σ1and σ2were fitted to the data, together withτΞ. The fit results for each year are given inTable 4.
The measuredΞ−andΞ¯+lifetimes are:
τΞ−=
0.165±0.007(stat.)±0.012(syst.) ns, τΞ+=
0.170±0.008(stat.)±0.012(syst.) ns, τΞ−+Ξ+=
0.167±0.006(stat.)±0.012(syst.) ns,
